Words from the Directorncts.ncku.edu.tw/files/Annual_Report/2011_Annual_Report.pdfWords from the Director ‹‹- 2 I which attracted many mathematicians and physicists. Promoting

‹‹- Words from the Director

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his is the th i rd year of phase three, a six

year project f unded by the National Science Council (NSC). On December 4, 2010 NSC conducted a thorough review of both mathematics and physics divisions of our center. The review committee members were from universities in Taiwan. I am very pleased to report that the committee spoke highly of the impor tant role NCTS has played, and contributions NCTS has made in promoting theoretical research as well as training young theorists in Taiwan. They were very impressed by the achievements of theoretical scientists in Taiwan. Both of the mathematics and physics division received grade A in main project and subproject I, grade A- in the subproject II.

There have been important leadership changes this year. Director Li Wen-Ching went back to Penn State in August after her two years sabbatical leave. She plans to come back to resume her job as NCTS Director as well as Mathematics Division Director in next May. During the period August 2010-April 2011, I shall substitute her as the Acting Director. Professor Ling-Fong Li will resign his job as the Director of physics Division after December 31, 2011. We are very grateful to him for his selfless service, devotion , and leadership in the past two years. A new physics division director will be searched by NSC in the near future.

The PI and Co-PI of Subproject I in Taipei are Professor Wei-Shu Hou from the Physics Department of National Taiwan University (NTU) and Professor Ch iu n- Chu a n Chen f rom t he Mat hemat ics

Department of NTU, respectively. The PI of Subproject II in Tainan is Professor Yan-Tien Lu from the Physics Department of National C he ng Ku ng Un ive r s i t y ; t he mathematics Co-PI of Subproject II is Professor Ching-Hung Lam from the Mathematics Institute of Academia Sinica.

Internat ional cooperat ion is a very important mission of the center. This year we signed a new MOU with Poncelet lab (a joint lab between CNRS France and Russia).

The cooperation between NCTS and these two institutions are in the working. Since the MOU was signed with Pohang Mathematics Institute (PMI), Postech, Korea. NCTS and PMI started cooperation in 2009 when Director Li led 5 delegates from Taiwan to attend a workshop in number theory at Postech. The second workshop was held in Hsinchu in July 2010. This year we had the third workshop in Korea in July 2011. We plan to have a joint workshop in PDE next October. The interaction between physicists of the two countries began much earlier when NCTS joined APCTP, headquartered at Postech. This year, many APCTP members attended a big conference in theoretical physics held at NCTS. In addition to Korea, NCTS have many joint workshops and conferences in PDE, Scientific computation with Japan. We also have joint workshop with France in Geometry and Discrete Mathematics.

The highlight at the center this year was the visit by Professor Gehard Huisken, Director of the Max Planck Institute for Gravitational Physics in Posdam, Germany. During his visit Oct. 24-27, Professor Huisken gave 4 two-hour lectures on "Mean Curvature Flow in Geometry and Physics",

Words from the Director

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I which attracted many mathematicians and physicists. Promoting interactions between mathematicians and physicists is one of The mission of the center. In December 2011, there is an inter-disciplinary workshop between mathematicians and theoretical physicists on the subject of Cold Atom System and Its Mathematical Models; This February there was

a bilateral Taiwan-France mathematical physics conference on symplectic geometry and quantum symmetries.

Through collective efforts, the level of theoretical research has been elevated progressively. We are proud of our achievements this year and look forward to a prosperous next year.

Mathematics Division

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his is the third year of phase III of NCTS, a six year project, funded by the National

Science Council (NSC). Thanks to the collective efforts, the mathematics division received high praises in last year's review conducted by NSC. The review committee spoke highly of the role NCTS has played in promoting research and training future leaders in mathematics in Taiwan. The members were very impressed by the high quality research activities conducted at NCTS and results obtained by people involved with the NCTS programs.

The Mathematics Co-PI at the Subproject I in Taipei has been Professor Chiun-Chuan Chen of the National Taiwan University since 2009. Professor Ching-Hung Lam of the Mathematics Institute, Academia Sinica, has served as the Mathematics Co-PI at the Subproject II in Tainan since April 2010. Professor Lam was also appointed as an adjunct professor at the National Cheng Kung University.

2011 NCTS Distinguished Lecture Series were delivered by Professor Gerhard Husken, the Director of the Max Planck Institute for Gravitational physics in Potsdam, Germany . During his visit Oct. 24-27, 2011, he gave four two-hour lectures on "Mean Curvature Flows in Geometry and Physics". His beautiful lectures have attracted many mathematicians and physicists.

For international cooperation, first in the past one year we have three conferences jointly supported by NSF and NCTS, namely Workshop on PDE Models on Biological Process, Dec. 13-17, 2010; Workshop on Fluid-Structure Interaction Problems, May 26-28, 2011; International Conference on Galois Representations, Automorphic Forms and Shimura Varieties, June 20-23, 2011. In July 2010, the mathematics division of NCTS signed an MOU with Pohang Mathematics Institute (PMI) of Postech, Korea, to promote international cooperation with Korean mathematicians. This year we have the third

joint workshop in Number Theory in PMI. We plan to invite our Korea friends in Postech to have joint workshop in Partial Differential equations at NCTS, Hsinchu in Oct. 2012. In July 2010 the director of Poncelet lab (a joint lab between CNRS France and Russia) and the vice president of Independent University of Moscow visited Taiwan. An MOU was signed between NCTS and these two institutions at Feb. 2011. This July Professor Alexey Zykin from Russia visited NCTS under this MOU. The NCTS (Taiwan)-CPT (France) joint workshop on Symplectic Geometry and Quantum Symmetries in Mathematical Physics was held at Feb. 21-25, 2011. Taiwan-Norway joint workshop on Analysis was held in June 2011. Taiwan-Japan Joint workshop on PDEs and Geometric Analysis is held in 19-21, 2011.

To carry out the NCTS tradition of nurturing young mathematicians, we have CTS fellow programs to support the young mathematicians to go abroad for conferences and short visits. Our focus programs have various summer and winter programs to stimulate and train our graduate students. In Feb. 2011 Professor Guo Jong-Shenq (Tamkang University) and Professor Jann-Long Chern (NCU) led a group of graduate students in applied mathematics to visit Meiji University to have joint workshop with Japanese students. In July 2011 Professor W.C. Li led a group of young number theorists to attend a workshop at Postech, Korea.

In the past two years we have accomplished many good research results. We have published many papers in top mathematical journals. In pure mathematics, we have published papers in Invent. Math., Journal of AMS, American Journal of Mathematics, Transaction AMS, Memoirs of AMS, Journal of Different ial Geometry , Journal of Functional Analysis, Math. Ann., J. Algebra, International Math. Research Notes, Acta Arithmetica, J. of London Math. Society,

Report of the Rivision Head

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‹‹- Report of the Rivision Head

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Advanced in Mathematics . In applied mathematics, we have Journal of computation physics, Archive Rational Mechanics and Analysis, SIAM J. Applied Mathematics, SIAM J. Mathematical Analysis, SIAM J. Matr ix Analysis and Applications , SIAM J. on Scientif ic Computing , Journal of Differential Equations, Journal of Dynamics and Differential Equations, J. of Mathematical Biology, Indiana Mathematical Journal, Communication in Mathematical Physics.

There are three new recipients of the distinguished fellow Award of NCTS in 2011. They are Professor Dung Ho Tsai of National Tsing-Hua University, specializing in Geometric Analysis and Differential Geometry, Professor I-Fang Yang of National Chiao-Tung University in Number Theory, Professor Ming-Chih Lai of National Chiao-Tung University

in Scientific Computation. These recipients were selected from all applicants by the Executive Committee based on the rigorous evaluations by international experts. It is a great pleasure to see so many outstanding mathematicians in our mathematical community. We hope in the near future the NCTS Taipei office shall have the budget for their outstanding people for distinguished fellow and S.S. Chern fellow as we did in the main project.

We designed the "NCTS thematic year" by allocating more resources to one subject area on rotating basis. This year the theme is geometry. The academic and executive committees have agreed that the theme of 2011 will be applied mathematics, followed by algebra in 2012. We look forward to lively and productive years ahead!

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6‹‹-Executive Commi�ee Members

B Executive Committee Members

Committees Affiliation

Chiun-Chuan Chen National Taiwan University

Jung-Kai Chen National Taiwan University

Jann-Long Chern National Central University

Sze-Bi Hsu National Tsing-Hua University

Ching-Hung Lam Academia Sinica

Wen-Ching Winnie Li National Center for Theoretical Sciences

Yuah-Chung Sheu National Chiao Tung University

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7 ‹‹- Academic Commi�ee Members

CAcademic Committee Members

Committees Affiliation

Gerard J. Chang National Taiwan University

Jung-Kai Chen National Taiwan University

Kuo-Chang Chen National Tsing-Hua University

Shun-Jen Cheng Academia Sinica

Jann-Long Chern National Central University

Ming-Chih Lai National Chiao Tung University

Yng-Ing Lee National Taiwan University

Tai-Chia Lin National Taiwan University

Yuah-Chung Sheu National Chiao Tung University

Dong-Ho Tsai National Tsing Hua University

Zhu Eugene Xia National Cheng Kung University

Yifan Yang National Chiao Tung University

Chia-Fu Yu Academia Sinica

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‹‹-Highlights of the Focus Programs 8

Coordinators: Jungkai Chen (National Taiwan University)

D.1 Algebraic Geometry

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e have regular weekly seminar on the topics we proposed. We also have regular

student seminar weekly as part of the project. These seminars are really the foundation of our current project. During summer, we have many visitors visiting NCTS. Among them, some of them are our former students who are junior scholars or studying abroad now. The 4th conference “Algebraic Geometry in East Asia”was e held in Nov. 16-20 in NTU, Taipei. The organizing committee consists of Jungkai Chen (NTU), Meng Chen (Fudan Univ.), Yujiro Kawamata (Tokyo Univ.) and JongHae Keum (KIAS). The proceeding of the conference is accepted to be published in the prestigious proceeding series “Advanced studies in Pure Mathematics”.

Accord i ng to t he recent concer n on the identification between NCTS/TPE and TIMS(Taida Inst itute for Mathematical Sciences), we did not include the result of the theme on Quantum Cohomology led by Chin-Lung Wang and Hui-Wen Lin. The interaction and collaboration is still ongoing anyway.

1-1 Local Algebraic Geometry GroupJheng-Jie Chen (NCTS), Jiun-Cheng Chen

(NTHU), Jungkai Chen (NTU), Wan Keng Cheong (NCKU), We-Yen Chuang (NTU), Tatsuki Hayama (NTU), Bong Lian* (Brandies and NTU), Hui-Wen Lin (NTU), Chin-Lung Wang (NTU), Eugene Xia (NCKU) , Jeng-Daw Yu (NTU).*Bong Lian from Brandies University visit NTU for the academic year 2011-2012 under the support of NSC.

1-2 Visitors Chenyang Xu (Utah), Caucher Birkar (Cambridge,

UK), Gorden Heier (Texas), V. Maillot (Paris VI), Chen-Yu Chi , (Harvard), Shin-Yao Jow (U. Penn.)

2-1. ConferenceThe 4th conference “Algebraic Geometry in

East Asia”was e held in Nov. 16-20, 2011 in NTU. Invited speakers are either algebraic geometers from Japan, Korea, China, Vietnam, UK and Taiwan. The organizers are Jungkai Chen, Meng Chen, Yujiro Kawamat,a and JongHae Keum.The list of invited speakers is:• Yujiro Kawamata (Univ. Tokyo)• Sijong Kwak (KAIST, Korea)• Wu-yen Chuang (NTU)• Shinnosuke Okawa (Univ. Tokyo)• Jun-Muk Hwang (KIAs, Korea)• Xiaotao Sun (Chinese Academy of Science)• Hui-Wen Lin (NTU)• Keiji Oguiso (Osaka Univ.)• Miles Reid (Warwick Univ., UK)• Phung Ho Hai (Vietnam Academy of sciences and

Technology)• Jungkai Alfred Chen (NTU)• Shunsuke Takagi (Univ. Tokyo)• Yongnam Lee (Sogang Univ., Korea)• Baohua Fu (Chinese Academy of Science)• Wan-Keng Cheong (NCKU)• Shigeharu Takayama (Univ. Tokyo)• Jihun Park (POSTECH, Korea)• Jilong Tong (Univ. Bordeaux)• Jiun-Cheng Chen (NTHU)• Yoshinori Gongyo (Univ. Tokyo)• JongHae Keum (KIAS, Korea)

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Highlights of the Focus Programs

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‹‹- Highlights of the Focus Programs 9

DThis is the 4th meeting of “Algebraic Geometry in East Asia”. The previous ones was in Kyoto (2001), Hanoi (2005), and Seoul (2008) respectively. Base on the success of the 4th meeting, the organizing committee decided to make it a bi-annual meeting. The next meeting will be in Beijing in 2013. The proceeding of the conference will appear in the prestigious series “Advanced Studies in Pure Mathematics” published by the Mathematical Society of Japan. We are grateful to the support of NCTS for this conference.

2-2 SeminarsThe regular joint seminar with TIMS was

organized by Jungkai Chen and Chin-Lung Wang. One of the main focuses of the seminar was on recent breakthrough in higher dimensional minimal model program. There are many more improvements of presentation of the materials developed by Birkar, Cascini, Hacon and McKernan, such as Paun and Birkar’s work. Some attempts to attack the problems of termination and abundance was discussed in the seminar as well.

The other main focus was on the Gromov-Witten theory and quantum cohomology around the joint project of Yuan-Pin Lee, Hui-Wen Lin and Chin-Lung Wang.

There is also a regular student seminar organized by Jungkai Chen. The participants consist of NCTS research assistants and students from NTU and some faculty members. The main topic is on derived categories in birational geometry. Some aspects of geometry of arc spaces was discussed as well.

3. Accomplishments1.Birational classification of threefolds

The collaboration between Meng Chen(Fudan Univ.) and Jungkai Chen on birational classification of threefolds is still ongoing and produced many more results. Those threefolds of general type with small invariants are investigated more closely. For example, threefolds of general type with fractional genus 1/2 are proved to have volume greater or equal to 1/12, which is sharp. It is also proved that the m-canonial map is birational for m greater or equal to 12 for such threefold. Moreover, some Noether type inequality

is obtained. It is then natural to formula “geography of threefolds of general type”. However, the right formulation is yet to be determined.

Meanwhile, the canonical volume for all threefold of general type is improved to greater or equal 1/1680. It is expected to be very close to being optimal for there is an example with canonical volume 1/420.

2. Birational geometry of threefoldsBirational geometry concerns the geometry inside

a birational equivalence class. It is well known by minimal model program that any two birational equivalent model are connected by a sequence of divisorial contraction to a point, divisorial contraction to a curve, divisorial extraction over a point, divisorial extraction over a curve, f lip and flop. By the work of Jungkai Chen (partly join with Christopher Hacon), it is shown that a f lip and a divisorial contraction to a curve can be factored into a sequence of divisorial extraction over a point with minimal discrepancies, divisorial contraction to a point, blowup along a lci curve in a smooth threefold, and flop. It is conjectured that the essential building blocks are divisorial contraction to a point with minimal discrepancies and blowup along a smooth curve.

We also prove an explicit resolution of three dimensional terminal singularities by a sequence of divisorial extraction over a singular point with minimal discrepancies.

3.Iitaka’s conjecture and minimal model programA variety with Kodaira dimension zero plays an

important role in the classification theory of algebraic varieties. It is conjectured by Ueno that such varieties can be factored into abelian varieties and Calabi-Yau varieties according to the irregularity. In a joint work with Christopher Hacon (Utah Univ.), the conjectured of Ueno’s was confirmed. As a consequence, Iitaka’s conjecture Cnm was proved when base variety is of maximal Albanese dimension. In the recent joint work in progress with Caucher Birkar (Cambridge) and Hajime Tsuji (Tokyo Univ.), the above mentioned results was extend to log pairs al lowing klt singularities.

4.Stacky method in algebraic geometry The stacky method developed by Jiun-Cheng

Chen (NTHU) find some more applications. In his

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article appeared in Advanced Studies in Pure Math., it is prove that a variety with large pseudo-index has Picard number one. There is also some result on varieties with maximal length extremal rays. All these kind of varieties are closely related to projective spaces and Fano varieties. In his joint work with H.H. Tseng (Ohio State Univ.), he proved a version of Bogomolov-Miyaoka-Yau inequality from the method of Deligne-Mumford stack method. The important contribution is to provide a stacky point of view and simple stacky interpretation of Bogomolov-Miyaoka-Yau inequality.

4. Publications (year 2009, 2010- and preprints)[1] J. C. Chen* and H. H. Tseng Cone Theorem

via Deligne-Mumford stacks, Mathematische Annalen, Volume 345 (2009), no. 3, 525-545

[2] J. A. Chen, C. D. Hacon, On the geography of threefolds of general type, J. Alg., 321, (2009), 2500-2507.

[3] J. A. Chen , C. D. Hacon , On Ueno’s Conjecture K, Math. Ann., 345, (2009), 287-296

[4] J. A. Chen, M. Chen, Explicit birational geometry of threefolds of general type, I, Ann. Sci. École Norm. Sup (43) 2010, 365-394

[5] J. C. Chen* On Fano varieties with large

pseudo-index, Proceeding of 2008 East-Asia Conference in Algebraic Geometry, Advanced Studies in Pure Mathematics, 60 (2010)

[6] J. A. Chen, M. Chen, Explicit birational geometry of threefolds of general type, II, Jour. Diff. Geom, 86 (2010), 237-271

[7] J. A. Chen, C. D. Hacon, Factoring 3-fold flips and divisorial contractions to curves. Jour. Reine Angew. Math., 657, (2011), 173-197

[8] J. J. Chen, J. A. Chen, M. Chen, On weighted complete intersections. J. Alg. Geom, 20, (2011), 239-262

[9] C.Y. Chi, C.L. Wang, S.S. Wang, Extensions of multiply twisted pluri-canonical forms, preprint 2010.

[10] J.A. Chen, C. D. Hacon, Kodaira dimension of irregular varieties, Invent. Math. To appear

[11] J.C Chen, H.H. Tseng, On the Bogomolov-Miyaoka-Yau inequalit y for Deligne-Mumford surfaces, submitted, 2011

[12] J. A. Chen, M. Chen, On 3-folds of general type with small genus, I: g=1/2. preprint

[13] J.A. Chen, O. Debarre, Z. Jiang, Varieties w i t h v a n i s h i n g h o l o m o r p h i c E u l e r characteristic, preprint

[14] J.A. Chen, Factoring threefold divisorial contractions to points. preprint.

Coordinators: Gerard Jennhwa Chang (National Taiwan University) and Li-Da Tong (National Sun Yat Sen University).

D. 2 Discrete Mathematics

iscrete mathematics is an active research area in Taiwan. In the program of discrete

mathematics supported by the NCTS, we organize various activities to broaden the spectrum of research in Taiwan, to promote international collaborations, and to provide training and opportunities for young scholars and students. The activities we have organized and related results are as follows.

D.2.1 Regular weekly seminarThere is a weekly seminar every Wednesday

afternoon at National Taiwan University, and a weekly seminar every Tuesday morning at National Sun Yat-sen University. They are platform for the center members, visitors, post doctoral fellows and students to share their research experiences. The contents of the seminars could be talks on previous results as well as current idea for a research topic.

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D.2.2 WorkshopsAs part of the Si-Tsi Wan Combinatorics Series,

there is a one-day workshop on Combinatorics on January 20 of 2010 held at Department of Applied Mathematics, National Sun Yat-sen University. The aim of this workshop is to provide a platform for the local discrete mathematicians to present and share their research experiences. Five one-hour speakers are invited. Themes include graph coloring, decomposition, labeling, combinatorics and their applications. The speakers and their topics are as follows. The conference is quit successful. It attracts many participants.• Xuding Zhu, Decomposition of graphs into forests.• Gerard Jennhwa Chang, First-fit chromatic numbers

of graphs.• Tao-Ming Wang, Group magic sum spectrum of

graphs.• Sen-Peng Eu, Construction on cyclic sieving

phenomenon.• Bey-Chi Lin, An architecture for TSI-Free

nonblocking optical TDM switches.As a part of the France-Taiwan cooperation,

we have the second workshop of which is the 2011 Workshop on Graph Theory, March 11-12 of 2011 held at National Taiwan University. There are twelve speakers from France and Taiwan. Many of the talks are on graph coloring. This reflects the fact that we have a strong group of discrete mathematician in Taiwan working on the direction of graph coloring. The speakers and the titles are listed as follows.• Jaroslav Neset r i l , Lif ts and shadows (and

orientations).• Hong-Gwa Yeh, Spread of inf luence in social

networks.• Xuding Zhu, Application of polynomial method to

on-line list colouring of graphs.• Arnaud Pecher, The circular chromatic number of

circular-perfect graphs is computable in polynomial time.

• Peng-An Chen, A new coloring theorem of Kneser graphs.

• Nicolas Roussel, Power domination in hypergraphs.• Andre Raspaud, Partitions of graphs with bounded

maximum average degree.• Mickael Montassier, Vertex-partition of graphs into

cographs and stars.• Frederic Havet, New results and problems on the

Grundy number.• Li-Da Tong, The Hamiltonian number of a digraph.• Nathann Cohen, Induced decomposition into small

graphs.• Gerard Jennhwa Chang, First-fit chromatic numbers

of graphs.As the continuation of the cooperation with

Japanese mathematicians, we have the thi rd workshop of this year which is the 2011 Taiwan-Japan Conference of Combinatorics and its Applications, April 2-4 of 2011 held at Tamkang University. The main theme of the workshop is on the design theory. The speakers and their titles are listed as follows.• Hung-Lin Fu, Heterogeneous Steiner quadruple

systems.• Miwako Mishima, Decomposition of the 2-design

formed by the planes of AG(2n,3).• Ryoh Fujihara, A general recursive construction for

multi-structured designs.• Kuo-Ching Huang, K3-design of Kn\F with F a

spanning odd forest.• Ying Miao, On perfect difference families.• Masahide Kuwada, Characterization of balanced

fractional 2m factorial designs of resolution 2l+1 derived from simple arrays.

• Shinji Kuriki, Incomplete split-plot designs.• Hong-Gwa Yeh, Circular coloring and periodic

scheduling.• Chih-Hung Yen, Maximum coloring and equitable

△ -coloring of graphs.• Zhi-Shi Pan, Oriented circuit double cover and

circular flow and coloring.• Masakazu Jimbo, Quantum jump codes and related

combinatorial designs. • Yao-Tsu Chang, Decoding the binary quadratic

residue codes.• Nobuko Miyamoto, An extension of authentication

codes based on BIBDs.• Hsun-Wen Chang, Enumeration of RNA secondary

structures based on skeleton trees.• Kazuhiko Ushio, Balanced (C5, C20)-foil designs

and related designs.• Chiang Lin, C4-supermagic labeling of the grid.

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• Ming-Hway Huang, (4, 5)-Cycle systems of complete multipartite graphs.

• Bit-Shun Tam, Connected graphs with maximal Q-index: the one-dominating-vertex case.

• Li-Da Tong, The differences of convexity spectra of graphs.

• Yi-Ling Lin, Constructions of a t-SEED and its application.

• Yeong-Nan Yeh, Cyclic permutations of sequences and uniform partitions.

• Hong-Bin Chen, Pooling designs of classifying multiple mutually-obscuring positives.

• Chin-Mei Kau, Cycle decomposition of complete graphs.

D.2.3 Hosting aboard visitors The visitors from aboard of this year are listed as

follows. The visitors have close discussions with the Center members. Some join work is done during their visiting, as will be described below.• Andre Raspaud, Bordeaux University I, France,

2011/02/26~2011/03/14.• Mickael Montassier, Bordeaux University I, France,

2011/02/26~2011/03/14.• A r n aud Pe che r, Borde au x Un ive r s i t y I ,

100/03/01~100/03/12.• Frédéric Havet, INRIA Sophia Antipolis, France,

2011/03/09~2011/03/18.• Nathann Cohen, INRIA Sophia Antipolis, France,

2011/03/09~2011/03/18.• Miwako Mishima, Gifu University, Japan,

100/04/01~100/04/05.• Kazuhiko Ushio, Kinki University, Japan,

100/04/01~100/04/05.• Masahide Kuwada, International Institute for

Natural Sciences, 100/04/01~100/04/05.• Shinji Kuriki, Osaka Prefecture University, Japan,

100/04/01~100/04/05.• Nobuko Miyamoto, Tokyo University of Science,

Japan, 100/04/01~100/04/05.• Kazuhiko Ushio, Kinki University, Japan,

100/04/01~100/04/05.• Ryoh Fujihara, University of Tsukuba, Japan,

100/04/01~100/04/06.

• Ying Miao, University of Tsukuba, Japan, 100/04/01~100/04/06.

• Masakazu Jimbo, Nagoya University, Japan, 100/04/02~100/04/04.

D.2.4 Research resultsIn this year, the research of the group concerns

several aspects of graph theory. Graph colouring and graph labeling have always been a main area of our research. There are problems in this area that we have been working on for a long time. Other topics include domination, intersection graph, additive combinatorics, network flow etc.

1. Parity and strong parity edge-coloring of graphs. A subgraph (or a walk) of an edge-colored graph is called parity if it uses each color an even number of times. Let p(G) be the least number of colors in a parity edge-coloring of G (an edge-coloring having no nontrivial parity path), and let p'(G) be the least number of colors in a strong parity edge-coloring of G (an edge-coloring having no open parity walk). Note that χ'(G) ≤ p(G) ≤ p'(G). We establish some general properties and results for parity and strong parity edge-colorings. In particular, results on some complete bipartite graphs are obtained. This answers part of the conjectures by West et al.

2. Algorithmic aspects of domination in graphs. (This is an invited chapter in the Handbook of Combinatorial Optimization, eds. Panos Pardalos, Ding-Zhu Du and Ronald Graham, Springer.) Domination in graph theory has many applications in the real world such as location problems. A dominating set of a graph G = (V, E) is a subset D of V such that every vertex not in D is adjacent to at least one vertex in D. The domination problem is to determine the domination number γ(G) of a graph G that is the minimum size of a dominating set of G. Although many theoretic theorems for domination and its variations have been established for a long time, the first algorithmic result on this topic was given by Cockayne, Goodman and Hedetniemi in 1975. They gave a linear-time algorithm for the domination problem in trees by using a labeling method. On the other hand, at about the same time, Garey and John constructed the first (unpublished) proof that the domination problem is NP-complete.

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Since then, many algorithmic results are studied for variations of the domination problem in different classes of graphs. This chapter is to survey the development on this line during the past 36 years. Polynomial-time algorithms using labeling method, dynamic programming method and primal-dual method are surveyed on trees, interval graphs, st rongly chordal graphs, permutation graphs, cocomparability graphs and distance-hereditary graphs. NP-completeness results on domination are also discussed.

3. The competition number of a graph with exactly two holes. Given an acyclic digraph D, the competition graph C(D) of D is the graph with the same vertex set as D and two distinct vertices x and y are adjacent in C(D) if and only if there is a vertex v in D such that (x,v) and (y,v) are arcs of D. The competition number κ(G) of a graph G is the least number of isolated vertices that must be added to G to form a competition graph. WE prove that the competition number of a graph with exactly two holes is at most three.

4. Near automorphisms of paths. The total relative displacement of a permutation f of vertices of a connected graph G is δ_ f(G) =Σ |d_G(x,y)–d_G(f(x),f(y))|, where the sum is taken over all n(n–1)/2 unordered pairs of distinct vertices of G. Let π(G) denote the smallest positive value of δ_ f(G) among the n! permutations f. Aitken proved that π(P_n) = 2–4 for the n-path P_n, which was conjectured by Chartrand, Gavlas and VanderJagt. We give a short and elegant proof of the result.

5. On the number of subsequences with a given sum in a finite abelian group. Suppose G is a finite abelian group and S is a sequence of elements in G. For any element g of G, let N_g(S) denote the number of subsequences of S with sum g. The purpose is to investigate the lower bound for N_g(S). In particular, we prove the result that either N_g(S) = 0 or N_g(S) ≥2^{|S|-D(G)+1}, where D(G) is the smallest positive integer k such that every sequence over G of length at least k has a nonempty zero-sum subsequence. We also characterize the structures of the extremal sequences for which the equality holds for some groups.

6. Thue choice number of trees are unbounded. Thue Theorem is a classical result which is viewed as the starting point of Formal Language Theory

or Automata Theory - these are fundaments of Computer Science. Thue theorem is easy to state and understand: there is an infinite sequence in three symbols, say 0,1,2, (i.e., ) such that any two adjacent blocks are distinct, i.e., for any i and n , . The Thue choice number of a graph asks the following question: What is the smallest integer k for which the following holds: If each vertex v is given a set L(v) of k colours, then there is a colouring c of the vertices of G so that c(v) belongs to L(v) for each v, and for any path P of G, any two adjacent blocks of colour sequence on this path are distinct. Last year, we proved that the Thue choice number of a path is at most 4. We asked the question whether trees have bounded Thue choice number. This year, we proved that the answer is no. This is a joint work with three French mathematicians.

7. Entire colouring of plane graphs. We proved that every simple plane graph has entire chromatic number at most Δ+4, which is a more than 30 year old conjecture.

8. Fractional chroamtic number of product of graphs. We proved that the fractional chromatic number of the categorical product is equal to the minimum of the fractional chromatic numbers of the factor graphs. This is the fractional version of Hedetniemi’s conjecture. As a consequence of this result, we proved Burr-Erdos-Lovasz conjecture, which is also more than 30 old.

9. On line list coloring of graphs. This is a concept introduced not long time ago. We worked on this concept last year, and proved that graphs of chromatic number k and with n vertices has on-line choosability at most k ln (n). This year, we continued research in this area. We proposed on-line version of Ohba’s conjecture and verified some special cases. The proofs us polynomial method. Some of the techniques used in the proof are due to Tsai-Lien Wong and Po-Yi Huang, which are interesting and might be useful elsewhere.

10. Orientat ion of graphs. The study of orientations of graphs is widely studied in graph theory. An acyclic orientation of a graph is also a useful tool for the investigation of structure and property in graph theory; such as, cover graphs and circular chromatic numbers. First, we study the relations among dmin(G), the circular chromatic

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numbers and fully orientable graphs. Second, we discuss geodesic sets, hull sets, and convex sets in the orientations of graphs.

D.2.5 Publications[1] C.-C. Lin, G. J. Chang and G.-H. Chen, The

degree-preserving spanning tree problem in strongly chordal and directed path graphs, Networks 56 (2010), 183-187

[2] G. J. Chang, J. Wu and X. Zhu, Rainbow domination on trees, Disc., Appl. Math.158 (2010), 8-12

[3] L.-H. Huang, G. J. Chang and H.-G. Yeh, On minimum rank and zero forcing sets of a graph, Linear Algebra Appl. 432 (2010), 2961-2973

[4] W.-H. Lin and G. J. Chang, Equitable colorings of Kronecker products of graphs, Disc. Appl. Math.158 (2010), 1816-1826

[5] Y. Zhao and G. J. Chang, On competition polysemy and m-competition polysemy, Ars Combin.97 (2010), 17-26

[6] Y. Zhao and G.J. Chang, Multicompetition numbers of some multigraphs, Ars Combin. 97 (2010), 457-469

[7] L.-H. Huang, G. J. Chang and H.-G. Yeh, A note on universally optimal matrices and field independence of the minimum rank of a graph, Linear Algebra Appl. 433, (2010), 585-594

[8] G. J. Chang, J. Hou and N. Roussel, On the total choosability of planar graphs and of sparse graphs, Inform. Process. , Letters 110 (2010), 849-853

[9] L. Cai, W. Wang and X. Zhu, Choosability of toroidal graphs without short cycles, J. Graph Theory, 65 (2010) 1-15.

[10] M. Montassier, A. Pecher, A. Raspaud, D. B. West and X. Zhu, Decomposition of sparse graphs, with application to game coloring number, Discrete Math. 310 (2010), 1520-1523.

[11] X. Zhu, On-line list colouring of graphs, Elect. , J. Comb. 16 (2009), #127, 16pp (2010),

[12] Y.-P. Chen, Y.-M. Huang and L.-D. Tong, R e a r r a n g e a b l e n o n b l o c k i n g o p t i c a l interconnection network fabrics with crosstalk constraints, IEEE/ACM Trans., Networking 18 (2010), 1413-1421.

[13] N. Roussel and X. Zhu, Total coloring of planar graphs of maximum degree eight, Inform. Proc., Letters 110 (2010), 321-324.

[14] G. J. Chang and C. Lu, The L(2,1)-F-labeling problem of graphs, Taiwanese J. Math. 15 (2011), 1277-1285.

[15] G. J. Chang, L.-H. Huang and H.-G. Yeh, A characterization of graphs with rank 4, Linear Algebra Appl. 434 (2011), 1793-1798.

[16] G. J. Chang, S.-H. Cheng, Y. Qu, G. Wang and H. Zhang, On the number of subsequences with a given sum in a finite abelian group, Elect. J. Combin. 18 (2011), #P133

[17] G. J. Chang, J. Hou and N. Roussel, Local condition for planar graphs of maximum degree 7 to be 8-totally colorable, Discrete Appl. Math. 159 (2011), 760-768

[18] G. J. Chang, Near automorphisms of paths, J. Graph Theory (accepted)

[19] W.-H. Lin and G. J. Chang, Resource-sharing systems and hypergraph colorings, J. Combin. Optim. (accepted)

[20] G. J. Chang, C. Lu, J. Wu and R. Yu, Vertex-coloring edge-weightings of graphs, Taiwnese J. Math. (accepted)

[21] Y. Zhao and G. J. Chang, Consecutive edge-colorings of generalized θ-graphs, Graph Combin. (accepted).

[22] B.-J. Li and G. J. Chang, The competition number of a graph with exactly two holes, J. Combin. Optim. (accepted).

[23] G. J. Chang, T.-P. Chang and L.-D. Tong, The Hamiltonian numbers of Mobius double loop networks, J. Combin. Optim. (accepted).

[24]G. J. Chang and N. Roussel, (Δ+1)-total choosability of planar graphs with no cycles of length from 4 to k and without close triangles, Discrete Math. (accepted).

[25] G. J. Chang, Algorithmic aspects of domination in g raphs , Handbook of Combinator ia l Optimization, eds. Panos Pardalos, Ding-Zhu Du and Ronald Graham, Springer

[26] H.-C. Hsu and G. J. Chang, Parity and strong parity edge-colorings of graphs, J. Combin. Optim. (accepted)

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[27] H.-H. Lai, K.-W. Lih, C.-Y. Lin, and L.-D. Tong, When is the direct product of generalized Mycielski graphs a cover graph, Ars Combin. (accepted).

Coordinators: Kuo-Chang Chen (National Tsing-Hua University), Chih-Wen Shih (National Chiao Tung University)

D.3 Dynamical System

The primary investigators of this focus program are Kuo-Chang Chen (NTHU),

Ming-Chia Li (NCTU), Song-Sun Lin (NCTU), Chih-Wen Shih (NCTU), Cheng-Hsiung Hsu (NCU)Coordinators: Kuo-Chang Chen, Chih-Wen ShihThe other investigators include Jung-Chao Ban (NDHU), Chang-Yuan Cheng (NPUE), Yi-Chuan Chen (Academia Sinica), Wen-Chiao Cheng (CCUT), Shyan-Shiou Chen (NTNU), Bau-Sen Du (Academia Sinica), Jin-Long Li ((NHCTC), Ken Palmer (NTU), Jun-Hsiung Hsia (NTU), Chen-Chang Peng (NCU), Shih-Feng Shieh (NTNU), Li-Chin Yeh (NHCTC), Je-Chiang Tsai (NCCU), Ting-Hui Yang (Tamkang), Tzi-Sheng Yang (Tonghai), Suh-Yuh Yang (NCU)

Dynamical System is one of the major and classical research areas in mathematics and mathematical science. The discipline traces back to Newton, Poincare, and Birkhoff. Current interesting research topics in the field contain the ones of classical origin: celestial mechanics, Hamiltonian systems, the ones developed since the sixties: chaotic dynamics and ergodic theory, and the ones that attract increasing attention: random dynamical systems. In addition to the theoretical side, the application of dynamical system is closely linked to the nonlinear dynamics in Physics, both historically and contemporarily. The range of applications crosses from physics, biology, information science, engineering, to economy and finance. There are more than twenty active researchers in dynamical systems in Taiwan. Their research topics include n-body problem, homoclinic orbits, entropy, delayed equation, chaotic saddle, synchronization, multi-dimensional perturbation, heterodimensional cycles, noisy oscillators, anti-

integrable systems, geometric singular perturbation, monotone dynamics, t raveling waves, lat t ice dynamical systems, and chaotic attractors. Regular seminars have been held at a weekly base with talks given by visiting scholars, and local researchers. Summer school in dynamical systems was arranged with focus on specific topic. International conference or workshop is organized every year here in NCTS. Some mini courses are arranged in the workshops. These activities broaden the spectrum of current research in Taiwan, promote the collaboration with international scholars, and enhance the training of graduate students. Both individual and group researchers have delivered significant works in the past few years. We also have joint activities with the topical programs of mathematical biology and scientific computation on some applications and computational aspects of dynamical systems. The activities this year are listed below.

D.3.1 Conference and Workshop:

2011 NCTS Workshop on Dynamical Systems 2011/05/12-2011/05/14

Introduction: Dynamical Systems is a major and active field of research in mathematical science. In this annual meeting on dynamical systems, we plan to invite world leading experts to deliver lecture series on active research subjects, and arrange several one-hour talks. Our aim is to broaden the spectrum of current research in Taiwan, to enhance the collaboration with international scholars, and to lift up the academic standard of our graduate students.

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[28] T.-P. Chang and L.-D. Tong, The hamiltonian numbers of graphs, Ars Combin. (accepted).

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Organizers:1.Jung-Chao Ban (National Dong-Hwa University)2.Kuo-Chang Chen (National Tsing-Hua University)3.Cheng-Hsiung Hsu (National Central University)4.Ming-Chia Li (National Chiao-Tung University)5.Chih-Wen Shih (National Chiao-Tung University)

Invited Speakers:Mini Courses Speakers:1.Leonid Bunimovich (Georgia Inst it ute of

Technology, USA) 2.Han-Feng Li (SUNY at Buffalo, USA)3.Weixiao Shen (National University of Singapore,

Singapore)One Hour talks speakers:1.Jung-Chao Ban (National Dong Hwa University,

Taiwan) 2.Wen-Chiao Cheng (Chinese Culture University,

Taiwan) 3.Xiong-Ping Dai (Nanjing University, China)4.Bau-Sen Du (Academia Sinica, Taiwan) 5.Bao-Jun Huang (Hwaibei Normal University,

China) 6.Shin Kiriki (Kyoto University of Education, Japan) 7.Kenneth Palmer (National Taiwan University,

Taiwan) 8.Shigui Ruan (University of Miami, USA) 9.Xingfu Zou (University of Western Ontario,

Canada)

D.3.2 Courses and Seminars:

2010 NCTS Summer Course: Measures and Computations for Dynamical Systems

Instructors:1. Prof. Jung Chao Ban 班榮超 (National Dong Hwa

Univ.)2. Prof. Yun Zhao 趙雲 (SooChow Univ.)3. Prof. Wen-Chiao Cheng 鄭文巧 (Chinese Culture

Univ.)4. Prof. Shu-Ming Chang 張書銘 (National Chiao

Tung Univ.)

Dates of Course and Student Seminar: 7/6-8/26 Tuesdays and Thursdays from 2:00-4:00 pm

This summer course is intended for graduate students and advanced undergraduate students

who are interested in dynamical systems. Students are expected to have some basic knowledge about measure theory and differential equations.

There will be three topics on measure theoretic aspects of dynamical systems delivered by three Instructors working in related fields, plus a topic related to computational dynamics.Topics to be covered include: 1. Measures in dynamical systems ( 班榮超 , 東華大

學 ) 2. Measure-preserving transformations ( 趙雲 , 蘇州

大學 )

3. Measure-theoretic entropy ( 鄭文巧 , 文化大學 ) 4. Computational dynamical systems ( 張書銘 , 交通

大學 )

References: (1) Peter Walters, An Introduction to Ergodic theory,

Cambridge University Press, 2000. (2) Karl Peterson, Ergodic theory, Cambridge

University Press, 1983.Prerequisite: Real Analysis

2011 NCTS Short Course: Topics on the N-Body Problem

Instructor: Kuo-Chang Chen, Department of Mathematics, National Tsing Hua University

Contact Information: E-mail: [email protected], (03)5715131 Ext.

33067Hours and Days: May 5, 19, 26, June 2, 9, 16, 13:30 -

15:30Place: CTS Lecture RoomPrerequisite: Differential equations, real analysis

Course Description: The classical celestial mechanics, known as the

(Newtonian) n-body problem, concerns the motion of n celestial bodies moving in space in accordance with Newton’s law of universal gravitation. It is classic field of research in mathematics with many unsolved problems.

In this series of talks I will introduce currently active research topics on the n-body problem and their major difficulties.

Topics to be covered include: 1.Introduction to the n-body problem

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2.Restricted n-body problem 3.Central configurations and relative equilibria4.Existence theory by variational methods 5.Stability and instability 6.Final motion and singularity

Major References.1.Chen, K.-C., Existence and minimizing properties

of retrograde orbits to the three-body problem with various choices of masses. Annals of Math, 167, 325-348 (2008).

2.Chen, K.-C.; Lin, Y.-C., On action-minimizing retrograde and prograde orbits of the three-body problem. Comm. Math. Phys., 291, 403-441 (2009).

3.Chenciner, A., Action minimizing solutions in the Newtonian n-body problem: from homology to symmetry. Proc. of the International Congress of Mathematicians (Beijing, 2002). Vol III, 279-294.

4.Chenciner, A.; Montgomery, R., A remarkable periodic solution of the three-body problem in the case of equal masses. Annals of Math. 152, 881-901 (2000).

5.Ferrario, D.; Terracini, S., On the existence of collisionless equivariant minimizers for the classical n-body problem. Invent. Math. 155, 305-362 (2004).

6.Gordon, W., A minimizing property of Keplerian orbits, Amer. J. Math. 99, 961-971 (1977).

7.Siegel, C.L.; Moser, J. K., Lectures on celestial mechanics, Springer-Verlag, 1971.

2011 NCTS Short Course: Introduction to Dirich Series and the Zeta Function

Instructor: Dr. Chi-Hua Chan 詹其樺 (NCTS)Time: 1:30-3:30pm,Thursday,

3/17、3/24、3/31、4/7、4/14、4/21, 2011Place: Lecture Room B (3/17, 3/24, 3/31, 4/14, 4/21),

R723 (4/7) NCTS, The 3rd General Building, National

Tsing Hua University

Dirichlet series is a "discrete" transform of frequent occurrence in analysis. In this mini course, we want to introduce the theory of Dirichlet series. The theory involved will be simple in the sense that much of it could be conjectured from the theory of power series. And yet this "discrete" transform will provide a sort of model for the more complicated integral transforms to follow.

As a special type of Dirichlet series, some properties of the zeta function will of course confirm and illustrate the results of Dirichlet series, but in addition it will have specific properties resulting from its special definition.

Contents: 1. The def in it ion of Dir ichlet ser ies and the

convergence of Dirichlet series. 2. Analyticity of Dirichlet series and the formulae for

calculating the abscissa of convergence. 3. Uniqueness and the behavior of Dirichlet series on

vertical lines. 4. Inversion formula and a Mean-Value Theorem.5. Euler product for the zeta function and its zeros.6. Order of the zeta function and its derivative on

vertical line and the functional equation for the zeta function.

Reference: D. V. Widder: An introduction to transform theory

2011 NCTS Summer Program on Dynamical Systems

This summer course is intended for graduate students and advanced undergraduate students who are interested in dynamical systems. Students are expected to have some basic knowledge about measure theory and differential equations. There will be three topics on measure theoretic aspects of dynamical systems delivered by three instructors working in related fields, plus a topic related to computational dynamics. Topics to be covered include:

July 14 & 19 (Th & Tu) AM 10:30-12:00 & PM 1:30-3:00陳國璋教授 ( 清華大學數學系 ) Introduction to twist maps 7/14 (R723, 7F), 7/19 (Lecture Room A, 4F)

July 20 & 21 (W & Th) AM 10:30-12:00 & PM 1:30-3:00陳賢修教授 ( 臺灣師範大學數學系 )An Introduction to Hopf bifurcationLecture Room A

July 26 & 28 (Tu & Th) AM 10:30-12:00 & PM 1:30-3:00

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鄭文巧教授 ( 中國文化大學應用數學系 )An introduction to fractal geometryLecture Room A

August 3 & 4 (W & Th) AM 10:30-12:00 & PM 1:30-3:00班榮超教授 ( 東華大學應用數學系 )The sofic shifts and sofic measuresLecture Room B

August 10 & 11 (W & Th) AM 10:30-12:00 & PM 1:30-3:00鄭昌源教授 ( 屏東教育大學應用數學系 )Type-K monotone systems and the applicationsLecture Room B

References: 1. M. Pollicott and M. Yuri: Dynamical Systems and

Ergodic Theory, London Mathematical Society, Cambridge University Press, 1998. (Chapter 1,6,13)Available at http://www.warwick.ac.uk/~masdbl/book.html

2. M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995.

(1) Speaker: Professor Wen-Xin Qin (Suzhou Univ, China)

Time: PM 2:00-3:00, Tuesday, Jan. 26, 2010 Topic: Monotonicity in the Frenkel-Kontorova

Model(2) Speaker: Dr. Bing Li (National Taiwan University) Time: March 19, 2010 Topic: Recurrence and Hitting Problems in

Dynamical Systems

2010 NCTS Seminars on Dynamical SystemsSpeaker: 詹其樺博士

Time: PM 1:30-3:00, Friday, Oct. 15, 2010 Topic: Some Eigenvalue Problems for Vectorial

S t u r m - L i o u v i l l e E q u a t i o n s w i t h Eigenparameter Dependent Boundar y Conditions

Speaker: Dr. Chung-Che Hu 胡忠澤 (NTHU)Time: PM 1:30-3:00, Friday, Oct. 29, 2010 Topic: Perturbation of the Chaotic 1D Mixed Wave

System Causes the Unbounded Growth of the Snapshots of the Gradient

Speaker: Professor Tomoki Kawahira (Nagoya University)

Time: PM 4:00-5:00, Tue., Nov. 9, 2010 Topic: Dynamically Stable Perturbation of Parabolic

Cycles

Speaker: Prof. Mitsuru Shibayama (Kyoto University)Time: PM 2:00-4:00, November 19 (Fri.), 2010Topic: Non-I nt eg rabi l i t y of Homogeneous

Hamiltonian Systems through McGehee Coordinates

Speaker: Prof. Mitsuru Shibayama (Kyoto University)Time: PM 2:00-4:00, November 26 (Fir.), 2010Topic: A Variational Approach to the n-body

Problem

Speaker: Dr. Chi-Ru Yang (National Tsing Hua University)

Time: PM 1:30-3:00, Fri., Dec. 3, 2010 Topic: Traveling Wave Solutions in Diffusive

Predator-Prey Type Model

Speaker: Professor Fumiaki Sugisaki (Kumamoto University)

Time: PM 3:30-4:30, Tue., Dec. 21, 2010 Topic: Extensions of Cantor Minimal Systems and

Order Embeddings of Simple Dimension Groups

D. 3. 3 The accompl ished and the anticipations

2010[1] J.-C. Ban, Y.-L. Cao and H.-Y Hu “Hausdorff

Dimension and Var iat ional Pronciple for Repellers” Trans Amer. Math. Soc. vol. 362, no.2, 727-751 (2010)

[2] K.-C.Chen, X. Dong, On the barycenter of the tent map. Proc. Amer. Math. Soc., 138, 4025-4035 (2010).

[3] K.-C.Chen, Variational constructions for some satellite orbits in periodic gravitational force fields. Amer. J. Math., 132, 681-709 (2010).

[4] John M. Hong, Cheng-Hsiung Hsu and Weishi

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Liu (2010), Inviscid and viscous stationary waves of gas f low through contracting-expanding nozzles, Journal of Differential Equations 248, 50--76.

[5] John M. Hong, Cheng-Hsiung Hsu and Weishi Liu (2010), Viscous standing asymptotic states of isentropic compressible flows through a nozzle, Archive for Rational Mechanics and Analysis 196, 575--597.

[6] Cheng-Hsiung Hsu and Ting-Hui Yang (2010), Traveling wave solutions of delayed lattice differential system in Lotka-Volterra type, Discrete and Continuous Dynamical Systems-B 14, 111--128.

[7] Cheng-Hsiung Hsu, Suh-Yuh Yang, Ting-Hui Yang and Tzi-Sheng Yang (2010), Stability and bifurcation of a two-neuron network with distributed time delays, Nonlinear Analysis-Real World Applications 11, 1472--1490.

[8] S. Gonchenko and M.-C. Li, 2010, Shilnikov's cross-map method and hyperbolic dynamics of three-dimensional Henon-like maps, Regular and Chaotic Dynamics, 15, 165-184.

[9] S. K i r ik i , M.-C. Li and T. Soma, 2010, Coexistence of invariant sets with and without SRB measures in Henon family, Nonlinearity, 23, 2253-2269

[10] M.-C. Li and M.-J. Lyu, 2010, Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition, Journal of Differential Equations, 250, 799-812.r.

2011[1] Jung-Chao Ban, Wen-Guei Hu, Song-Sun Lin and

Yin-Heng Lin (2011) “Zeta functions for two-dimensional shifts of finite type”Memoirs of the Amer. Math. Soc., to appear.

[2] Jung-Chao Ban, Chih-Hung Chang and Song-Sun Lin (2011)“Diamond in multi-layer cellular neural networks”International Journal of Circuit Theory and Applications, to appear.

[3] Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen and Mei-Shao Lin (2011) “The Complexity of Permutive Cellular Automata”Journal of Cellular Automata, to appear.

[4] J.-C. Ban and C.-H. Chang “Factor, Diamond and Density of Pressure” Proc. Amer. Math. Soc. to appear.

[5] Cheng-hsiung Hsu, Qin Jiang, Zhi-Xian Yu and Rong Yuan (2011), Traveling waves for nonlinear cellular neural networks with distributive time delays, Journal of Differential Equations 251, 630--650.

[6] H.-J. Chen and M.-C. Li, 2011, Environmental tax policy, habit formation and nonlinear dynamics, Nonlinear Analysis-Real World Applications, 12, 246-253.

[7] M.-C. Li and M.-J. Lyu, 2011, Positive topological entropy for multidimensional perturbations of topologically crossing homoclinicity, Discrete and Continuous Dynamical Systems, ser. A, 20, 243-252.

[8] Kang-Ling Liao, Chih-Wen Shih, Snapback Repellers and Homoclinic Orbits for Multi-dimensional Maps, J. Math. Anal. Appl., 386 (2011), 387-400.

[9] K.- C. Chen , J.S. Hsiao, Convex cent ra l configurations of the n-body problem which are not strictly convex, Journal of Dynamics and Differential Equations, to appear.

Preprints

[1] J.-C. Ban, C.-H. Chang, T.-J. Chen and M.-S. Lin, “Dimension Spectrum for Sofic Systems” Submitted (2010)

[2] J.-C. Ban and C.-H. Chang “Fractral Dimension of One-Dimensional Cel lu la r Automata” Submitted (2010).

[3] J.-C. Ban, Y.-L. Cao and Y. Zhao “Multi-fractal Analysis for Products of Positive Matrices Under Countable Symbol Spaces” Submitted (2010).

[4] John M. Hong, Cheng-Hsiung Hsu and Weishi Liu, Sub-to-super transonic steady states and their linear stabilities for gas flows, submitted.

[5] Cheng-Hsiung Hsu, Chi-Ru Yang, Ting-Hui, Yang and Tzi-Sheng Yang, Existence of traveling wave solutions for diffusive predator-prayer type model, submitted (2010)

[6] Cheng-Hsiung Hsu, Jian-Jhong Lin and Ting-Hui Yang, Traveling wave solutions for delayed lattice reaction diffusion system, submitted (2011).

[7] Cheng-Hsiung Hsu, Chi-Ru Yang and Tzi-Sheng Yang, Bifurcation analysis of a neural loop with distributed time delays, submitted (2011)

[8] Cheng-Hsiung Hsu, Inviscid and viscous stationary waves of gas flow through nozzles of

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Coordinators: S.-C. Chang (NTU), Y.-I. Lee (NTU), D.-M Nhieu (NCU), C.-J. Sung (NTHU), N.-K. Ho (NTHU), D.-H. Tsai (NTHU), R. Chiang (NCKU).

D.4 Geometric Analysis and Differential Geometry

varying area, submitted (2011).[9] John, M. Hong, Cheng-Hsiung Hsu, Bo-Chih

Huang and Tzi-Sheng Yang, Geometric singular perturbation approach to the steady state traffic flow model, submitted (2011).

[10] Cheng-Hsiung Hsu, Ming-Shu Peng, Zhi-Xian Yu and Rong Yuan, Traveling waves dor delayed cellular neural networks with non-monotonic output functions, submitted (2011).

[11] Chih-Wen Shih , Ju i-Pin Tseng, Global Synchronization and Asymptotic Phases for a

Ring of Identical Cells with Delayed Coupling, submitted.

[12] A. Friedman, C.-Y. Kao, and C.-W. Shih*, 2011, “Transcriptional control in cell differentiation: asymptotic limit”, submitted.

[13] K.-L. Liao, C.-W. Shih*, C.-J. Yu, 2011, “Rigorous numerical verification forsnapback repellers and homoclinic orbits”, preprint.

eomet r ic Analysis and Different ial Geometry is a big branch of study in

mathematics. It consists of many important areas and subjects. The mathematicians in Taiwan whose researches are related to this category have a wide variety of research topics and directions. During the past year, we mainly focus on, but not limited to, the following directions: Geometric Evolution Equations, Function and Map Theory, and Geometric Structures.

Main research focus of GADG group at NCTS

• Geometric Evolution Equations:(i) Mean curvature flow in higher co-dimension. (ii) The torsion flow and geometrization problem

of contact 3-manifolds. (iii) The curvature flow of curves and hypersurfaces.

• Function and Map Theory:(i) Funct ion theor y on pseudoher mit ian

manifolds.(ii) A nalysis on sub -man ifold i n a sub -

Riemannian manifold.(iii) Har monic f unct ion theor y, min imal

s u b m a n i fold s , h a r mon ic fo r m s on manifolds, heat flow of harmonic maps.

• Geometric Structures: (i) Special Lagrangian and Hamiltonian

stationary sub-manifolds. (ii) CR structures in Cauchy-Riemann geometry

and topology of contact manifolds. (iii) The Calabi-Yau problems for CR manifolds.

• Other Topics:The geometry research at Tainan ranges from

symplectic geometry to algebraic geometry or geometric analysis. Research topics include: moduli spaces of vector bundles, representation varieties, moment maps in var ious geometr ies, contact homology, Lagrangian submanifolds, orbifolds, quantum cohomology, cohomological crepant resolutions, local positivity and syzygies of algebraic varieties, geometric flows and harmonic maps.

D.4.1 Researcher in local focus group

PI: Y.-I. Lee (NTU), S.-C. Chang (NTU), D.-M Nhieu (NCU), N.-K. Ho (NTHU), C.-J. Sung (NTHU), D.-H. Tsai (NTHU), River Chiang (NCKU).

AI: M.-D. Wang (Columbia U, NTU), C..-C. Chen (NTU), T.-C. Lin (NTU), J. Wang (NTU), J.-H. Cheng (Sinica), J.-F. Hwang (Sinica), D.-C. Wu (Sinica), C.-C. Hsieh (Sinica), K.-M. Hui (Sinica),

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T.-H. Chang (Sinica), A. N. Wang (NTU), K.-W. Lee (NTU), K.-L, Lin (NTU), C.-J. Liu (NTU), J-.N. Tsai (NTU), T.-R. Guo (NTU), C.-C. Lin (NTNU), J.-T. Chen (NTNU), J.-S. Guo (Tamkang U.), M.-L. Yau (NCU), H.-L..Chiu (NCU), R.-T. Huang (NCU), D. Neuyen (NTHU), C.-I. Ho (NCTS), L.-C. Chang (NTHU), S.-C. Chu (NCCU), C.-C. Poon (NCCU), S.-Y. Hsu (NCCU), Y.-C. Lin (NCKU), R. Chen (NCKU), Y-J Hong (NCKU), E. Z. Xia (NCKU), N.-C. Wong (NSYU), H.-G. Chan (NPUE), C.-T. Wu (NPUE).

D.4.2 Visitors

Otto Van Koert (Seoul National University), Martin Guest (Tokyo Metropolitan University), WANG,CHANG-PIAN (Pek ing Universit y), Tommaso Pacini (Scuola Normale Superiore, Pisa), Johannes Nordström (Imperial College), Mao-Pei Tsui (The University of Toledo), Knut Smoczyk (Leibniz University), Ian McIntosh (University of York), Yong-Geun Oh (Univeristy of Wisconsin), Dominic Joyce (University of Oxford), Mohammed Abouzaid (MIT & Clay Mathematics Institute), Ildefonso Castro Lóp (Universidad de Jaén), Mark Haskins (Imperial College), Mu-Tao Wang (Columbia University), Tom Ilmanen (ETH Zürich), Pascal Romon (Université de Marne-la-Vallée), Richard M. Schoen (Stanford University), Martin Schlichenmaier (Univ. Luxembourg) ,Horst R. Thieme (Arizona State University) ,Alex Vasiliev (University of Bergen) ,Irina Markina (University of Bergen), Wei Wang (Zhejiang University), Po Lam Yung (Rutgers University), Siye Wu (University of Hong Kong), Erlend Grong (University of Bergen), Mauricio Godoy Molina (University of Bergen), Georgy Ivanov (University of Bergen), Shing-Tung Yau (Harvard University), Xiaojun Chen (University of Michigan), Graeme Wilkin (National University of Singapore), Gerhard Huisken (Max Planck Institute for Gravitational Physics), Naoyuki Ishimura (Hitotsubashi University), Mitsuro Sugimoto (Nagoya University), Chisato Iwasaki (University of Hyogo), Kenro Furutani (Tokyo University of Science), Yohei Tsutsui (Osaka University), Shinya Okabe (Tohoku University), Yutian LI (City University of Hong Kong), Wolfram Bauer (Universität Göttingen),

Wataru Takahashi (Tokyo Institute of Technology), Tatsuo Nishitani (Osaka University), Der-Chen Chang (Georgetown University), Tomoo Matsumura (KAIST, Korea), Jinpeng An (Peking University), Viktor Ginzburg (UC Santa Cruz, USA), Patrick Iglesias-Zemmour (Laboratoire d’Analyse Topologie et Probabilité, CNRS, Marseille)

D.4.3 Workshops, Course and Lecture

• The Second Taiwan Geometry Symposium, May 14 (Saturday), 2011

Organizers: Yng-Ing Lee, National Taiwan UniversityRiver Chiang, National Cheng Kung UniversityNan-Kuo Ho, National Tsing Hua UniversityInvited Speakers: Jih-Hsin Cheng, Academic SinicaYu-Chu Lin, National Tsing Hua University Chin-Tung Wu, National Pingtung University of Education

• 2011 NCTS Taiwan-Norway Joint Workshop on Analysis and Its Applications, June 7-10, 2011

The 2011 Taiwan-Norway Joint Workshop on Analysis and Its Applications will be held at the National Center for Theoretical Sciences on June 7-10, 2011. This is the continuation of the previous Taiwan-Norway workshop which was held in December 2009. The aim of this workshop is to bring together active researchers with different backgrounds to discuss recent and prospective advances in the areas related to Fourier Analysis, Geometric Analysis and Mathematical Physics. This year we have arranged lectures related to sub-elliptic partial differential equations, sub-Riemannian geometry and problems related to mathematical physics. We hope to use this opportunity to discuss possible joint projects between researchers in Taiwan and Norway. We also hope to attract young scholars and Ph.D. students to do research along these directions. During the workshop, we will discussion sessions every afternoon for postdocs and graduate students to promote the advances between Norway and Taiwan. This workshop is partially supported by the National Center for Theoretical Sciences (Taiwan Hsinchu)

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and the Norwegian Research Council.Organizers: Der-Chen Chang, Georgetown University, USAChiung-Jue Sung, National Tsing Hua University, TaiwanAlex Vasiliev, Bergen University, NorwayInvited Speakers: Alex Vasiliev (Bergen University, Norway) Irina Markina (Bergen University, Norway) Galia Dafni (Concordia University, Canada) Wei Wang (Zhejiang University, China) Po Lam Yung (Rutgers University, USA) Der-Chen Chang (Georgetown University, USA)

• Special Day in Fourier Analysis, June 13, 2011This conference will start a series of bi-year

international conferences on Differential Geometry in Taiwan. An important area in Geometry will be specified as the main theme each time. Our purpose is to create a discussion and interaction platform in the chosen area, and at the same time to foster future co-operations and introduce new people into the field. Additional short courses may also be arranged around the same time as the conference. The topic for the conference in 2011 is “Special Lagrangians and Related Topics”, which will include special Lagrangians, Lagrangian mean curvature f low, J-holomorphic curve techniques for Lagrangians, and the calibrated geometries in general. An intensive summer school on related introductory background will take place one week before the conference from June 27 to July 1, 2011. The tentative topic for 2013 is “Geometry and General Relativity.” Organizers: Der-Chen Chang, Georgetown University, USAChiung-Jue Sung, National Tsing-Hua University, TaiwanInvited Speakers:

Hang-Chin Lai (Chung Yuan Christian University, Taiwan), Galia Dafni (Concordia University, Montreal, Canada), Der-Chen Chang (Georgetown University, USA), Wei Wang (Zhejiang University, China), Po Lam Yung (Rutgers University, USA), Ying-Chieh Lin (Academia Sinica, Taiwan), Ting-Hui

Chang(Academia Sinica, Taiwan)

• 2011 Taiwan International Conference on Geometry: Special Lagrangians and Related Topics, July 04 ~ 07, 2011

This conference will start a series of bi-year international conferences on Differential Geometry in Taiwan. An important area in Geometry will be specified as the main theme each time. Our purpose is to create a discussion and interaction platform in the chosen area, and at the same time to foster future co-operations and introduce new people into the field. Additional short courses may also be arranged around the same time as the conference. The topic for the conference in 2011 is “Special Lagrangians and Related Topics”, which will include special Lagrangians, Lagrangian mean curvature f low, J-holomorphic curve techniques for Lagrangians, and the calibrated geometries in general.An intensive summer school on related introductory background will take place one week before the conference from June 27 to July 1, 2011." The tentative topic for 2013 is “Geometry and General Relativity.” Invited Speakers:Mohammed Abouzaid (MIT & Clay Mathematics Institute, USA)Ildefonso Castro López (Universidad de Jaén, Spain)Jason Lotay (University College London)Mark Haskins (Imperial College, UK)Tom Ilmanen (ETH Zürich, Switzerland)Dominic Joyce (University of Oxford , UK)Ian McIntosh (University of York, UK)Johannes Nordström (Imperial College, UK)Yong-Geun Oh (Univeristy of Wisconsin, Madison, USA) Tommaso Pacini (Scuola Normale Superiore, Pisa, Italy)Pascal Romon (Université de Marne-la-Vallée, France)Richard M. Schoen (Stanford University, USA)Knut Smoczyk (Leibniz University, Hannover, Germany)Mu-Tao Wang (Columbia University , USA)Brian White (Stanford University, USA)Organizers:

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Dominic Joyce (University of Oxford , UK) Yng-Ing Lee (National Taiwan University) Mu-Tao Wang (Columbia University , USA)

• NCTS Summer Minicourse on String Topology and Morphic Cohomology, July 29, 2011

Lectures :Prof. Xiaojun Chen (University of Michigan at Ann Arbor)Prof. Jyh-Haur Teh (National Tsing Hua University)

• 2011 NCTS Summer Course in Geometry Analysis, July 11-15, 2011

Lecturer: Prof. Duy-Minh Nhieu 饒維明 (National Central University)

• NCTS Special Lecture, July 29, 2011 Speakers: Prof. S. T. Yau 丘成桐院士 ( 哈佛大學

講座教授 , 1982 年費爾茲獎得主 )Title: Mass and Momentum in General Relativity

• NCTS Summer Minicourse on Curve & Surface Theory, August 8, 11, 15, 17, 22, 25, 2011

Lecturer: Prof. Tsai, Dong-Ho 蔡東和 (National Tsing Hua University)

Topic: We will cover some interesting topics related to the geometry of curves and surfaces in R3: These topics are chosen from the reference below.

• 2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis, December 19- 21, 2011

The 2011 Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis will be held at the National Center for Theoretical Sciences on December 19-21, 2011. The aim of this workshop is to bring together active researchers with different backgrounds to discuss recent and prospective advances related to Geometric Analysis and Partial Differential Equations. The workshop will contain lectures related to elliptic and sub-elliptic partial differential equations, sub-Riemannian geometry and problems

related to mathematical physics. We hope to use this opportunity to discuss possible joint projects between researchers in Taiwan and Japan. We also hope to attract young scholars and Ph.D. students to do research along these directions. During the workshop, there will be discussion sessions every afternoon for postdocs and graduate students to promote the advances between Taiwan and Japan. This workshop is partially supported by the National Center for Theoretical Sciences (Taiwan Hsinchu) and the Japan Society for the Promotion of Science. Organizers:Der-Chen Chang (Georgetown University)Dong-Ho Tsai (National Tsing Hua University)Invited Speakers: Wolfram Bauer (Universität Göttingen)Der-Chen Chang (Georgetown University)Kenro Furutani (Tokyo University of Science)Chisato Iwasaki (University of Hyogo)Naoyuki Ishimura (Hitotsubashi University)Jin-Cheng Jiang (National Tsing Hua University)Yoshitsugu Kabeya (Osaka Prefecture University)Yutian Li (City University of Hong Kong)Tatsuo Nishitani (Osaka University)Michiaki Onodera (Mittage-Leffler Institute)Shinya Okabe (Tohoku University)Mitsuro Sugimoto (Nagoya University)Wataru Takahashi (Tokyo Institute of Technology)Yohei Tsutsui (Tohoku University)Hwaichiuan Wang (National Tsing Hua University)

• 2011 NCTS Short Course on Analysis, 3/17、3/24、3/31、4/7、4/14、4/21, 2011

Instructor: Dr. Chi-Hua Chan 詹其樺 (NCTS)Introduction to Dirich Series and the Zeta Function.

• 2011 NCTS/TPE Summer School on Geometry, June 28-July1, 2011

This summer school will provide some introductory courses and background for talks in “2011 Taiwan International Conference on Geometry: Special Lagrangians and Related Topics” in the following week. There are nine 90 minute lectures in total

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given by three speakers. The topics will include introductions to special Lagrangian geometry, Lagrangian mean curvature f low, and the gluing construction method.Organizers:Yng-Ing Lee (National Taiwan University)Mao-Pei Tsui (The University of Toledo, USA)

• Third Taiwan Geometry Symposium, September 24, 2011

The purpose of the Taiwan Geometry Symposium is to foster discussions and interactions within the geometry community in Taiwan. It hopes to meet regularly in the years to come, running on a Saturday from late morning to late afternoon, with 3 speakers, followed by dinner. All people interested in geometry including faculty, students, postdoctors, and young scholars are encouraged to participate.The first symposium took place on Nov 20, 2010 at NCTS (South), NCKU, Tainan. The second symposium took place on May 14, 2011 at NCTS (North), NTU, Taipei.Organizers:Yng-Ing Lee, National Taiwan UniversityRiver Chiang, National Cheng Kung UniversityNan-Kuo Ho, National Tsing Hua UniversityInvited Speakers: Eugene Xia (National Cheng-Kung University), Chung-Jun Tsai (National Taiwan University), Rung-Tzung Huang (National Central University)

• 2011 NCTS Distinguished Lecture Series, October 24-27 2011

Speaker: Prof. Gerhard Huisken (Director, Max Planck Institute for Gravitational Physics, Germany)Topics include: Mean Curvature Flow in Geometry and Physics, Regularity Properties and Estimates for Mean Curvature Flow, Structure of Singularities and Surgery for Mean Curvature Flow, Applications to Isoperimetric Inequalities and General Relativity.

D.4.4 Seminars and Student Seminars

•NCTS/TPE& TIMS Student Geometry SeminarSpeakers include：楊皓昀、劉奕賢、陳仁豪、程大容、

廖鴻仁

• NCTS/TPE & TIMS Joint Geometry SeminarSpeakers include：姚美琳、Otto Van Koert

• NCTS/TPE working seminar on Riemannian Geometry and General Relativity

Speakers include：廖鴻仁、李國瑋、呂楊凱、王以晟

• NCTS/TPE Geometry seminarSpeakers include：Po-Ning Chen

• NCTS/TPE one day student geometry seminarSpeakers include: 張博堯、陳仁豪、王以晟、黃景芃

• NTU & NCTS/TPE Geometry SeminarSpeakers include: 蔡忠潤

• 2011 NCTS Seminar on Geometry, June 14, 2011 Speaker: Prof. SiyeWu (University of Hong Kong)Topic: Moduli Space of Higgs Bundles and Duality I, II

•2011 NCTS Seminar in Geometry, July 4& 6, 2011 Speaker: Prof. Jinpeng An (Peking University, China)Topic: Gromov's Rigid Geometric Structures and Isometric Actions

• 2011 NCTS & NTHU Joint Geometry and Topology Seminar, Sep. 19, 2011

Speakers include: Prof. Graeme Wilkin (National University of Singapore)、Dr. Chung-I Ho 何忠益

(NCTS)Topic include: Cohomology of Higgs Bundle Moduli Spaces, Generalized Complex Geometry.

• 2011 NCTS Geometry Learning SeminarOrganizer: Prof. Chiung-Jue Sung (National Tsing Hua University)Speakers include: Mr. Nguyen Thac Dung (NTHU)、Dr. Liang-Chu Chang 張喨筑 (NCCU)、Miss Wen-Cheng Wu 巫玟錚 (NTHU)、Mr. Chiou-Yung Li 李邱勇 (NTHU)、Mr. 陳義麟 (NTHU)、Miss 王一珊 (NTHU)Topics include: The Spectrum of Laplace-Beltrami Operator on a Bounded Pseudoconvex Domain,

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Conformal Invariants Associated to a Measure, p-harmonic 1-forms on Kahler and Quaternionic Kahler Manifolds, On the Parabolic Kernel of the Schrodinger, Curvature Estimates for Minimal Hypersurfaces, Symmetric Diffusion Operators on Complete Riemannian Manifolds, The Bottom of the Spectrum of the Laplacian on Kahler Manifolds, The Function Theory on Compete Smooth Metric Measure Space, On Spaces of Harmonic Functions.

• 2011 NCTS Geometry Learning SeminarOrganizers: Prof. Jyh-Haur The (National Tsing Hua University)Speakers include: 吳旻駿、李育浚、官侑萱、曾煥鑫、廖軒毅

Topics include: Smooth Manifolds, Atiyah Conjecture, Proof of $\partial$-bar Poincare Lemma, Feynman Path Integral, Tangent Spaces, Kahler Manifold, The Brown Theorem, Fractional Feynman Path Integral, The Proof of the Sard Theorem, Lefschetz Operator, Schemes, K-theory, Chow Forms, Lawson's Magic Fan, Axiomatic Cohomology, Construction of Homotopy Sequence, Lawson Homology Groups.

• 2011 NCTS Summer Student Seminar on Reading Course

Organizers: Prof. Shu-Jung Kao 高淑蓉 (NTHU)Speakers include: Mr. 杜昇展 (NTHU)、Mr. 黃于哲

(NTNU)、Mr. 賀逸然 (NTNU)、Miss. 葉又菁 (SCU)Topics include: Topological Space, The Topology of Euclidean Space, Differentiable Mappings, Cardinality, Continuous Mappings, Compact and Connected Sets.

• Geometry Seminar at NCTS (south)We held geometry seminars throughout the year. Some speakers gave more than one lecture. Our speakers from 2011/1 to 2011/12 include: Mei-Lin Yau (NCU), River Chiang (NCKU), Tomoo Matsumura (KAIST, Korea), Jinpeng An (Peking University), Viktor Ginzburg (UC Santa Cruz, USA), Patrick Iglesias-Zemmour (CNRS, Marseille).

D.4.5 Accomplishments

In below we list papers published (or accepted) in the year 2011.

[1] J.-H Cheng, J.-F. Hwang, A. Malchiodi and P. Yang, A Codazzi-like equation and the singular set for smooth surfaces in the Heisenberg group, to appear in Journal fur reine und angewandte Mathematik, 2011.

[2] Y.-I. Lee, A.-N. Wang, and S.-W. Wei, A Generalized 1-harmonic Equation and the Inverse Mean Curvature Flow, Journal of Geometry and Physics, vol. 61 (2011), p.453-461.

[3] Y.I. Lee, Self-similar Solutions and Translating Solutions, Complex and Differential Geometry, Springer Proceedings in Mathematics, vol. 8 (2011), p.193-204.

[4] K.W. Lee and Y.I. Lee, Mean Curvature Flow of the Graphs of Maps Between Compact Manifolds, Trans. Amer. Math. Soc., vol. 363 (2011), 5745-5759.

[5] Y.I. Lee, The Existence of Hamiltonian Stationary Lagrangian Tori in Kahler Manifolds of Any Dimension (2011), to appear in Calc. Var. Partial Differential Equations.

[6] N.-K. Ho, C.-C. Melissa Liu: Anti-perfect Morse Stratification, Selecta Mathematica 17, 2011, no. 2, 505-532.

[7] Goldman, William M.; Xia, Eugene Z.: Ergodicity of mapping class group actions on SU(2)-character varieties. Geometry, rigidity, and group actions, 591–608, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 2011.

[8] William M. Goldman, Eugene Z. Xia.: Action of the Johnson-Torelli group on Representation Varieties, to appear in Proceedings of the AMS, 2011.

[9] Xia, Eugene Z.: Dehn twists and invariant classes, to appear in Proceedings of the AMS, 2011.

[10] S.-C. Chang, C.-Y. Lin and C.-T. Wu, Eigenvalues and Energy Functional with Monotonicity Formulae under the CR Yamabe Flow on a Closed Pseudohermitian 3-manifold, J. Nonlinear Studies, Vol. 18, N0. 3 (2011), 377-392.

[11] Y.I. Lee, The Metric Properties of Lagrangians, Surveys in Geometric Analysis and Relativity, Advanced Lectures in Mathematics (ALM) 20, p. 327-341, Higher Education Press and International Press, Beijing-Boston, 2011..

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[12] D. Joyce, Y.I. Lee and R. Schoen, On the Existence of Hamiltonian Stationary Lagrangian Submanifolds in Symplectic Manifolds, Amer. J. Math., vol. 133 (2011), 1067-1092.

[13] S.-C. Chang and C.-T. Wu, The Diameter Estimate and Its Application to CR Obata's Theorem on Closed Pseudohermitian (2n+1)-Manifolds, to appear in Transactions of AMS, 2011.

[14] S.-C. Chang, T.-J. Kuo and S.-H. Lai, Li-Yau Gradient Estimate and Entropy Formulae for the CR heat equation in a Closed Pseudohermitian 3-manifold, to appear in J. Diff. Geom., 2011.

[15] L.-C. Chang, C.-J. Sung: A note on p-harmonic k-forms on complete manifolds, to appear in Pacific J. Math, 2011.

[16] Y.-C. Lin, C.-C. Poon, D.-H. Tsai: Contracting convex immersed closed plane curves with slow speed of curvature, to appear in Transactions of the AMS, 2011.

[17] D.-C. Chang, I. Markina and A. Vasilev: Hopf Fibration I: Geodesics and Distances, to appear in Journal of Geometry and Physics, 2011.

[18] D.-C. Chang, S.-Y. Feng: Geometric Analysis on Generalized Hermite Operators, to appear in Advanced in Applied Math., 2011.

[19] D. - C . C h a n g , W. E b y, E . G r i n b e r g : Deconvolution for the Pompeiu problem on the Heisenberg group, I, to appear in "The mathematical Legacy of Leon Ehrenpreis", edited by D. Struppa and I. Sabadini, Springer-Verlag, 2011.

[20] Lin, Yu-Chu; Poon, Chi-Cheung; Tsai, Dong-Ho. Contracting convex immersed closed plane curves with slow speed of curvature, to appear in Transactions of the AMS.

Coordinators: Sze-Bi Hsu (National Tsing-Hua University), Chih Wen Shih (Natinal Chiao-Tung University)

D.5 Mathematical Biology

he purpose of the topical program in Mathematical Biology is to promote the

interdisciplinary interaction between mathematicians, biologists, physicists, statisticians and computer scientists on the new problems arising from biology. In the past one year, we held a weekly seminars in Partial Differential Equations with Application to Mathematical Biology, an summer course in Mathematical Physiology . We also invite several speakers to give talks in population biology, uniformly persistence theory and traveling waves. We state as follows:

Local Group: Zy-You Chen(NTHU), Jann-Long Chern (NCU), Sze-Bi Hsu (NTHU), Kuo-Chih Hung (NTHU), Chui-Ju Lin (NTHU), Chih-Wen Shih (NCTU), Yong-Li Tang(NCU), Shin-Hwa Wang

(NTHU), Chih-Jiang Tsai (NCCU), Ting-Hui Yang (Tamkang University)

D.5.1 Course & Seminars

I. 2011 NCTS Summer Course in Mathematical Physiology

Dates : 7/11-8/1, Every Monday(7/11, 7/18, 7/25, 8/1) 10:00am-12:00pm, 2:00pm-3:00pmSpeaker: Prof. Je-Chiang Tsai 蔡志強 (National Chung-Cheng University) In this course we study the following topics: (1) Cellular Homeostasis: The Cell

Membrane,Diffusion, Passive and Active Transport, The Membrane Potential, and Membrane Ion Channels.

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(2) Excitability: The Hodgkin-Huxley Model, The FitzHugh-Nagumo

Equations, Fast-Slow system, Traveling waves, CU curve.

(3) Bifurcation theory.(4) Wave Propagation in Higher Dimensions: Eikonal

Equation, Spatial Patterns, and Spiral Waves. NOTE: 學生將被要求做簡單的數學分析及使用

Matlab 解決數學模型問題。

II.2011 NCTS Focus Program in Mathematical Biology: PDE with Application to Mathematical Biology

Organizers:Professor Sze-Bi Hsu 許世壁 (NTHU)Professor Jann-Long Chern 陳建隆 (NCU)Professor Shin-Hwa Wang 王信華 (NTHU)Professor Ting-Hui Yang 楊定輝 (Tamkang University)

The weekly seminar (2/21/2011~5/9/2011) was held every Monday, 10:00am-12:00, 2:00pm-4:00pm.Basically the post doctors and graduate students present some important work in PDE and Mathematical Biology, and their own work. The topics are followings:(1)Speaker: 洪國智 (Post doctor, NTHU) Title: The Periodic Lotka-Volterra Competition

System with Diffusion (2)Speaker: Dr. Zhi-You Chen (Post doctor,NTHU) Title: On the Uniqueness and Structure of Solutions

to the Equation and System Arising from Chern-Simons Models

(3)Speaker: Chui-Ju Lin (Ph.D student, NTHU) Title: The Linear Periodic -Parabolic Eigenvalue

Problem (4)Speaker: Dr. Zhi-You Chen (NTHU) Title: On the Uniqueness and Structure of Solutions

to the Equation and System Arising from Chern-Simons Models I

(5)Speaker: Sze-Bi Hsu (NTHU) Title: On the Blow Up for the Solutions of a Systems

of ODE Arising from Condensed Physics(6)Speaker: Dr. Yong-Li Tang ( Ph.D student, NCU) Title: Existence and Uniqueness of Positive

Solutions to Sublinear Elliptic Systems

III.2011 NCTS Seminar on Mathematical Biology1. Time: 10:10 am-12:10 pm, March, 7,2011 Speaker: Prof. Ting-Hui Yang (Tamkang

University) Title: Traveling Wave Solutions for Time-Delayed

Lattice Reaction-Diffusion Systems2. Time: 3:00-4:30pm, Thursday, February 17, 2011 Speaker: Dr. Yun-Huei Tzeng 曾雲輝 (Graduate

Institute of Biostatistics, China Medical University,Taichung)

Topic: Subfunctionalization Buffers Dosage Imbalances Enabling the Evolution of Genetic

Redundancy3. Time: 10:10-12:00pm, Monday, April 11 2011 Speaker: Professor Liang Xing (China Technology

University, PRC) Topic: Maximizing the Spreading Speed of KPP

Fronts in Two-dimensional Stratified Media4. Time: 10:10-12:00pm, Monday, April 18 2011 Speaker: Professor Liang Xing (China Technology

University, PRC) Topic: Spreading Speed and Travelling Waves

of a Spatially Diffusive Logistic Model with a freeBoundary

5. Time: 10:10 am-12:00 pm, May 16, 2011 Speaker: Prof. Lih-Ing Wu Roeger 吳麗櫻 (Texas Tech. University)

Tit le: Compar ing the Discrete -Time and Continuous-Time Winnerless and

Lotka-Volterra Competition Models6. Time: 3:10 pm-4:00 pm, May 16, 2011 Speaker: Prof. Shigui Ruan (University of Miami,

USA) Title: Mathematical Modeling of Some Infectious

Diseases in Mainland China7. Time: 10:10 am-11:00 am, May 23, 2011 Speaker: Prof. Horst R. Thieme (Arizona State

University) Title: Population Persistence without a Compact

Attractor8. Time: 11:10 am-12:00 pm, May 23, 2011 Speaker: Prof. Shigui Ruan (University of Miami,

USA) Title: Modeling Transmission Dynamics of

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Antibiotic-Resistant Bacteria in Hospital9. Time: 11:10 am-12:00 pm, May 30,2011 Speaker: Prof. Horst R. Thieme (Arizona State

University) Title: Apparent Paradoxes in Disease Models with

Horizontal and Vertical Transmission10. Time: 3:10 pm-4:00 pm, May 30, 2011 Speaker: Prof. Horst R. Thieme (Arizona State

University) Title: An Epidemic Model with Post-Contact

Prophylaxis of Distributed Length11. Speaker: Dr. Kohei Yoshiyama (River Basin

Research Center, Gifu University, Japan) Time: PM 3:00-4:00, Wed., August 24, 2011 Topic: Vertical Distributions of Phytoplankton:

Observations and Theories


[1] Sze-Bi Hsu and Xiaoqiang Zhao , A Lotka-Volterra Competition Model with Seasonal Succession, Journal of Mathematical Biology (2011).

[2] S.B.Hsu and Y.Y.Chen, Synchronized reproduction promoting species coexistence through reproductive facilitation,, Journal of Theoretical Biology274 (2011) 130-144

[3] S.B.Hsu,F.B.Wang and X.Q.Zhao, Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, Journal of Dynamics and Differential Differential Equations(2011)

[4] S.B.Hsu,F.B.Wang and Jifa Jiang, Reaction-diffusion equation of two species competing for two complementary resources with internal storage, Journal of Differential Equations (2011)

[5] J.Grover, S.B.Hsu,and F.B.Wang, Competition between micro-organism for a single limiting resource with cell quota structure and spatial variation, Journal of Mathematical Biology (2011)

[6] S.B.Hsu and F.B.Wang, On a mathematical model arising from competition of phytoplankton species for a single nutrient with internal storage: Steady state analysis, Commu. Appl. Analysis 10(2011)no.5,1479-1501

[7] K.-L. Liao, C.-W. Shih* and J.-P. Tseng, 2011, “Synchronized oscillations in a mathematical model of segmentation in zebrafish”, Nonlinearity (under minor revision)

[8] Chih-Wen Shih* and Jui-Pin Tseng, “Global synchronization and asymptotic phases for a ring of identical cells with delayed coupling”, SIAM J. Math. Anal., Vol. 43, 4, (2011)1667-1697

[9] Je-Chiang Tsai and James Sneyd, Traveling Waves in the Buffered FitzHugh-Nagumo Model, SIAM J. Applied Math.(2011)

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Coordinators: Wen-Ching Li (Penn State University and NCTS), Liang-Chung Hsia (National Normal University), Yifan Yang (National Chiao-Tung University), Chia-Fu Yu (Academia Sinica)

D.6 Number Theory and Arithmetic Geometry

s this year (2011) is a special year in number theory at NCTS, there are more

number theory activities at NCTS including one international conferences and one Taiwan-Korea joint workshop in number theory. The main themes cover the field of automorphic/modular forms, Galois representations, and related topics. Besides the above mentioned topics, the existing research topics – traditional algebraic number theory, arithmetic geometry and Diophantine geometry and arithmetic of algebraic function fields are also the main focus of number theory at NCTS. The scope of our number theory group is broadening, several international cooperation programs have been established this year. The following is a list of the main research areas in number theory.

Main Research Focus of the working groupArithmetic and geometry of moduli spacesDiophantine geometryModular forms, modular curves, and Shimura curvesAutomorphic Representations and zeta functionsCoding theoryTranscendence theory in positive characteristic

D.6.1 Local participating members

C.-Y. Chang (NCU and NCTS, postdoc), C.-A Chen (NCU, Ph.D. student), Y.-M. J. Chen (NCU), H.-J. Chen (NCTS, postdoc.), Y.-H. Chen (NCU, postdoc.), W.-C. Chi (NTNU), C.-Y. Chuang (NTHU, Ph.D. student), Y.-L. Guan (NCU), L.-C. Hsia (NCU and NNU), M.-L. Hsieh (NTU), P.-Y. Huang (NCKU), P.-C. Hung (NCU, Ph.D. student), M.-C. Kang (NTU), M.-H. Kang (NCTU), C.-W. Kuo (NTHU, Ph.D. student), K.-F. Lai (NSYSU), M.-G. Leu (NCU), A. Li (Fu Jen U.), H.-C. Li (NTNU), W.-C. Li (NCTS),

Y.-H. Lin (NCTU, student), C. Nien (NCKU), A. Schweizer (Academia Sinica), S.-C. Shih (AS, research assistant), K.-S. Tan (NTU), F.-T. Tu (NCTU, student), C.-J. Wang (NCU), J.-Y. Wang (Academia Sinica), J.-H. Wang (NCU, Ph.D. student), F.-T. Wei (NTHU, postdoc), J.-W. Xue (NCTS postdoc), W.-C. Yao (TMUE), T.-C. Yang (NTU, Ph.D student), Y. Yang (NCTU), C.-F. Yu (AS), J.-D. Yu (NTU), Jing Yu (NTU), Y.-J. Yu (N. Cheng-Chi U).

D.6.2 Visitors

The speaker for our distinguished lecture series this year is Prof. Jean-Pierre Serre of the College de France, Paris, France. Prof. Serre won the Fields Medal in 1954, the Wolf Prize in 2000, and the Abel Prize in 2003.There are many short term visitors this year.

Vistors at Hsinchu:Alexey Zykin (State University-Higher School of Economics, 2011-07-16 ~ 2011-07-27), Richard Ng (Iowa State University, 2011-07-12 ~ 2011-07-21), Ling Long (Iowa State University, 2011-07-12 ~ 2011-07-21), YoungJu Choie (Postech, 2011-07-04 ~ 2011-07-15), Jingpeng An (Peking University, 2011-07-01 ~ 2011-07-07), Jiu-Kang Yu (Purdue University, 2011-07-01 ~ 2011-07-05), Kai-Wen Lan (Princeton University, 2011-06-19 ~ 2011-06-23), Ulrich Gortz (Universitat Duisburg-Essen, 2011-06-19 ~ 2011-06-24), Ching-Li Chai (University of Pennsylvania, 2011-06-19 ~ 2011-06-25), Suh-Hyun Choi (KAIST, 2011-06-19 ~ 2011-06-23), Tong Liu (Purdue University, 2011-06-19 ~ 2011-06-25), Ye Tian (Academia Sinica, China, 2011-06-19 ~ 2011-06-26), Tonghai Yang (University of Wisconsin, 2011-06-19 ~ 2011-06-26), Matija Kazalicki (University of Zagreb, 2011-06-19 ~ 2011-06-28), Bill Hoffman (University of

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Minnesota, 2011-06-18 ~ 2011-06-28), John Voight (University Vermont, 2011-06-15 ~ 2011-06-25), Ravi Ramakrishna (Cornell University, 2011-06-13 ~ 2011-06-26), Henri Darmon (McGill University, 2011-06-09 ~ 2011-06-24), Takao Yamazaki (Tohoku University, 2011-04-10 ~ 2011-04-20), Jean-Pierre Serre (College de France, 2011-04-10 ~ 2011-04-17), Rene Schoof (Universita di Roma, 2011-04-04 ~ 2011-04-26), Federico Pellarin (University of Saint-Etienne, 2011-02-27 ~ 2011-03-09), Maosheng Xiong (Hong Kong University of Science and Technology, 2011-1-16 ~ 2011-1-29), Ryan Flynn (Penn State University, 2011-6-19 ~ 2011-6-26), Pei-Yu Tsai (Harvard University, 2011-6-16 ~ 2011-6-23), Jonas Kibelbek (Penn State University, 2011-6-13 ~ 2011-7-6), Nguyen Ngoc Dong Quan (University of Arizona, 2011-6-12 ~ 2011-6-28).

Vistors at Taipei: Pei-Yu Tsai (Harvard student, one month in 2011/1), Vincent Maillot (CNRS and Universite Paris 7, 3 weeks in 2011/4), Ching-Li Chai (Pennsylvania, one month in 2011/06), Ulrich Goertz (Duisburg-Essen, one week in 2011/06 at AS), Wen-Wei Li (Morningside Center of ASC, 2 weeks in 2011/7), Gerard Freixas (CNRS, Universite Paris 7, 3 weeks in 2011/08), Takeshi Saito (Tokyo, 5 days in 2011/11 at AS), T. Katsura (Tokyo, 5 days in 2011/11 at AS), Terasoma (Tokyo, 5 days in 2011/11 at AS), Shiho (Tokyo, 5 days in 2011/11 at AS), Oliver Brinon (Paris, 5 days in 2011/11 at AS).

D.6.3 International Conferences and Workshops

In the area of number theory, this year there are one international conference, one bilateral workshop, and several mini-workshops. Details are as follows.

Hsinchu:2011 NCTS International Conference on Galois representations, Automorphic forms, and Shimura varieties:

This conference was organized by KingFai Lai (National Sun Yat San University) and Wen-Ching W. Li (National Center for Theoretical Sciences). It

was held at Hsinchu, June 20 – 23, 2011. There were eighteen invited speakers from five foreign countries as well as local number theorists. They are from six countries – Canada, China, Germany, Korea, Taiwan and United States. The total number of participants was over 60. This conference was co-sponsored by NCTS and NSF through an NSF conference grant awarded to Wen-Ching Li. NSF paid for international travel expenses of the invited speakers from the US, and also all expenses except lodging of the four invited graduate students from Harvard, Penn State, and University of Arizona. NCTS paid for the remaining expenses. This kind of international cooperation is very important to us and it is beneficial to number theorists from both countries.

The purpose of this conference was to showcase the multi-facets of Galois representations and their interconnections. Recent advances in and applications of Galois representations, automorphic forms and arithmetic of Shimura varieties, from theoretical and computational aspects, were addressed by the invited experts. Participants came from 7 different countries.

Two short courses, each for 6 hours, were offered by internationally renowned number theorists as a prelude to the conference. These were the course by Prof. Henri Darmon, McGill University, on "Algebraic cycles and p-adic deformations", June 15 and 17, 2011, and the course by Prof. Ravi Ramakrishna, Cornell University, on "A survey on Serre's conjecture and its generalizations", June 16-17, 2011.

2011 NCTS Special Day on Noncongruence Modular Forms:

This workshop was organized by Wen-Ching W. Li (National Center for Theoretical Sciences). It was held on June 27, 2011, following the international conference mentioned above. There were f ive international speakers from two foreign countries, Croatia and United States. The purpose of this workshop was to bring together the participants in the above mentioned conference who worked on the arithmetic of noncongruence modular forms for them to report their recent progress on this topic, and to provide a less formal environment to facilitate discussions in this area. Several domestic number theorists also got interested in this topic.

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Taipei:Mini-Workshop of Algebra (organized by M.-C. Kang), Jan. 11-14: 6 speakers include M. Chen, M.-K. Chuah, O. Fujino, S. Kuroda, M.-Y. Xu, and Chia-Fu Yu. Each speaker gives two 75 minute talks.One-day workshop of Algebra (organized by M.-C. Kang), June 10: 4 speakers include Chu, M.-L Hsieh, Y. Yang, M. Eie and each speaker gives a 50 minutes talkOne-day workshop of Algebra (organized by M.-C. Kang), August 16: 7 speakers include H.-J. Chiang-Hsieh, V. Young, S.-C. Huang, A. Yamasaki (Kyoto Univ), H. Kitayama (Osaka Univ), A. Hoshi (Rikkyo Univ) and M.-C. Kang. Each speaker gives a 50 minute talk.

Foreign country:2011 PMI, Korea-NCTS, Taiwan Workshop on Number Theory:

This is a continuation of our international cooperation program with the Pohang Mathematics Institute (PMI) of POSTECH, Korea, initiated in 2009. Organized by YoungJu Choie (POSTECH, Korea) and Wen-Ching W. Li (National Center for Theoretical Sciences), this conference was held at Postech Korea, July 24 – 26, 2011. Invited speakers consisted of 9 mathematicians from Korea and 8 from Taiwan. Over 50 people participated.

D.6.4 Lecture Series

This year, there have been several lecture series of length at least two weeks given by our visitors from abroad or members in our focus group. In Hsinchu area we have 2011 NCTS lectures by Jean-Pierre Serre (8 hours in two weeks) and 2011 NCTS lecture series on number theory by Rene Schoof (12 hours in three weeks). Professor Serre was also the speaker of the Distinguished Lectures in last year (2010). In Taipei area, Gerard Freixas (CNRS, Inst. Math. Jussieu) visited Taipei for three weeks and he gave a lecture series on Arakelov Geometry (8 hours).

Hsinchu: “Introduction to the Sato-Tate Conjecture for

Algebraic Varieties”given by Prof. Jean-Pierre Serre

(College de France, 1954 Fields medalist, 2000 Wolf Prize winner, 2003 Abel Prize winner, visiting NCTS from April 10 to April 17, 2011). This series of lectures gave an overview of the Sato-Tate conjecture and its generalizat ion to higher-dimensional abelian varieties. The lecture notes are available at: http://www.math.cts.nthu.edu.tw/publish/publish.php?class=103

This is the highlight of the year. NCTS devoted one month to run intensive courses to prepare the audience for Serre's lectures; there were many lively discussions after Serre's lectures among number theorists. People from all over the country came to Hsinchu to hear Serre. It was a great success. Based on the two lecture series given at NCTS in 2009 and 2011, Serre wrote a book titled "N_p(X)", to be published by AK Peters. NCTS is grateful to Serre, who graciously allowed us to post his book on our website prior to its publication.

Another series of lectures were given by Prof. Rene Schoof (University of Roma II, visiting NCTS from April 4 to April 26, 2011) on “Finite group schemes over ring of integers of number fields”. After a quick course on group scheme over number fields, Schoof gave a proof of Fontaine’s theorem and some generalization due to himself. Although this course on arithmetic geometry is of very high level, Schoof's lively and beautiful lectures had attracted the attention of the audience from the beginning to the end. Many people from Taipei traveled to Hsinchu regularly to attend his course.

Taipei: “Lectures series on Arakelov geometry” given by Gerard Freixas (CNRS, Inst. Math. Jussieu) visited Taipei for three weeks and he gave a lecture series on Aralekov Geometry (8 hours).

D.6.5 Seminars and Courses

Hsinchu:A regular seminar in number theory is held on

weekly basis at Hsinchu. In addition, starting from September 2011, a seminar specializing on Shimura curves will take place every week. The purpose of this seminar is to prepare the participants for conducting research in this important, yet challenging subject.

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Several short courses were given by the members in the focus group. These courses include courses on the Weil conjectre, Serre’s conjecture, Langlands program given by local researchers. There are also several short courses given by visitors to NCTS.

Taipei:There is a regular seminar on ar ithmet ic

geometry and representation theory at NCTS (Taipei). Arithmetic geometry group at Taipei join the TIMS number theory seminar and attend several international conferences and lecture series organized in Hsin-Chu. About 36 talks scheduled in Taipei and two one-semester courses given. The purpose of these courses is aiming at training PhD students.

1. 2011 NCTS Spring Course on Abelian Varieties. This is the second half of one year topics course. The purpose is to provide graduate students working knowledge on abelian varieties. We covered the topics including the Mordell-Weil Theorem, cohomology of line bundles, semi-simple algebras with positive involutions, CM abelian varieties, endomorphisms of abelian varieties and basic Dieudonne theory. We covered about half of the book by Mumford. The pace is slow and we plan to offer and continue another year of course on abelian varieties in order to strengthen participants the basic ability on abelian varieties.

2. 2011 NCTS Fall Course on Topics on Abelian varieties. This is the continuation of the last year NCTS course. We plan to make further study on ableian varieties based on the background we already have and hope to be able to discuss some current research topics like some questions endomorphism algebras of abelian varieties, and a bit more on the integral theory. We plan to run the following topics: The Honda-Tate theory, supersingular abelian varieties, the local-global principle for embedding fields in simple algebras with involutions, CM and QM abelian varieties and construction, linear algebras about PEL -datum.

D.6.6 Summer Programs for Students

A summer program in number theory was offered at Hsinchu in July and August of this year. The program, organized by L.-C. Hsia and W.-C. Yao, gave an introduction to algebraic number theory and arithmetic of elliptic curves. This program gave undergraduate students and beginning graduate students some flavor about modern number theory.

D.6.7 Important Results,Breakthroughs

There are many progresses. Here we mention only the following directions:

In the arithmetic of function fields of positive characteristic, many results have been obtained in this research area. In a joint work with Papanikolas, C.-Y. Chang proved the Brownawell-Yu conjecture on the algebraic independence of Drinfeld logartihms of algebraic points. He has also been working on a natural generalization: algebraic independence of the logarithms of algebraic points for pair-wise non-isogenous Drinfeld modules.

L.-C. Hsia with his collaborators studied questions on “unlikely intersections” in the setting of arithmetic dynamics. The classical problem on unlikely intersection was raised by Pink and Zilber regarding the unlikely intersection of a subvariety V of a semiabelian variety A and a family of algebraic subgroups of A of codimensions greater than the dimension of V. They obtained a nearly necessary and sufficient condition for the dynamical unlikely intersection problem. Some further generalizations were in progress.

M.-L. Hsieh continued his work toward the Iwasawa main conjecture for Galois representations associated to elliptic curves twisted by infinite order p-adic characters of the absolute Galois group of an imaginary quadratic number field. To sum up, we construct an ordinary p-adic Eisenstein series with optimal constant terms on the unitary group GU(3,1) associated to the imaginary quadratic number field. He also generalized Hida’s results on Hecke L-values for CM fields modulo p to the case where the ramified prime factors of the branch conductor are square-free.

M.-H. Kang classified the toroidal fullerenes with Cayley graph structure and gave an explicit construction of a family of fullerenes with a prescribed HOMO- LUMO gap. These constructions

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provide some advantages on designing fullerenes with the desired electronic spectral property.

W.-C. Li continued her research in two different areas. She and C.-J. Wang have successfully obtained a closed form expression for zeta functions attached to 2- dimensional complexes arising from finite quotients of the building of Sp(4). Concerning the arithmetic of noncongruence modular forms, together with her collaborators, she has established the Atkin-Swinnerton-Dyer congruences for the case when Scholl representations admit quaternion multiplication, proved the modularity of low degree Scholl representations (with Liu and Long), and proved the unbounded denominator conjecture for one-dimensional space of cusp forms with rational Fourier coefficients (with Long).

In the direction of Diophantine approximation over function fields of characteristic zero, J. T.-Y. Wang and her collaborator established an effective version of Schmidt’s subspace theorem for general projective varieties with divisors coming from hypersurfaces. In the direction related to non-Archimedean Nevanlinna theory, she, joint with Ta Thi Haoi An and Aaron Levin, established some results on algebraic degeneracy and non-Archimedean hyperbolicity for projective varieties omitting divisors. Most recently, she treated Hensley’s problems and Buchi’s problems for function fields, complex meromorphic functions and non-Archimedean meromorphic functions. These Diophantine problems are related to Hilbert’s Tenth Problem.

Y. Yang studied modular forms of half-integral weights of eta type on SL(2,Z) and determined the precise image of these modular forms under the Shimura correspondence. Since the second half of the last year, he focused his research on automorphic forms on Shimura curves. He showed that if a Shimura curve has genus zero, then automorphic forms on it can be expressed in terms of solutions of the Schwarzian differential equations. He then devised a method to compute Hecke operators on these functions. By interpreting hypergeometric functions as automorphic forms on Shimura curves, he and F.-T. Tu established some elegant identities among hypergeometric functions. In addition, he continued his collaboration with Shinji Fukuhara on periods of cusp forms and obtained new formulas for the number of ways to write a positive integer as sums of squares.

C.-F. Yu continued his study on arithmetic of Siegel modular varieties. For example, he and his collaborator investigated Siegel modular varieties in positive characteristic with Iwahori level structure. The goal was to understand how the Newton stratification and the Kottwitz-Rapoport stratification are related to each other. They also obtained structural results about the supersingular locus in the case of Iwahori level structures. In addition, he and F.-T. Wei have recently teamed up to study arithmetic of quaternion algebras and central division algebras in higher dimension over function fields.


[1] Ta Thi Hoai An and Julie T.-Y. Wang, Hensley's problem for complex and non-Archimedean meromorphic functions, J. Math. Anal. Appl., 381(2011), 661-677.

[2] Ta Thi Hoai An, Aaron Levin and Julie T.-Y. Wang , a p-adic Nevanlinna-Diophantine correspondence, Acta Arithmetica, 146(2011), 379-397.

[3] Oliver Atkin, Wen-Ching Li, Tong Liu, and Ling Long, Galois representations with quaternion multiplications associated to noncongruence modular forms, submitted.

[4] Jean-Yves Briend and Liang-Chung Hsia, on Julia set of cubic polynomials over non-Archimedean fields, submitted.

[5] Jean-Yves Briend and Liang-Chung Hsia, Weak Neron model for cubic polynomials over a non-archimedean field, preprint.

[6] A. Burungale and Ming-Lun Hsieh, vanishing of the $\mu$-invariant of p-adic Hecke L-functions for CM fields, preprint 2011, 7 pages.

[7] Heng Huat Chan, Ling Long, and Yifan Yang, a cubic analogue of the Jacobsthal identity, Amer. Math. Monthly 118:4 (2011), 316—326.

[8] Heng Huat Chan, Yoshio Tanigawa, Yifan Yang, and Wadim Zudilin, new analogues of Clausen’s identities arising from the theory of modular forms, Adv. Math, in press.

[9] Chieh-Yu Chang, transcendence of special values of quasi-modular forms, to appear in Forum Math.

[10] Chieh-Yu Chang, special values of Drinfeld

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modular forms and algebraic independence, to appear in Math. Ann.

[11] Chieh-Yu Chang, Frobenius difference equations and difference Galois groups, submitted.

[12] Chieh-Yu Chang, on periods of the third kind for rank 2 Drinfeld modules, preprint.

[13] Chieh-Yu Chang and M. A. Papanikolas, algebraic relat ions among per iods and logarithms of rank 2 Drinfeld modules, Amer. J. Math.133 (2011), 359—391.

[14] Chieh-Yu Chang and M. A. Papanikolas, algebraic independence of per iods and logarithms of Drinfeld modules. With an appendix by B. Conrad, to appear in J. Amer. Math. Soc. 25 (2012), 123—150.

[15] Chieh-Yu Chang and M.A. Papanikolas, on Carlitz tensor powers and polylogarithms, preprint.

[16] Chieh-Yu Chang, M. A. Papanikolas and Jing Yu, Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic, Algebra & Number Theory 5 (2011), 111—129.

[17] Yang Fang, Chian-Jen Wang, and Wen-Ching Li, the zeta functions of complexes from Sp(4), submitted.

[18] Shinji Fukuhara and Yifan Yang, a basis for and representations of integers as

sums of squares, accepted for publication by the Ramanujan Journal.

[19] D. Ghioca, L.-C. Hsia and T. Tucker, Preperiodic points for family of polynomials, preprint.

[20] U. Görtz and Chia-Fu Yu, on the supersingular locus in Siegel modular varieties with Iwahori level structure, arXiv:0807.1229, 27 pages. to appear in Math. Ann., 2011. (NCTS/TPE Technical Report 2008-013).

[21] Ki-Ichiro Hashimoto, Ling Long, and Yifan Yang, Jacobsthal identity for Q(sqrt(-2)), Forum Math., in press.

[22] Liang-Chung Hsia and Joseph Silverman, a quantitative estimate for quasi-integral points in orbits, Pacific J. Math. 249 (2011), 321—342.

[23] Ming-Lun Hsieh, on the non-vanishing of Hecke L-values modulo p, to appear in Amer. J. Math., preprint.

[24] Ming-Lun Hsieh, on the $\mu$-invariant of anticyclotomic $p$-adic $L$-functions for CM fields, preprint.

[25] Ming-Lun Hsieh, special values of anticlotomic Rankin-Selberg L-functions, preprint.

[26] Hsiu-Lien Huang and Julie T.-Y. Wang, the analogue of B\"uchi's cubic problem over function fields, preprint.

[27] Wen-Ching Li, zeta functions of group based graphs and complexes. Fields Institute Com- munications, vol 60, 2011, Volume WIN - Women In Numbers, 225—236.

[28] Wen- Ch ing Li and Ling Long, Four ier coeff icients of noncongruence cuspforms, Bulletin London Math. Soc., to appear.

[29] Wen-Ching Li and Maosheng Xiong, statistics of zeros of families of L-functions over function fields: a survey, submitted.

[30] A.W. Mason and Andreas Schweizer, the cusp amplitudes and quasi-level of a congruence subgroup of SL(2) over any Dedekind domain, Proc. London Math. Soc., to appear.

[31] Meemark Y. and Prinyasart T., On symplectic graphs modulo pn, Discrete Math. 311(2011), 1874–1878.

[32] Min Ru and Julie T.-Y. Wang, an effective Schmidt's subspace theorem for projective varieties over function fields, International Math. Research Notices, in press.

[33] Mathias Schütt and Andreas Schweizer, on the uniqueness of elliptic K3 surfaces with maximal singular f ibre, Annales Institut Fourier, to appear.

[34] Andreas Schweizer, strong Weil Curves over Fq(T) with Small Conductor, J. Number Theory 131 (2011), 285—299.

[35] Andreas Schweizer, entire functions sharing simple a-points with their f irst derivative, submitted.

[36] Sheng-Chi Shih, Tse-Chung Yang and Chia-Fu Yu, embeddings of fields in simple algebras over global fields, preprint.

[37] Fang-Ting Tu and Yifan Yang, lattice packing f rom quaternion algebras, accepted for publication, RIMS Kokyuroku Bessatsu.

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[38] Fang-Ting Tu and Yifan Yang, algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves, preprint.

[39] Julie T.-Y. Wang, Hensley's problem for function fields, Intern. J. Number Theory, to appear.

[40] Fu-Tsun Wei and Chia-Fu Yu, mass formula of division algebras over global function fields, arXiv:1102.5465. 14 pp. NCTS/TPE Technical Report 2010-008.

[41] Fu-Tsun Wei and Jing Yu, on definite Shimura curves and autormophic forms over function fields, preprint.

[42] Fu-Tsun Wei and Jing Yu, on theta series from quaternion algebras over function fields, preprint.

[43] Fu-Tsun Wei and Jing Yu, Theta Series and Function Field Analogue of Gross Formula. To appear in Documenta Math.

[44] Yifan Yang, congruences of the partition function, Int. Math. Res. Not., 2011, 3261—3288.

[45] Yifan Yang, modular forms of half-integral weights on SL(2,Z), preprint.

[46] Yifan Yang, Schwarzian differential equation and automorphic forms on Shimura curves, preprint.

[47] Chia-Fu Yu, geometry of the Siegel modular threefold with paramodular level structure, Proc. Amer. Math. Soc. 139 (2011) 3181—3190.

[48] Chia-Fu Yu, on Hermitian forms over dyadic non-maximal local orders, arXiv:1005.4825, 20 pp., to appear in Pure Appl. Math. Q. 2011.

[49] Chia-Fu Yu, on the existence of maximal orders, to appear in Int. J. Number Theory, 22 pp.

[50] Chia-Fu Yu, superspecial abelian varieties over finite prime fields, print.

[51] Chia-Fu Yu, an explicit reciprocity law arising from superspecial abelian varieties, preprint.

[52] Chia-Fu Yu, embeddings of fields into simple algebras: generalizations and applications, preprint.

[53] C h i a - F u Yu , w h i c h p o l y n o m i a l s a r e characteristic?, preprint.

[54] Jeng-Daw Yu, special lifts of ordinary K3 surfaces and applications, Pure Appl. Math. Q. 8 (2012), 805-824.

[55] Jeng-Daw Yu, variation of the unit root along certain families of Calabi-Yau varieties, to appear in the Fourth International Congress of Chinese Mathematicians.

[56] Jeng-Daw Yu, on ordinary crystals with logarithmic poles, preprint 2011

D. 6 . 9 E xc h a n g e p r o g r a m s a n d international cooperations

This year NCTS has supported young members, Ph D st udents in ou r focus g roup to at tend conferences, schools as well as individual visits for international collaborations. These activities include (in terms of countries):

Canada: J.-D. Yu visited Queens University in this summer, working with N. Yui. W.-F. Wei will spend 6 months visiting McGill University in Montreal, working with Henri Darmon. China: In December 2010, several members from our focus group attended ICCM 2010 held in Beijing as invited speakers. W.-C. Li and J. Yu were invited plenary speakers for this conference. She was also an invited speaker in “Number theory and related topics – conference in honor of Prof. Keqin Feng’s 70th birthday”, Hefei and Huangshan. J. Wang was an invited speaker in the joint meeting of the American Mathematical Society and the Shanghai Mathematical Society, held in December 2010. C.-F. Yu visited Tsing-Hua University in Peijing for two weeks in this April/May. He gave a series of 4 lectures on abelian varieties.France: In late June 2011, L.C Hsia visited Jean-Yves Briend at CMI, University of Provence to work on their project on p-adic dynamics and gave a colloquium talk. C.-F. Yu will visit Institut de Mathematiques de Jussieu, Unviersite Paris 7 for three weeks in this November/December.Germany: In January 2011, A. Schweizer visited Professor Ernst-Ulrich Gekeler of the University of Saarbrucken and gave a colloquium talk and a number theory seminar talk. He also visited Professor M. Schutt at the Leibniz University, Hannover, and gave a talk in the algebraic geometry seminar. C.-F. Yu visited Universitaet Duisburg-Essen in this

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summer for maintaining the cooperation with Ulrich Gortz. J.-D. Yu will spend one academic year 2011-12 visiting Universitaet Duisburg-Essen, working with Helene Esnault. M.-L. Hsieh was invited to give a lecture in Algebraische Zahlentheorie, Oberwolfach, this June. He will also give an invited lecture in the conference Iwasawa 2012 in Heidelberg in 2012 August.Japan: In December 2010, Y. Yang was invited to give a talk in the conference Algebraic number theory and related topics held at RIMS, Kyoto. C.-F. Yu was invited to give a lecture in the Conference of Algebraic and Arithmetic Geometry held in University of Tokyo this January. M.-L. Hsieh was invited to give a lecture in Mini-workshop on Iwasawa Theory, held in Kyoto University, this April. In July, 2011, Y. Yang visited Ki-Ichiro Hashimoto at Waseda University. He and M.-L. Hsieh are invited to a conference in Okinawa in the coming October. In addition, he will visit the Tohoku University in November. Fang-Ting Tu is visiting the Waseda University for one year under the auspice of NSC.Korea: In April, A. Schweizer was invited by Professor Daeyeol Jeon to visit the Korean Institute for Advanced Study and gave a number theory seminar talk there. In July 2011, W.-C. Li co-organized (with YoungJu Choie, Postech) the PMI, Korea-NCTS, Taiwan workshop on number theory. A group of eight number theorists from Taiwan visited Postech and gave talks in the workshop. They were Y.-H. Chen, H.-J. Chen, C.-A. Chen, M.-L. Hsieh, M.-G. Leu, W.-C. Li, F.-T. Tu, and Y. Yang. In August 2011, A. Schweizer was invited to speak at the International Conference on the Arithmetic of Function Fields and Related Topics, held at Dongguk University, Gyeongju.USA: Jih-Jeng Yu attended the conference on Galois representations held in Princeton in this spring. In September 2011, L.-C. Hsia visited Professor Lucien Szpiro at Graduate Center of CUNY for two weeks. He gave one talk at their collaborative number theory seminar and two talks at their impromptu seminar. In October 2010, W.-C. Li gave an invited lecture at the Elliptic Curves and Crypto Workshop 2010, Microsoft Research. In April 2011, she co-organized (with Ramin Takloo-Bighash, University of Illinois at Chicago) the Atkin Memorial Lecture and Workshop on Galois representations, and delivered

the 2011 Atkin Memorial Lecture. She also delivered Distinguished Women Lecture at the University of Texas at Austin, Number theory seminar at the University of Wisconson, Madison, and the Colloquium at the Ohio State University. In October 2011 she will be the keynote speaker at the Rocky Mountain Discrete Math Days, Laramie, Wyoming, in November she will speak in Algebra seminar at U. Pennsylvania, and in December she will give an invited talk at the Palmetto Number Theory Series, Clemson, South Carolina.United Kingdom: In March 2011, J. Wang was invited to speak in the conference Frontier of the Nevanlinna Theory, held at the University College, London in March 2011. In June, C.-Y. Chang was invited to speak in the Workshop on the arithmetic of function fields. In September 2011, A. Schweizer visited Professor A. Mason at the Glasgow University, preparing their 7th joint paper.

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Coordinators: Jong-Shenq Guo (Tamkang University), Tai-Chia Lin (National Taiwan University), Jenn-Nan Wang (National Taiwan University), Jann-Long Chern (National

Central University), Yung-Fu Fang (National Cheng Kung University)

D.7 Partial Differential Equations

1. Research Goals and Contents

he topics investigated focus on the following problems.

I. Nonlinear Schrödinger equations • Blowup solutions and stability of bound states

of NLSE. • Bilinear estimatesII. Poisson-Boltzmann equations with nonlocal

nonlinearity and ion channels III. Biological systems and quasilinear parabolic

equations • Wave segment, wave spot and rotation wave in

two dimensions • Predator-prey system; travelling waves for 3

species competition system • Formation of singularitiesIV. Nonlinear elliptic problems: • Existence, uniqueness, bifurcations and

stability of positive solutions for nonlinear Schrodinger system, cooperative system, and Liouville-type system.

• Cafarelli-Kohn-Nirenberg inequality • Chern-Simons-Higgs Model • Spectral analysis on graphs and p-Laplacian

operatorsV. Inverse problems • Derivation of asymptotic behaviors of

solutions to the Navier-Stokes equations • Quantitative uniqueness estimates for the

shallow shell equations • Size estimate for the shallow shell equations • Reconstruction of inclusion in the Helmholtz

equation by boundary measurements

The motivations and goals of some of the study are highlighted with more details.

Nonlinear Schrödinger equations(1) Blowup solutions of nonlinear Schrödinger

equations (NLSEs) may describe nonlinear wave collapse, which is universal to many areas of physics including nonlinear optics, plasma physics, and Bose-Einstein condensates (BECs). The spatial profile of a collapsing wave may evolve into a universal, self-similar, circularly symmetric shape with a single peak known as the Townes profile, which has been observed experimentally by amplified laser beams. Theoretically, one may find the Townes profile by investigating self-similar solutions of self- focusing cubic NLSEs. In high-power laser beams, different collapsing behaviors may develop blowup ring profiles which break into filaments with multi-Townes profiles under the effect of noise. It would be naive to think that ring profiles can be obtained by finding the blowup solutions of NLSEs. However, until now, there exist only solutions with infinite L2 norm which may not maintain the ring profile all the way up to the singularity. Recently, H1 vortex blowup solutions with ring profiles have been found. However, so far, it is still an open issue whether there exist H1 non-vortex blowup solutions with ring profiles. Here we want to solve the open problem theoretically.

(2) Recently, optical lattices have created many interest ing phenomena in Bose–Einstein condensates (BECs) and attracted a great deal of attention. Two types of optical lattices are considered: a linear optical lattice (OL) and a nonlinear OL. A linear OL is a series of potential wells having a periodic (in space) intensity pattern which may confine atoms of BECs in the potential minima. A nonlinear OL can be obtained by inducing a periodic spatial variation of the atomic scattering length,

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leading to a periodic space modulation of the nonlinear coefficient in the Gross–Pitaevskii equation (GPE) governing the dynamics of BECs. The GPE is a nonlinear Schrödinger (NLS) equation in the presence of the Kerr nonlinearity describing a BEC in a linear and a nonlinear OL.

The underlying dynamics of GPE is dominated by the interplay between adjacent potential wells of linear OLs and nonlinearity of nonlinear OLs. When the nonlinearity is self-focusing, a balance between these two effects may resist collapse or decay and result in bright solitons. Experimentally, bright solitons can be observed in linear and nonlinear OLs, respectively. One may find stable bright solitons in three-dimensional linear OLs. On the other hand, two-dimensional bright solitons can also be investigated in two-dimensional nonlinear OLs. Consequently, under the influence of linear and nonlinear OLs, two-dimensional bright solitons must have suitable stability for experimental observations. However, most theoretical results focus on the orbital (dynamical) stability of only one-dimensional single-spike bound states which are steady state bright solitons in one-dimensional nonlinear OLs without the effect of linear OLs. To see how linear and nonlinear OLs affect the stability of two-dimensional single-spike bound states, we want to develop mathematical theorems for the orbital stability and instability of two-dimensional single-spike bound states of GPE under different conditions of linear and nonlinear OLs.

Poisson-Boltzmann equations with nonlocal nonlinearity The Poisson–Boltzman n (PB) equat ion is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. Here we study a new Poisson–Boltzmann type (PB n) equation with a small dielectric parameter and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin type boundary conditions with various coefficient scales, we want to demonstrate the asymptotic behaviors of one-dimensional solutions of PB n equations as the parameter approaches zero.

Biological systems and parabolic equations (1) Pattern formation and travelling waves We study the existence and uniqueness of

stabilized propagating wave segments in wave front interaction model which is established by Zykov and Showalter. Also we are interested in the problem whether for this model whether rotating spots in a disk exist.

We also study the n-species competition-diffusion system of Lotka-Volterra-Gause type, which is very important in mathematical ecology. When n=2, the system is a monotone f low. There has been a lot of study on the existence, uniqueness, stability of the traveling waves. We focus on travelling wave solutions of the system when n=3. For this case, the system is no longer a monotone flow. There are few methods which can be applied and only limited results about it are known.

(2) Formation of singularity: We are interested in the study of non-self-similar singularities of quasilinear equations. For the locations of singularity, we investigate whether a zero of the potential can be a blow-up point if the solution blows up in finite time.

Nonlinear elliptic equations (1) Minimizers of Caffarelli- Kohn-Nirenberg

Problem and C-K-N inequality with singularities on the boundary of the domain.

(2) Chern-Simons-Higgs model and Louville type equation

(3) Poperties of nodal solution for elliptic equations and Sturm-Liouville equations

(4) Multiple positive solutions for semilinear elliptic equations

Inverse ProblemsUsing Carleman estimate techniques, we studied

the asymptotic behaviors of any nontrivial solution to the stationary Navier-Stokes equations. The main result is an estimate of decaying rate at infinity for any nontrivial solution. From this result, we can deduce some uniqueness property of the stationary Navier-Stokes equation in terms of their decaying behavior at infinity. On the other hand, we have successfully derived some quantitative uniqueness

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estimates for the shallow shell equations. By these estimates, we studied the size estimate under the fatness assumption.

For the reconstruction problem of an inclusion by boundary measurements, we aim to develop an enclosure type method in which the complex geometrical optics solutions play a decisive role. Since the equation we considered in this project is not positive, we need to work harder to obtain needed estimates.

Other TopicsAsymptotic behaviors of solutions to the Navier-

Stokes equations; size estimate for the shallow shell equations; spectral analysis on graphs and p-Laplacian operators; spiral wave of lambda-omega system; bilinear estimates for Schrödinger equations.

2. Visitor

Sergei Pilyugin (St. Peterburg State U)Huseyin Kocak (U of Miami)Shui-Nee Chow (School of Mathematics George Institute of Technology)Peter Kloeden (Goethe Universitaet) Tzyy-Leng Horng (Feng Chia U)Takayoshi Ogawa (Tohoku U)Ching-Long Lin (U of Iowa)

Bogdan Kazmierczak (Polish Academy of Science)Jhih-Fei Jhang (Peking U)Yong Liou (Peking U)Bin Liu (Peking U)Hsin-Yuan Huang (U of Minnesota)Zhi-An Wang (Hong Kong Polytechnic U)Neil Trudinger (Australian National U)Eiji Yanagida (Tokyo Institute of Technology)Fang-Hua Lin (New York U)Nassif Ghoussoub (U of British Columbia)Gabriella Tarantello (U di Roma "Tor Vergata")Shih-Hsien Yu (National U of Singapore)Tsorng-Whay Pan (U of Houston) Kenji Nakanishi (Kyoto U) Nobu Kishimoto (Kyoto U) Hideo Kozono (Tohoku U)Sanghyuk Lee (Seoul National U)Tohru Ozawa (Waseda U)Hideo Takaoka (Hokkaido U)Kotaro Tsugawa (Nagoya U)Hideo Ikeda (Toyama U)Yuusuke Iso (Kyoto U)Masayasu Mimura (Meiji U)Hirokazu Ninomiya (Meiji U)Tsorng-Whay Pan (U of Houston)

3. Conference and WorkshopDate Venue Title Participant Country

2011/01/07 National Taiwan University

Conference in Dynamical Systems: A Celebration in honor of Kenneth James Palmer on his Retirement

Taiwan, USA, Germany, Russia

2011/01/14-17 National Cheng Kung University

19th Workshop on Differential Equations and Its Applications

Germany, Japan, Korea, Taiwan, Hong Kong

2011/02/25-27 Meiji University, Japan

The 2nd Japan-Taiwan Joint Workshop for Graduate Students in Applied Mathematics Taiwan, Japan,

2011/03/17 Tamkang University Mini-Workshop on Applied Analysis Taiwan

2011/07/08-09 National Taiwan University

A Conference in Honor of the 60th Birthday of Chang-Shou Lin

Taiwan, USA, Japan, Italy, Canada, Australia, China

2011/12/17-18 National Tsing Hua University

2011 NCTS Interdisciplinary Workshop between Mathematics and Theoretical Physics: Cold Atom System and Its Mathematical Models

Taiwan, USA

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4. Important Results, Breakthrough

1. For the blowup solutions of NLSEs, we prove simultaneous blow-up solutions with ring profiles of two-component systems of NLSEs. As for the idea of self-similar solutions, we use pseudo-conformal invariance to transform the system into a system of nonlinear elliptic equations, and then we generalize the variational method developed by the Ambrosetti’s group only for single NLSEs to construct ring profile solutions of two-component systems of NLSEs.

2. For the stability problem of bound state solutions of GPE, we get the higher order expansion on the energy functional with respect to standing wave solutions, and study the spectrum of l inear ized operator to prove the theorems rigorously. Currently, most theoretical results focus on the orbital (dynamical) stability of only one-dimensional single-spike bound states which are steady state bright solitons in one-dimensional nonlinear optical lattices without the effect of linear optical lattices. Here we develop mathematical theorems for the orbital stability and instability of two-dimensional single-spike bound states of GPE under different conditions of linear and nonlinear optical lattices. Our results are most general on the orbital stability problem.

Blowup ring profiles have been investigated by f inding non-vor tex blowup solutions of nonlinear Schrödinger equations (NLSEs) (cf. Fibich, Gavish, and Wang, Physica D 211, 193-220 (2005) and Physica D 231, 55-86 (2007)). However, those solutions have infinite L2 norm, so one may not maintain the ring profile all the way up to the singularity. To find H1 non-vortex blowup solutions with ring profiles, we study the blowup solutions of two component systems of NLSEs with nonlinear coefficients under suitable conditions. The two-component system can be transformed into a multi-scale system with fast and slow variables which may produce H1 blowup solutions with non-vortex ring profiles. We use the localized energy method with symmetry reduction to construct these solutions rigorously. On the other hand, these solutions may describe steady non-vortex bright ring solitons. Various types of ring profiles including m-ring and ring-ring profiles are presented by numerical solutions.

About stability of bound states of NLSEs, most theoretical results (e.g. G. Fibich, Y. Sivan, M.I. Weinstein, Phys. D 217 (2006) 31–57 and Phys. Rev. Lett. 97 (2006) 193902) focus on the orbital (dynamical) stability of only one-dimensional single-spike bound states which are steady state bright solitons in one-dimensional nonlinear OLs without the effect of linear OLs. Instead of one-dimensional problem, our recent results are for two spatial dimensions. To see how linear and nonlinear OLs affect the stability of two-dimensional single-spike bound states, we develop mathematical theorems for the orbital stability and instability of two-dimensional single-spike bound states of NLSEs under different conditions of linear and nonlinear OLs.

3. We show that in case of electroneutrality, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as nonelectroneutrality occurs, solutions of 1D PB n equations may have blow-up behavior which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations. These results have been published in Nonlinearity 24 (2011) 431–458.

For the problem of PB equations in higher dimensions, we find a way to estimate solutions w it h bou nd a r y laye r s w it hout u si ng t he conventional method which uses the asymptotic expansions of solutions to get various order terms of the small parameter. The main idea is to derive the generalized differential inequality and also use the Pohozaev identity and the inverse Holder inequality to develop our theorems.

The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe electrostatic interactions between molecules in ionic solutions (electrolytes) and have many applications in the fields of chemical physics and biophysics. Conventionally, the PB equation for electrolytes with two species densities is the combination of the Poisson equation and the Boltzmann distribution which has been studied extensively by many people. Here we study a new Poisson–Boltzmann type (PB n) equation with a small dielectric parameter and non-local nonlinearity which takes into consideration the

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preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviors of one-dimensional solutions of PB n equations as the parameter approaches zero.

4. J.-S. Guo and M. Shimojo, Blowing up at zero points of potential for an initial boundary value problem, Communications on Pure and Applied Analysis 10 (2011), 161-177.

We study nonnegative radially symmetric solutions for a semilinear heat equation in a ball with spatially dependent coefficient which vanishes at the origin. Our aim is to construct a solution that blows up at the origin where there is no reaction. For this, we first prove that the blow-up is complete, if the origin is not a blow-up point and if there is no blow-up point on the boundary. Then we prove that a threshold solution exists such that it blows up in finite time incompletely and there is no blow-up point on the boundary. On the other hand, we prove that any zero of nonnegative potential is not a blow-up point for a more general problem under the assumption that the solution is monotone in time.

5. X. Chen, J.-S. Guo and B. Hu, Dead-core rates for the porous medium equation with a strong absorption, Discrete and Continuous Dynamical Systems - Series B (to appear).

We study the dead-core rate for the solution of the porous medium equation with a strong absorption. It is known that solutions with certain class of initial data develop a dead-core in finite time. We prove that, unlike the cases of semilinear heat equation and fast diffusion equation, there are solutions with the self-similar dead-core rate. This result is based on the construction of a Lyapunov functional, some a priori estimates, and a delicate analysis of theassociated re-scaled ordinary differential equation.

6. J.-S. Guo, H. Ninomiya, and C.-C. Wu, Existence of rotation wave pattern in a disk for wave front interaction model, preprint.

We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant

angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front and wave back respectively. Using a delicate shooting argument with the help of comparison principle, we derive the existence and uniqueness of rotating wave patterns for any admissible angular speed with convex front in a given disk.

7. C.-C. Chen1, L.-C. Hung, M. Mimura, and D. Ueyama, Exact travelling wave solutions of three-species competition-diffusion systems, Discrete and Continuous Dynamical Systems - Series B (to appear).

We construct exact non-monotone traveling waves of three-species competition-diffusion systems for some parameter region and use AUTO to track more travelling waves bifurcates from these exact solutions. These waves indicate the competition mediated coexistence can happen for three species system and have a lot of importance biological meaning.

Further numerical study suggests the existence of two types of waves: the fast and slow travelling waves and indicates that if the species (u; v) initially behave like a trivial traveling wave, and the exotic species w is introduced into an overlapping zone of (u; v), then the resulting solution can evolve into the stable fast wave for a large initial data of w, while the resulting solution will tend to the trivial traveling wave for a small initial data of w.

For the Liouville-type system, cooperative system, Schrodinger-type system, Bennett-type System and Hamiltonian-type, etc. we have studied the degenerate and non-degenerate property for the respective linearized systems, bifurcations and variational structures of the solutions the uniqueness, existence and stability properties. The results are listed as follows.

8. Jann-Long Chern, Z.-Y. Chen and Y.-L. Tang, On the Solutions to a Liouville-type System Involving Singularity, To appear in Calculus of Variations and Partial Differential Equation, 2011. (30 Pages)

9. Jann-Long Chern*, Z.-Y. Chen and Y.-L. Tang,

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Uniqueness of Finite Total Curvature and Structure of Radial Solutions for Nonlinear Elliptic Equations, Transactions of the American Mathematical Society, 363 (2011), 3211–3231. (21 Pages)

10. Jann-Long Chern, J. Shi and Y.-L. Tang, Existence, uniqueness and stability of positive solution to sublinear elliptic systems, Proc. Royal Society of Edinburgh, 141A, 45-64, 2011. (20 Pages)

11. Jann-Long Chern* and S.-G. Yang, The Non-topological Fluxes of a Two-particle System in the Chern-Simons Theory, Submitted, 2011.

12. Jann-Long Chern*, Z.-Y. Chen and S.-G. Yang, A Classification of Semilocal Vortices in a Chern-Simons theorey, Submitted, 2011.

13. Jann-Long Chern, Z.-Y. Chen and Y.-L. Tang, Singular Bennett-type System in Modeling One-particle Distribution of Dissipative Stationary Plasmas, Submitted , 2011.

14. Jann-Long Chern, C.-S. Lin and E. Yanagida, Singular Entire Solutions to A Critical Elliptic Equation Without Monotonicity, Preprint 2011.

15. Jann-Long Chern and J. Shi, Uniqueness of solution to a coupled cooperative system, Preprint 2011.

16. Jann-Long Chern and C. S. Lin, The Uniqueness and Degeneracy of Solutions to a Hamiltonian-type Elliptic System, Preprint 2011.Previously, we have proved the strong unique

continuation property for the Lame system with Lipschitz coefficients. Recently, we extended this result to the case where one coefficient is Lipschitz and the other one is only essentially bounded [17]. Using Carleman estimate, we were able to derive an asymptotic behavior of nontrivial solution to the stationary Navier-Stokes equations. This is so-far the first result of this kind for the Navier-Stokes equations [18]. In [19], we developed an enclosure type method for the Helmholtz equation. This system is no longer positive. The usual technique involving the Sobolev embedding technique is not going to work. Here to obtain the desired estimates, we use estimates from Li and Vogelius paper where they considered second order elliptic equations with discontinuous coefficients. 17. Ching-Lung Lin, Gen Nakamura, Gunther

Uhlmann, and J.N. Wang, Quantitative strong unique continuation for the Lame system with less regular coefficients, Methods Appl. Anal., Vol. 18 (2011), 85-92.

18. Ching-Lung Lin, Gunther Uhlmann, and J.N. Wang, Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain, to appear in Indiana Univ. Math. J.

19. Sei Nagayasu, Gunther Uhlmann, and J.N. Wang, Reconstruction of penetrable obstacles in acoustic scattering, SIAM J. Math. Anal., Vol 43 (2011), 189-211. We use Carleman estimates to derive certain

asymptotic behaviors of solutions to some systems of equations. Especially, we have derived asymptotic behaviors of solutions to the Navier-Stokes equations. This result indicates that if the solution decays too fast at the infinity, then this solution must be trivial. Our result on the Navier-Stokes equation is the first result of this kind in this subject. On the other hand, we extended the strong unique continuation property result to the Lame system with one of coefficients is only essentially bounded. This result is by far the best result in this field.

5. Related Results in the Past Years

1. For multiple Townes profiles, some theorems had been developed (see Physica D 220 (2006), no. 2, 99—115) under different conditions of coefficients of nonlinear Schrodinger systems. However, these results are nothing to do with the blow-up ring profile (see Physica D 239 (2010) 613—626) which is one of our main works in last year.

2. Without the effect of linear and nonlinear optical lattices, orbital stability of bound states of semi-classical nonlinear Schrödinger equations with critical nonlinearity has been investigated and published in SIAM J. Math. Anal. 40 (1) (2008) 365–381.

3. J.-S. Guo, C.-T. Ling and P. Souplet, Non-self-similar dead-core rate for the fast diffusion equation with strong absorption, Nonlinearity 23 (2010/03), 657-673

4. J.-S. Guo, H. Ninomiya, and J.-C. Tsai, Existence and Uniqueness of stabilized propagating wave segments in wave front interaction model, Physica D: Nonlinear Phenomena 239 (2010/02), 230-239.

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6. Research Topics in 2012

Wave patterns and singularities in biological systems and reaction-diffusion equations1. Travelling waves for three species competition-

diffusion equationsWe will use two approaches to investigate the

3-species system: (1) finding more exact travelling wave solutions; (2) the method of bifurcation of heteroclinic orbits in dynamical systems.(1) exact solutions:

For the 2-speciessystem, Rodrigo and Mimura developed some methods to find exact travelling wave (TW) solutions for special region of the parameters. From their result, one can derive important information such as the profiles and wave speeds of the TW. However due to the highly complexity, their method cannot apply to 3-species system. Recently, in a joint work with LC Hung, Mimura and Ueyama, with the help of Mathematica, exact solutions of non-monotone 3-species were constructed in terms of hyperbolic tan for special parameters. Using AUTO, we showed that a continuum of 3-species waves bifurcates from the exact solutions we found. We believe that there are more exact solutions and will investigate the problems:(a) Are there exact TW which can be expressed

by functions other than tanh?(b) How big can the exponents of tanh be in the

exact solutions?(c) Stability of exact solutions.(d) 2-hump exact TW.

(2) bifurcation methods: To find TW, the 2nd order 3-species u-v-w system can be transform into a system of 6 first order ODE equations. We propose the following approach. Suppose for some value of the parameters, there are both v-w TW connecting steady states O1 and O2 and w-u TW connecting O2 and O3. Then it is nature to consider the problem: after a small perturbation of the parameters, does there exist a TW connecting O1 and O3. Such a wave will be a v-w-u wave with the profile in which w is pulse-like lying between u and v.

2. Sign of wave speedThe sign of travelling wave speed provides a

lot of information about which species can survive more successfully and whether more complicated dynamics can emerge from well-prepared initial data. We shall investigate the sign of the speed of the 2-species bistable competition system in more detail.

3. Singularity formationWe continue to study the non-self-similar

singularity arising in the predator-prey systems. We expect to obtain for some extend the quenching behavior of some biological systems. Also, we are interested in the singularity formation for the complex-valued scalar parabolic equations.

4. Spiral patternsWe shall study the existence of spiral patterns

in the plane via the interfacial approach.

Elliptic systemsThe problems considered will include the Liouville

system, cooperative systems, Bennett-type systems and Hamiltonian-type systems.

Nonlinear Schrodinger equationsThe topics will cover the stability and blow-up

behavior of solutions.

Poisson-Boltzmann equations with nonlocal nonlinearity

We will consider the equat ions in higher dimension domains and their behavior of boundary layers. Also more complicated models will be derived to describe the phenomena in ion channels.

Inverse ProblemsWe continue our study on the quantitative estimates

for elliptic type of partial differential equations. Previously, we have successfully derived quantitative estimates for second and higher order elliptic equations. Those estimates are extremely useful in other problems such as inverse problems. Now we hope to study this problem when the coefficients are not continuous. This is an interesting direction in which many basic problems are yet to be answered.

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7. Publication

2010[1] X. Chen, T. C. Lin and J. Wei, Blowup and

solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems, Physica D 239 (2010) 613—626.

[2] T. C. Lin, J. Wei and W. Yao, Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices, JDE 249 (2010) 2111–2146.

[3] J.-S. Guo, C.-T. Ling and P. Souplet, Non-self-similar dead-core rate for the fast diffusion equation with strong absorption, Nonlinearity 23 (2010/03), 657-673

[4] J.-S. Guo, H. Ninomiya, and J.-C. Tsai, Existence and Uniqueness of stabilized propagating wave segments in wave front interaction model, Physica D: Nonlinear Phenomena 239 (2010/02), 230-239.

[5] Chen, C.-C. and Lin, C.-S., Mean field equations of Liouville type with singular data: sharper estimate, Discrete and Continuous Dynamical Systems Vol 28, No 3 (2010), 1237-1272

[6] Ching-Lung Lin, Gunther Uhlmann, and Jenn-Nan Wang, Optimal Three-Ball Inequalities and Quantitative Uniqueness For The Stokes System, Discrete and Continuous Dynamical Systems, Vol. 28, No 3, November 2010, 1~XX

2011[1] Jong-Shenq Guo and Masahiko Shimojo, Blowing

up at zero points of potential for an initial boundary value problem, Communications on

Pure and Applied Analysis 11 (2011), 161-177.[2] C.-C. Chen1, L.-C. Hung, M. Mimura, and D.

Ueyama, Exact travelling wave solutions of three-species competition-diffusion systems, Discrete and Continuous Dynamical Systems - Series B (to appear in 2011).

[3] Ching-Lung Lin*, Gen Nakamura,Gunther U h l m a n n a n d J e n n - Na n Wa n g (2 011) , Quantitative strong unique continuation for the Lame system with less regular coefficients, Methods and Applications of Analysis., 18, no 1, 85-92.

[4] Sei Nagayasu, Gunther Uhlmann, and J.N. Wang, Reconstruction of penetrable obstacles in acoustic scattering, SIAM J. Math. Anal., Vol 43 (2011), 189-211.

[5] X. Chen, Y.H. Cheng and C.K. Law (2011) Reconstructing potentials from zeros of one eigenfunction, Trans. Amer. Math. Soc.,363, 4831-4851. (SCI)

[6] C.Z. Chen, C.K. Law, W.C. Lian and W.C. Wang (2011) Optimal upper bounds for the eigenvalue ratios of one-dimensional p-Laplacian, Proc. Amer. Math. Soc., to appear. (SCI)

[7] Yung-fu Fang, On a Bilinear Est imate of Schrödinger Waves, RIMS Kôkyûroku Bessatsu B26: Harmonic Analysis and Nonlinear PDE, May, 2011 p1-14.

[8] Xinfu Chen, Jong-Shenq Guo and Bei Hu, Dead-core rates for the porous medium equation with a strong absorption, Discrete and Continuous Dynamical Systems - Series B (to appear).

Other publications of PDE group

NO Journal 2010 2011 Else1 Archive for Rational Mechanics and Analysis 12 Communications in Mathematical Physics 13 Communications in Partial Differential Equations 24 Journal of Differential Equations 25 Calculus of Variations and Partial Differential Equations 16 Proceeding Royal Society of Edinburgh, Section A 17 Transactions of the American Mathematical Society 18 Nonlinearity 19 Physica D 210 Communications on Pure And Applied Analysis 111 Nonlinear Analysis: Real World Applications 1

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Coordinators: Shuenn-Jyi Sheu(NCU),Yuan-Chung Sheu (NCTU) and Narn-Rueih Shieh (NTU)

D.8 Probability Theory & Related Topics

A. Research Goals and Contents

(a) Markov Chains and Mixing Times

he yearly project on finite Markov chains is to characterize the Lp-mixing time for

cutoff phenomenon. Currently, the only systematic method on bounding the Lp-mixing time was introduced by Diaconis and Saloff-Coste in 1996. They provided a discrete verdsion of the logarithmic Sobolev inequality and created an upper and lower bounds on the Lp-mixing time using the logarithmic Sobolev constant. But, however, the orders of bounds are different. To make an improvement on their work, a further study on the hypercontractivity of log-Sobolev inequality is required. This can be very tough and, instead, we consider nontrivial typical models and determine explicitly their Lp-mixing times. The first case to treat is the Ehrenfest chain, a standard model introduced by physician Paul Ehrenfest to explain the second law of thermodynamics. For Ehrenfest chains, we obtained a simple criterion on the Lp-cutoff and determine the exact mixing time. The results have been collected in an article and submitted for publication.

In the summer of 2011, Guan-Yu Chen taught a short course on the mixing of Markov chains. The course introduced the cutoff phenomenon of Markov chains, one of the recently focused topics in probability in the world, and displayed a list of results at the frontier. The course was set to be research oriented and open problems of interests are announced. (b) Stochastic Portfolio Theory

Stochastic calculus is a very powerful tool in mathematical finance. It\ {̂o}'s formula was applied to the pricing of options by Black-Scholes and Merton. The martingale representation theorem was used for the hedging problem of derivatives and Girsanov's

theorem was applied for constructing a risk neutral measure. As does much of mathematical finance, stochastic portfolio theory descents from the classical portfolio theory of Harry Markowitz (1952). It began with the papers of Fernholz(1999,2001) and was introduced in the monograph Fernholz(2002). Since then stochastic portfolio theory has evolved into a novel mathematical framework for analyzing portfolio behavior and equity market structure. Besides its possible applications to real equity markets, the study of stochastic portfolio theory raises many interesting and challenging open problems for theory of stochastic processes. On the fall semester of 2010, we had a NCTS-NCTU joint course on this interesting and challenging topic. Yuan-Chung Sheu and his master degree student, Guo-Jhen Wu, proved the existence of short-term relative arbitrage in generalized volatility-stabilized markets, which generalizes the earlier result of A.D.Banner and D.Fernholz. We will continue to work in this area and we plan to invite some experts from abroad to visit NCTS, and vice versa.(c) Bioinformatics and Image Analysis

The applications in bioinformatics and image analysis emphasize the analysis of biological and image data. For studies in bioinformatics, we investigate the network structure for biological pathways. For studies in image analysis, we investigate different types of images. For example, we study a variety of biological and medical images, including positron emission tomography (PET), Magnetic resonance imaging (MRI), ultrasound imaging, neuroimaging and so forth.(d) The Probability Program at Taipei

The Probability Program of NCTS at Taipei focuses on the interplay between analysis, probability, and their applications.

B. Important Research Results and

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Achievements

(a) Stochastic ControlWe consider a finite time optimal consumption

problem where an investor wants to maximize the expected HARA utility of consumption and terminal wealth. We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case that the investor can not observe the factor process and use only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. As a result, we derive the HJB equation. The equation can be solved to obtain an explicit form of the value function and the optimal strategy for this problem. (For details, see “An optimal consumption and investment problem with partial information”, by Hiroaki Hata and Shuenn-Jyi Sheu)(b) Markov Chains and Mixing Times

We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity. This was collected in the following article.

Guan-Yu Chen, Yang-Jen Fang and Yuan-Chung Sheu, The cutoff phenomenon for Ehrenfest chains, submitted, 2011.(c) Free Boundary Problems and Perpetual

American StranglesAn American option is an option that can be

exercised at any timeprior to its expiration time. For an American call option with a finite expiration time, Merton (1973) observed that the price of the American option (written on an underlying stock without dividends) coincides with the price of the corresponding European option. However

the American put option (even without dividends) presents a difficult problem. We have no explicit pricing formulas and the optimal exercise boundaries are not known. One exception is the perpetual American put option, i.e., an American put with infinite expiration time. Within the Black-Scholes model, the perpetual American put problem was solved by Mckean(1965). In the L\'evy-based models, by probabilistic techniques, Mordecki and Salminen (2002) obtained explicit formulas under the assumption of mixed-exponentially distributed and arbitrary negative jumps for the call options, and negative mixed-exponentially distributed and arbitrary positive jumps for put options. We study the pricing problem for the perpetual American strangles (which is a combination of a put and a call written on the same security) in the geometric jump-diffusion models. We assume further that the jump distribution is a two-sided mixture of exponential distributions. By solving a free boundary problem with smooth pasting principle, we determine the rational price of the perpetual American strangle options. In addition, we also work out an algorithm for computing the optimal exercise boundaries and the rational price of the option. The above work is reported in the preprint: Free Boundary problems and Perpetual American Strangles, by Ming-Chiu Chang and Yuan-Chung Sheu(d) Bioinformatics and Image Analysis

Networks are widely used in biology to represent the relationships between genes and gene functions. In Boolean biological models, it is mainly assumed that there are two states to represent a gene: on-state and off-state. It is typically assumed that the relationship between two genes can be characterized by two kinds of pairwise relationships: similarity and prerequisite. Many approaches have been proposed in the literature to reconstruct biological relationships. In this article, we propose a two-step method to reconstruct the biological pathway when the binary array data have measurement error. For a pair of genes in a sample, the first step of this approach is to assign counting numbers for every relationship and select the relationship with counting number greater than a threshold. The second step is to calculate the asymptotic p-values for hypotheses of possible relationships and select relationships with a large p-value. This new method has the advantages

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of easy calculation for the counting numbers and simple closed forms for the p-value. The simulation study and real data example show that the two-step counting method can accurately reconstruct the biological pathway and outperform the existing methods. Compared with the other existing methods, this two-step method can provide a more accurate and efficient alternative approach for reconstructing the biological network.

( Wa ng , H . , Lu , H . H .- S . , C hueh , T.-H . Constructing Biological Pathways by a Two-Step Counting Approach. PLoS ONE 6(6): e20074, 2011)

C. Seminars/Courses/Workshops/Visitors

(a) Short Courses/Special LecturesSpeaker: Prof. Wing Hung Wong 王永雄院士 (Stanford University)Time: AM 10:30-12:00, Wed., June 22, 2011Topic: Nonparametric Bayesian Inference by Optional

Pólya TreeAbstract:

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions that are also optional Pólya trees with computable parameter values.

Speaker: Professor Zhen-Qing Chen(University of Washingtopn)T i m e : P M 2 : 0 0 ~ 3: 3 0 , A u g u s t 11 , 2 011 , AM10:30~12:00, PM2:00~3:30, August 12, 2011Topic: Potential Theory for L\’evy-like ProcessesAbstract:

Studying discontinuous Markov processes are of current research interest, due to their importance both in theory and in applications. Many physical and economic systems should be and in fact have been successfully modeled by non-Gaussian

jump processes. The infinitesimal generator of a discontinuous Markov process in $\R^n$ is no longer a differential operator but rather a non-local (or, integro- differential) operator. For instance, the infinitesimal generator of an isotropically symmetric $\alpha$-stable process in $\R^n$ with $\alpha \in (0, 2)$ is a fractional Laplacian operator $c\, \Delta^{\alpha /2}:=- c\, (-\Delta) {̂\alpha /2}$. During the past several years there are also many interests from the theory of PDE (such as singular obstacle problems) to study non-local operators. In a series of three talks, I will cover some basic theory on multi-dimensional L\'evy processes and their Markovian (non-L\'vey) counterparts as well as some recent advances on the potential theory of these processes(b) Summer Course in ProbabilityLecturer: Prof. Guan-Yu Chen 陳冠宇 (NCTU)Dates: AM 9:30-12:00pm, Tuesday, July 5, 12, 19, 26 ,

2011 From the perspective of Markov chain Monte

Carlo theory, a particular Markov chain is run for a very long time, say T, until its distribution is close enough to the stationarity. In practice, one is interested in the time T to stop the simulation and, then, choose the random sample.

The time T is closely related to the mixing time of Markov chains. In recent years, for models of statistical mechanics and of theoretical computer science, there has been a our ish ing of new mathematical ideas to rigorously control the time.

In this short course, we will quickly review fundamental results on Markov chains and then step into the topic of mixing time. As the convergence of Markov chains is considered on special purposes, we will introduce the total variation, separation, entropy and the Lp-distance. The lectures focus on the following four topics.

1.Total variation and coupling.2.Separation and strong stationary time.3. L2-mixing for reversible Markov chain.4. Lp-mixing and logarithmic Sobolev inequality.

(c) 學術活動(1) 於 2011.2.23 在中央研究院數學研究所舉辦

Probability One Day Workshop，由黃啟瑞、許順吉、許元春籌畫，由新竹理論中心、中央研究院數

學研究所、中央大學合辦，邀請的國內及日本機

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率學者演講，日本學者有 Hideo Nagai，Makoto Maejima，Yusuke Watanabe，國內學者有許元春，韓傳祥，陳冠宇，黃啟瑞，透過這個活動國內的

機率學者有機會與日本學者相互做學術交流。

(2) 在中央大學在每週星期三舉行定期的機率及其應用研討會，主要成員有數學系同仁趙一峰，

許玉生，于振華，饒瑞彬，統計所的同仁有傅承

德，鄧惠文，中央研究院數學研究所同仁有謝仲，

楊如琛及清華大學同仁韓傳祥，藉由這個活動大

家有機會聚會討論，我們也請其他學校的同仁來

演講，讓我們增加與其他學校的學術互動。這一

年我們共安排 12 次演講。未來這一年我們將繼

續進行這個活動，統計所同仁也將在星期三安排

coupla 相關議題的討論會。

(3) 於每周星期五舉行數報討論會，讓學生有機會學習機率論專題，我們有兩個課題，分別於隔

周舉行，一個課題為 Stochastic Calculus，一個課

題為 Stochastic Control in Insurance，前者為機率

論的一個重要而基礎的課程，後者為機率論的一

個應用課程，後者未來可以延續而變成一個研究

題材，這個書報討論會在中央研究院數學所聚會，

中央大學的同仁也利用視訊連線參加，成員有學

生：李旭唐，張凱君，林柏佐；助理：陳韋國，楊如琛；

博士後：須上苑，吳政訓；同仁：姜祖恕，趙一峰，

許玉生，傅承德，林顯仁。我們了解學生或同仁平

時各自忙於自己的工作，因此以較緩慢的進度來

進行，透過經常的接觸漸漸對這些課題有些了解，

若要深入還是須邀找機會應用這些知識。

(d) NCTS/TPE Activity in Analysis/Probability/Applications

Speaker: Professor Toshihiro Uemura(Kansai University, Japan)

Title: Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms (I), (II)

Time: May 04, 2011 at 10:20~12:10Abstract:

Let E be a locally compact separable metric space and m be a positive Radon measure on it. Given a non-negative function k defined on E\times E off the diagonal whose anti-symmetric part is assumed to be less singular than the symmetric part, we construct an associated regular lower bounded semi-Dirichlet form $\eta$ on L^2(E;m) producing a Hunt process X^0 on E whose jump behaviours are governed by k. For an arbitrary open subset D\subset E, we also construct a Hunt process X^{D,0} on D in an analogous manner. When D is relatively compact, we show that X^{D,0} is censored in the

sense that it admits no killing inside D and killed only when the path approaches to the boundary. When E is a d-dimensional Euclidean space and m is the Lebesgue measure, a typical example of X^0 is the stable-like process that will be also identified with the solution of a martingale problem up to an \eta-polar set of starting points. Approachability to the boundary \partial D in finite time of its censored process X {̂D,0} on a bounded open subset D will be examined in terms of the polarity of \partial D for the symmetric stable processes with indices that bound the variable exponent \alpha(x). This is a joint work work with Professor Masatoshi Fukushima.Speaker: Professor Muneya Matsui( Nanzan

University, Nagoya, Japan)Title: Prediction and extensions in the Poisson cluster

model given in Matsui and Mikosch (2010)Time: August 03, 2011 at 10:30 - 11:30Abstract:1. We give a brief introduction to the Poisson cluster

model given in Mikosch (2009) or Matsui and Mikosch (2010).

2. Relation of the model with the claims reserving problem in non-life insurance is described.

3. Several predictors of the Poisson cluster process which are obtained in Matsui and Mikosch (2010) are explained.

4. Some extensions of the model and their predictors are presented.

References :Matsui, M. and Mikosch, T. (2010). Prediction in a

Poisson cluster model. J. Appl. Prob. 47, 3 50-366.Mikosch , T. (2009). Non-Life Insu rance

Mathematics. An Introduction with the Poisson Process. 2nd Edition. Springer, Heidelberg..(e) Visitors

Wing Hung Wong 王永雄院士 (Stanford University)Zhen-Qing Chen(University of Washingtopn)Daniel Hernandez-Hernandez (CIMAT, Mexico),Hideo Nagai (Osaka University, Japan)Yasushi Ishikawa(Ehime University, Japan)Naoyuki Ichihara (Hiroshima University, Japan)Hidehiro Kaise (Nagoya University, Japan)Yusuke Watanabe (Osaka University, Japan)Wolfgang Härdle (Humboldt-Universiät zu Berlin, Germany)

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Ostap Okhrin (Humboldt-Universiät zu Berlin, Germany)Andrija Mihoci (Humboldt-Universiät zu Berlin, Germany)Muneya Matsui(Nanzan University, Nagoya, Japan)Toshihiro Uemura(Kansai University, Japan)

D. Accomplishments

2010[1] Guan-Yu Chen and Laurent Saloff-Coste, The L2-

cutoff for reversible Markov processes. J. Funct. Anal. 258 (2010), 2246-2315.

[2] Jang-Yi Lee, Kehluh Wang, Cheng-Few Lee and Yuan-Chung Sheu, A Generalized Model for Optimum Future Hedge, Handbbok of Quantitative Finance and Accounting, 873-852(2010), Lee,Cheng-Few, Lee, John(Eds.), Springer.

[3] Lu, 10. Lu, H. H.-S., and Wu, H. M., "Visualization, Screening, and Classification of Cell Cycle-Regulated Genes in Yeast" , International Journal of Systems and Synthetic Biology, 1(2), 185-198., 2010

[4] G. Molina, C.H. Han, and J.P. Fouque: MCMC Estimation of Multiscale Stochastic Volatility Models, Handbook of Quantitative Finance and Risk Management, Edited by C.F. Lee and A.C. Lee, Springer, 2010.

[5] C.H. Han and Y. Lai: A Smooth Estimator for MC/QMC Methods in Finance, Mathematics and Computers in Simulation, 81(2010), pp536-550.

[6] C.H. Han and Y. Lai: Generalized Control Variate Methods for Pricing Asian Options, Journal of Computational Finance, 14/2, Winter2010.

[7] G. Molina, C.H. Han, and J.P. Fouque: MCMC Estimation of Multiscale Stochastic Volatility Models, Handbook of Quantitative Finance and Risk Management, Edited by C.F. Lee and A.C. Lee, Springer, 2010.

2011[1] Yu-Ting Chen and Jean-Francois Delmas, Smaller

population size at the MRCA time for stationary branching processes, Ann. Probability, to appear(2011)

[2] S.J.Sheu and H. Hata, An optimal consumption and investment problem with Partial information, to appear in Risk and Decision Analysis.

[3] Wang, H., Lu, H. H.-S., Chueh, T.-H. Constructing Biological Pathways by a Two-Step Counting Approach. PLoS ONE 6(6): e20074, 2011.

[4] Deng, L.-Y., Shiau, J.-J. H., Lu, H. H.-S., Large-order multiple recursive generators with modulus $2^{31}-1$. INFORMS Journal on Computing, 2011, Accepted.

[5] S.J.Sheu and H. Hata, On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: I. Existence of solution, submitted and under revision.

[6] S.J.Sheu and H. Hata , On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: II. Verification Theorem, submitted and under revision.

[7] Chueh, T.-H., and Lu, H. H.-S., “Boolean Networks”. Handbook of Computational Statistics: Statistical Bioinformatics, 2010, In Press.

[8] Yuan-Chung Sheu and Ming-Yau Tsai, .On optimal stopping problems for matrix-exponential L\'{e}vy processes. Journal of Applied Probability (2011), accepted

Preprints

[1] S.J.Sheu and Naoyuki Ichihara, Large time behavior of solutions of Hamilton-Jacobi-Bellman equations with quadratic nonlinearity in gradients, submitted

[2] Ming-Chi Chang, Yu-Ting Chen and Yuan-chung Sheu, Two-sided boundary value problem and perpetual callable bond. Submitted (2011)

[3] Ming-Chi Chang and Yuan-Chung Sheu, Free boundary problems and perpetual American strangles. Submitted (2011)

[4] C.H. Han, W.H. Liu, and T.Y. Chen: An Improved Procedure for VaR/CVaR Estimation under Stochastic Volatility Models, Submitted.

[5] C.H. Han Robust Hedging Performance and Volatility Risk in Option Markets. Submitted.

[6] C.H. Han and C.T. Wu: Efficient Importance Sampling for Estimating Lower Tail Probabilities

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under Multivariate Gaussian and Student T Distributions. Preprint.

[7] Narn-Rueih Shieh, Y.M. Xiao, Hausdorff and Packing dimension results for the images of random fields, Bernoulli, under revision.

[8] Guan-Yu Chen, Yang-Jen Fang and Yuan-Chung Sheu, The cutoff phenomenon for Ehrenfest chains, submitted, 2011.

Coordinators: Shun-Jen Cheng (Academia Sinica) and Ching Hung Lam (Academia Sinica)

D.9 Representation Theory

his research group invest igates the representation theory of groups, Lie

algebra, Lie superalgebras and vertex operator algebras. Research topics include the representation theory of f inite groups and p-adic groups, the investigations of the relationship between the representation theories of classical Lie algebras and Lie superalgebras and the structure theory of vertex operator algebras and their relationship with certain sporadic simple groups.

Investigators: Shun-Jen Cheng (Academia Sinica), Po Yi Huang (NCKU), Shih-Chang Huang (NCKU), Wen Fong Ke (NCKU), Ching Hung Lam (Academia Sinica), Ngau Lam (NCKU), Chu-Feng Nien (NCKU), Shih-Wei Yang (NCKU).

Visitors: Bob Griess (Michigan, USA), Weiqiang Wang (Virginia, USA), Hiroshi Yamauchi (Tokyo, Japan), Tomoyuki Arakawa (Nara, Japan), Hiromichi Yamada (Tokyo, Japan), Hiroki Shimakura (Aichi, Japan), Takao Yamazaki (Tohoku, Japan), Hubert K iechle (Hamburg, Ger many), Dihua Jiang (Minnestoa, USA), Johannes Meyer (Bloemfontein, South Afr ica), Bin Shu (East China Normal University), Edmund Puczylowski (Warsaw, Poland), Guenter Pilz (Linz, Austria), Jin Kui Wan (Beijing University of Technology), Mark Lewis (Kent State University), Frank Himstedt (Technische Universitat Munchen, Germany) .

The student seminar on Quantum Information and workshop on p-adic representation theory ran as planned. Two graduate students attended in the

seminar finished their master degree theses on quantum error corrected codes.

In February 2011, Professor Guenter Pilz visited for one month. Some lectures on applications of algebras were delivered. There were discussions on multiple intersection property of field generated planar nearrings, and effects of nonisomorphic 2-designs on agriculture. The discussions lead to the writing of two papers on the respective topics. Professor Ruibin Zhang could not find appropriate time to visit NCTS this year. Professor Hubert Kiechle from Hamburg University and Technical University Muenich visited in September. Discussions with Wen-Fong Ke on the equation axm + bym + czm = 1 over finite fields have made the project advanced a lot. A draft of the final paper has been written.

The conference on rings and algebra in honor of Professor P.-H. Lee were held in National Taiwan University in July. An algebra workshop in NCTS (South) was held after the conference. Proessors M. A. Chebotar, L. Makar-Lemanov, L. van Wyk, and R. Wisbauer were here for the workshop.

S.-C. Huang, C.-H. Lam, N. Lam, C.-F. Nien, and S.-W. Yang attended a five-day workshop on Representation and Lie theory in July 11-15 of 2011 held at the School of Mathematical Sciences Xiamen University.

C.-F. Nien visited East Normal University, Shanghai, China from March 31 through April 10.

S.-J. Cheng visited Shanghai Jiao-Tung University and the East China Normal University in March 2011,

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where he gave a colloquium talk and a of lecture series, respectively. In May he was invited to attend the International Workshop and Conference on Infinite-dimensional Lie Theory in the Institute of Physics and Mathematics in Tehran, Iran. He gave a lecture series in the workshop and an invited talk in the conference. He visited the University of Virginia in June, and attended the Cross-Straights workshop in Algebra in Xiamen University in July, where he gave an invited talk. In September he was invited to the Annual Meeting of the German Mathematics Society (DMV) in Cologne, where he gave an invited talk in the Symposium on Representation Theory of Lie superalgebras.

C.H. Lam was an invited speaker for the conference on vertex operator algebras, finite groups and combinatorics in Kyoto, Dec 2010. He also visited Hitotsubashi University of Japan on May 2011 and attended the Cross-Straights workshop in Algebra in Xiamen University in July. In addition, he is the organizer of the Conference on Vertex operator algebras, finite groups and related topics, which will be held at Academia Sinica, Taipei this Dec.

Important Results, Breakthrough

In his paper "Combinatorial Expressions for F-polynomials in Classical Types" (submitted), Shih-Wei Yang provides combinatorial formulas for F-polynomials in cluster algebras of classical types. The formulas are given in terms of the weighted paths in certain directed graphs. As a consequence he proves the positivity of F-polynomials in cluster algebras of classical types. Although there are other formulas to compute F-polynomials, Shih-Wei's work seems to be the most "down-to-earth" one by far.

S.-J. Cheng and N. Lam have been studying the relationship between representation theories of Lie algebras and Lie superalgebras. The main motivation is to solve the irreducible character problem in the BGG category O for Lie superalgebras of classical types, which has been a long outstanding problem in theory of Lie superalgebras. Their works over several years led to a conjectural relationship between the representation theories of Lie algebras and Lie superalgebras, called the super duality conjecture, which for type A case was formulated in

joint works of S.J. Cheng with Wang and Zhang in 2008. S.-J. Cheng and N. Lam proved the conjecture in 2010. In a collaboration with Wang, S.-J. Cheng and N. Lam then solved the irreducible character problem for Lie superalgebras of types B,C,D for a fairly general parabolic subcategory of the BGG category in [12]. The subcategory includes all finite-dimensional modules and in particular this solves the finite-dimensional irreducible character problem. In a further application of super duality the same three authors in [21] solved the irreducible character problem in the full BGG category O for the Lie superalgebra gl(2|n), for any n. The irreducible character for modules in the full BGG category O for the general linear Lie superalgebra gl(m|n) were conjectured by Brundan in his 2003 paper to be given by the Kazhdan-Lusztig polynomials defined on a certain quantum group module. In this year they made substantial progress in proving this conjecture.

S.-J. Cheng and W. Wang also have finished writing up a book titled Representations and Dualities of Lie superalgebras [22] this year. The book has been submitted and is currently under review.

S.-C. Huang made a progress on determining the decomposition numbers of Steinberg’s triality groups 3D4 (2

n ). As an application, they classify all absolutely irreducible representations of 3D (2n ) in non-defining characteristic up to a certain degree.

There is a signif icant progress by Ke on determining the number of solutions of the equations axm + bym + czm = 1 over a finite field GF(q) when q and m satisfy “circular” condition. This progress also includes a description of the cyclotomic numbers over GF(q).

Nien obtained an analogue of local converse theorem on classification of cuspidal representations of general linear group over finite fields in terms of twisted gamma factors is obtained. Also, a classification for representations of special orthogonal group admitting Generalized Shalika models is achieved.

C.H. Lam has cont inued h is prog ram on classifying holomorphic vertex operator algebras of central charge 24. He and H. Shimakura have constructed many new models by using Virasoro frames [14,18]. Moreover, they are very close

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to a complete classification of a special class of holomorphic vertex operator algebras (called framed VOA) of central charge 24. In addition, C.H. Lam and R. L. Griess of University of Michigan continued their work on studying some mysterious properties of the Monster group. In particular, they obtained a new existence proof of a group of Monster type using the theory of vertex operator algebras [26].

Accomplishments

2010[1] An, J.; Huang, S. C.; Yamada, H. Uno's invariant

conjecture for the finite symplectic group Sp4(q) in defining characteristic, Communications in Algebra 38 (2010), no. 10, 3868–3888.

[2] An, J.; Himstedt, F.; Huang, S. C. Dade's invariant conjecture for the symplectic group Sp4(2n) and the special unitary group SU4(2

2n) in defining characteristic, Communications in Algebra 38 (2010), no. 6, 2364—2403

[3] An, J.; Huang, S. C. Dade's invariant conjecture for the general unitary group GU4(q

2) in defining characteristic, International Journal of Algebra Computation 20 (2010), no. 3, 357—380.

[4] Himstedt, F.; Huang, S. C. Character tables of the maximal parabolic subgroups of the Ree groups 2F4(q

2), LMS Journal of Computation and Mathematics 13 (2010), 90—110.

[5] Dong, C.; Lam, C. H.; Wang, Q.; Yamada, H. The structure of parafermion vertex operator algebras. Journal of Algebra 323 (2010), 371—381.

[6] Huang, Po-Yi; Ke, Wen-Fong; Pilz, Guenter F. The cardinality of some symmetric differences. Proc. Amer. Math. Soc. 138 (2010), 787—797.

[7] Ke, Wen-Fong; Lai, Kingfai; Zhang, Ruibin Quantum codes from Hadamard matrices. Linear and Multilinear Algebra 58 (2010), 847—854.

[8] Ke, Wen-Fong; Pilz, Guenter F. Abstract algebra in statistics. Journal of Algebraic Statistics 1 (2010), 6—12.

[9] Ke, Wen-Fong; Meyer, Johan H.; Wendt, Gerhard. Matrix maps over planar near-rings. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140 (2010), 83—99.

[10] S.-J . Cheng, J . -H. Kwon and W. Wang, Kostant Homology Formulas for Oscillator Representations of Lie Superalgebras, Advances in Mathematics, 224 (2010), No. 4, 1548—1588.

[11] S.-J. Cheng and N. Lam, Irreducible Characters of General Linear Superalgebra and Super Duality, Communications in Mathematical Physics, 298 (2010), No. 3, 645--672.

2011 [12] Cheng, S.-J.; Lam, N.; Wang, W. Super duality

and irreducible characters of ortho-symplectic Lie superalgebras, Inventiones Mathematicae 183 (2011), 189-224.

[13] C.H. Lam, On the constructions of holomorphic vertex operator algebras of central charge 24, Comm. Math. Phys., 305(2011), no. 1, 153-198. 39.

[14] R.L. Griess Jr. and C.H. Lam, A moonshine path for 5A and associated lattices of ranks 8 and 16, J. Algebra, 331(2011), 338-361. 41.

[15] R.L. Griess Jr. and C.H. Lam, Diagonal lattices and rootless EE8 pairs, J. Pure and Applied Algebra, Volume 216, Issue 1, January 2012, Pages 154-169.

Accepted articles [16] G. Hoehn, C.H. Lam, H. Yamauchi, McKay's

E6 observation on the largest Fischer group, to appear in Comm. Math. Phys.

[17] C.H. Lam and H. Shimakura, Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24, to appear in Proc. London Math. Soc.

[18] Huang, S.-C.; Himstedt F. Dade’s invariant conjecture for the Ree groups 2F4(q

2), to appear in Communication in Algebra.

[19] Ke, Wen-Fong; Meyer, Johan H. Matrix near-rings and 0-primitivity. To appear in Monatshefte für Mathematik.

Submitted articles and Preprints [20] S.-J. Cheng, N. Lam, and W. Wang: Super

Duality for General Linear Lie Superalgebras and Applications, preprint 2011.

[21] S.-J. Cheng and W. Wang: Dualities and Representations of Lie Superalgebras, book submitted, xv+275 pp, version 2011/08/03.

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[22] Nien, Chufeng; Jiang Dihua; Qin, Yujun. Generalized Shalika models and classification for SO4n over p-adic local fields. (in preparation)

[23] Nien, Chufeng. Twisted gamma factor of cuspidal representations of GL(n) over a finite field. (In preparation)

[24] Ke, Wen-Fong; Kiechle, Hubert. On the equation axm + bym - czm = 1 and cyclotomic numbers over finite fields. (In preparation)

[25] R.L. Griess Jr. and C.H. Lam, A new existence proof of the Monster by VOA theory, preprint.

Coordinators: Ming-Chih Lai (National Chiao Tung University), Wen-Wei Lin (National Chiao Tung University), Wei-Cheng Wang (National Tsing Hua University)

Soon-Yi Wu (National Cheng Kung University)

D.10 Scientific Computation at NCTS

ue to the development of computer technology and mathematical science,

Scient if ic Computat ion (SC) has become an indispensable means for solving problems in both theoretical sciences and engineering disciplines. Numerical simulation tools have increasingly become a vital component in the research as well as application of modern technologies ranging from environment, aerospace, materials, biology, to electrical engineering. Based on the support of NCTS, Scientific Computation has gradually received proper attention among the mathematics community. I n add it ion to promot ing i nte rd iscipl i na r y research activity with other sciences, the Scientific Computation program at NCTS also cooperates well with the PDE, Mathematical Biology, and Dynamical Systems programs in Mathematics Division.

We now report the activities of SC group in this year. We have organized one international workshop. Meanwhile, we also have invited a number of distinguished researchers to offer some short courses and to conduct joint research collaboration with local groups. This year’s academic activities can be summarized as follows.

D.10.1 Visiting Scientists

1. Dr. Jay Chu (The University of Texas at Austin), 2011-01-01 ~ 2011-01-07

Dr. Chu visited NCTS and gave a short course on “Homogenization and Numerical Upscaling.

2. Professor Kenji Nakanishi (Kyoto University, Japan), 2011-01-13 ~ 2011-01-17

Prof. Nakanishi visited NCTS and gave a talk on “Center-stable manifolds of traveling waves for the nonlinear Klein-Gordon equation”

3. Professor Nobu Kishimoto (Kyoto University, Japan), 2011-01-13 ~ 2011-01-20

Prof. Kishimoto visited NCTS and gave a talk on “An introduction on the low-regularity well-posedness theory”

4. Professor Tsorng-Whay Pan (University of Houston, US), 2011-01-14 ~ 2011-01-16

5. Professor Ka-Fai Cedric Yiu(The Hong Kong Polytechnic, Hong Kong), 2011-03-20 ~ 2011-03-22

Prof. Yiu visited NCTS and gave a talk on “Optimal design of wireless distributed beamforming system”

6. Professor Makoto Yamashita (Tokyo Institute of Technology, Japan), 2011-04-10 ~ 2011-04-16

Prof. Yamashita visited NCTS and gave two talks on “Exploiting Sparsity in Sensor Network Localization Problem with the framework of SDP relaxation”And on “SDPA: High performance package for SemiDefinite Programs.”

7. Professor Tien-Yien Li (Shanghai Jiao Tong University), 2011-07-10 ~ 2011-07-31

Prof. Li visited NCTS and gave a talk on

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“Computing the Zeros of Polynomial Systems” 8. Professor Wenjun Ying (Shanghai Jiao Tong

University), 2011-07-10 ~ 2011-07-31 Prof. Ying visited NCTS and gave a talk on

“Kernal-free Boundary Integral Method for Elliptic PDEs”

9. Professor Shunsuke Hayashi (Kyoto University, Japan), 2011-08-10 ~ 2011-08-25 , 2011-09-05 ~ 2011-09-22

Prof. Nakanishi visited NCTS and gave two talks on “Robust Wardrop equilibrium in uncertain traffic assignment problem second-order cone based model” and on “Robust Nash equilibria for games with uncertain data.”

10. Professor Goong Chen (Texas A&M University), 2011-12-11 ~ 2012-01-11

D.10.2 Regular Seminar

1. Center-stable manifolds of traveling waves for the nonlinear Klein-Gordon equation, Prof. Kenji Nakanishi(Kyoto University, Japan), 2011-01-13

2. A fractional step immersed boundary method for Stokes flow with an inextensible interface, Prof. Ming-Chih Lai(National Chiao-Tung University), 2011-01-14

3. An introduction on the low-regularity well-posedness theory, Dr. Nobu Kishimoto(Kyoto University, Japan), 2011-01-18

4. Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations, Prof. Yimin Wei(Fudan University, China), 2011-03-21

5. O p t i m a l d e s i g n o f w i r e l e s s d i s t r i b u t e d beamforming system, Prof. Ka Fai Cedric Yiu(The Hong Kong Polytechnic University, Hong Kong), 2011-03-22

6. Part 1. Exploiting Sparsity in Sensor Network Localization Problem with the framework of SDP relaxation, Prof. Makoto Yamashita(Tokyo Institute of Technology, Japan), 2011-04-13

7. Part 2. SDPA : High performance package for SemiDefinite Programs, Prof. Makoto Yamashita(Tokyo Institute of Technology, Japan), 2011-04-15

8. An Evolution of The Splitting from Cosine To Eikonal Schemes, Prof. Qin Sheng(Baylor University, Texas, USA), 2011-05-24

9. Computing the Multiplicity of Zeros of Polynomial Systems, Prof. Tien-Yien Li(Michigan State University), 2011-05-25

10. Optimizations without Derivative Information, Prof. Weichung Wang(Dept. of Math., NTU), 2011-05-26

11. PDE based methods for image compression and denoising, Prof. Yintzer Shih (National Chung Hsing University), 2011-06-10

12. Bio-Medical Images and Statistical Analysis, Prof. Tai-Been Chen(I-Shou University), 2011-06-17

13. A Functional Ultrasound Image Based on a Generalized Rayleigh Distribution, Dr. Yu-Chen Shu(RCAS, Academia Sinica), 2011-06-24

14. Kernel-free Boundary Integral Method for Elliptic PDEs, Professor Wenjun Ying(Shanghai Jiao Tong University), 2011-07-27

15. Solving Large-Scale Algebraic Riccati Equations by Doubling, Prof. Eric K. Chu(Monash University, Australia), 2011-08-09

16. Vector Diffusion Maps and Its Application,Dr. Hau-Tieng Wu(Princeton University), 2011-08-24

17. Painleve’ Transcendants and the Information Theory of MIMO Systems, Professor Yang Chen(Imperial College London), 2011-08-25

18. Robust Nash equilibria for games with uncertain data, Prof. Shunsuke Hayashi(Kyoto University, Japan), 2011-09-13

19. Robust Wardrop equilibrium in uncertain traffic assignment problem:second-order cone based model, Prof. Shunsuke Hayashi(Kyoto University, Japan), 2011-09-15

20. An Arnoldi(M,W,G) approch for Generalized Eigenvalue Problems, Prof. Shao-Liang Zhang(Nagoya University., Japan), 2011-09-20

21. Application of Spline Approximation in Economic Dynamics with Uncertainties, Professor Matthew M. Lin(National Chung Cheng University), 2011-09-22

22. Numerical study of multi-scale sediment dynamics in estuaries and coastal oceans, Prof. Yi-Ju Chou(National Taiwan University), 2011-09-28

D.10.3 Schools and Short Courses

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1. Short course on Homogenization and Numerical Upscaling (2010-12-25~2011-01-06)

Speaker : Dr. Chia-Chieh Chu (University of Texas at Austin)

2. NCTS Spring Course on Computational Science and Engineering (2011-02-23~2011-06-22)

Speakers : Ming-Chih Lai (National Chiao Tung University), Chin-Tien Wu(National Chiao Tung University), I-Liang Chern (National Taiwan University), Chun-Hao Teng (National Chiao Tung University), Wen-Wei Lin (National Taiwan University).

3. NC T S Su m m e r P r og r a m o n S c ie n t i f i c Computation (2011-09-07~2011-09-09)

Speakers : Prof. Ming-Cheng Shiue (National Chiao Tung University)

D.10.4 Conferences and Workshops

1. NCTS Workshop on Fluid-Structure Interaction Problems (2011/05/26 ~ 2011/05/29, NCTS HsinChu)The focus of the workshop was on modeling and

analysis of fluid interaction problems, the theory and analysis of the related partial differential equations (PDEs), and recently developed novel numerical techniques, and the applications. The interactions include fluid-fluid, fluid and solid, fluid and elasticity materials interactions.Organizers:• Ming-Chih Lai (NCTU, Taiwan) - NCTS Center

Scientist• Zhilin Li (NCSU, USA) - NSF grant PIInvited Speakers: Philippe Angot (Aix-Marseille University, France), J. Thomas Beale (Duke University, USA), I-Liang Chern (NTU, Taiwan), Zhiming Chen (Chinese Academy of Sciences, China) Ching-Hsiao Cheng (NCU, Taiwan), Georges-Henri Cottet (Univ. de Grenoble and CNRS, France), Qiang Du (Penn State Univ., USA), Lisa Fauci (Tulane University, USA), Aaron Fogelson (Univ. of Utah, USA), Yongsam Kim (Chung-Ang Univ. Korea), Zhilin Li (NCSU, USA), Chaouqi Misbah (Univ. Joseph Fourier and CNRS, France), Michael Siegel (New Jersey Institute of Technology, USA), Mark Sussman (Florida State

University, USA) , Anna-Karin Tornberg (KTH, Sweden) , Gretar Tryggvason (Univ of Norte Dame, USA), Hongkai Zhao (UC-Irvine, USA) Other International Participants:B. C. Khoo (National University of Singapore, Singapore), Sarah King (North Carolina State University, USA), Long Lee (University of Wyoming, USA), Anita Layton (Duke University, USA), M. Yvonne Ou (University of Delaware, USA ), Sarah Olson (Tulane University, USA )Tsorng-Whay Pan (University of Houston, USA), Zhonghua Qiao (Hong Kong Baptist University, Hong Kong), Yunchang Seol (Chung-Ang University, Korea), Irena Vankova (University of Wyoming, USA), Sheng Xu (Southern Methodist University, USA)

D.10.5 Important Results, Breakthrough

With inspiration from the acdemic activities and close collaboration with international visitors, we have successfully promoted quality researches on Scientific Computation and related topics in Taiwan. We have published 20 SCI papers in 2011, many of them are published or accepted for publication on high-ranking research journals such as the SIAM series, Journal of Computational Physics, Numerische Mathematik, Computational Optimization and Application, Journal of Global Optimization, etc. The publication details can be found in the end of this report. Some of our research achievement include:

(1) We extend our previous work on the two-dimensional immersed boundary method for interfacial f lows with insoluble surfactant to the case of three-dimensional axisymmetric interfacial flows. Although the key components of the scheme are similar in spirit to the two-dimensional case, there are two differences introduced in the present work. Firstly, the governing equations are written in an immersed boundary formulation using the axisymmetric cylindrical coordinates. Secondly, we introduce an artificial tangential velocity to the Lagrangian markers so that the uniform distribution of markers along the interface can be achieved and

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a modified surfactant concentration equation is derived as well. The numerical scheme still preserves the total mass of surfactant along the interface. Further, we provide a simplified one-dimensional analysis and two-dimensional numerical experiments to predict that the overall accuracy for the pressure or indicator function in immersed boundary calculations is first-order accurate in L1 norm, half-order accurate in L2 norm, but has O(1) error in L1 norm.

(2) We develop and analyze eff icient methods for computing damped v ibration modes of an acoustic f luid confined in a cavity with absorbing walls capable of dissipating acoustic energy. The discretization in terms of pressure nodal finite elements gives rise to a rational eigenvalue problem. Numerical evidence shows that there are no spurious eigenmodes for such discretization and also confirms that the discretization based on nodal pressures is much more efficient than that based on Raviart-Thomas finite elements for the displacement field. The trimmed linearization method is used to linearize the associated rational eigenvalue problem into a generalized eigenvalue problem (GEP) of the form Ax=λBx. For solving the GEP we apply Arnoldi algorithm to two different types of single matrices B-1A and AB-1. Numerical accuracy shows that the application of Arnoldi on AB-1 is better than that on B-1A.

(3) We present a rigorous convergence analysis for the generalized MAC (gMAC) scheme on curvilinear domains. The error estimate for the velocity field is established by energy estimate utilizing the stream function and discrete identities associated with the spatially compatible discretization. The spatially compatible discretization also induces subtle stabilizing effect that renders the scheme uniform LBB bound even though gMAC is staggered and supported the same way as the Q1 − P0 finite element method, which is well known to be unstable under divergence constraint. As a result, full second order error estimate is achieved for both velocity and pressure with minimal regularity requirement..

(4) We propose the design of linear-phase finite impulse response (FIR) digital filters using

weighted peak-constrained least-squares (PCLS) optimization. The PCLS error design problem is formulated as a quadratically constrained quadratic semi-infinite programming problem. An exchange algorithm with a new exchange rule is proposed to solve the problem. The algorithm provides the approximate optimal solution after a finite number of iterations. In particular, the subproblem solved at each iteration is a quadratically constrained quadratic programming. We can rewrite it as a conic optimization problem solvable in polynomial time. For illustration, numerical examples are solved using the proposed algorithm.

Moreover, Prof. Soon-Yi Wu has been invited to give a plenary talk in the 5th Sino-Japanese Optimization Meeting (SJOM 2011), Beijing, China on September 26-29, 2011. Around 200 researchers attended this conference. Besides, Prof. Soon-Yi Wu is also nominated for the EURO Gold Medal 2012, the highest distinction within OR in Europe.

D.10.6 Publications

[1] X. J. Tong, L. Qi and S. Y. Wu (2011), A Smoothing SQP Method for Nonlinear Programs with Stabi l i ty Constraints Aris ing from Power Systems, to appear in Computational Optimization and Applications.

[2] L. P. Zhang and S. Y. Wu and S.-C. Fang (2011), An Entropy-Based Central Cutting Plane Algorithm for Convex Min-Max problems with Infinite Constraints, to appear in Journal of Computational and Applied Mathematics.

[3] L. P. Zhang and S. Y. Wu (2011), A new approach to the weighted peak-constrained least-square error FIR digital filter optimal design problem, to appear in Computational Optimization and Applications.

[4] X. J. Tong, C. Ling, S. Y. Wu and L. Qi (2011), A Generalized Semi-Infinite Programming Method for Solving Optimal Power Flow with Transient Stability and Variable Clearing Time of Faults, to appear in Journal of Global Optimization.

[5] M.-C. Lai, C.-Y. Huang and Y.-M. Huang, Simulating the axisymmetric interfacial flows with insoluble surfactant by immersed boundary

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method, International Journal of Numerical Analysis and Modeling, Vol 8, No 1, 105-117, 2011.

[6] C.-T. Wu, Z. Li and M.-C. Lai, Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method, International Journal of Numerical Analysis and Modeling, Vol 8, No 3, 466-483, 2011.

[7] Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible interfaces in incompressible flows, East Asian Journal of Applied Mathematics, Vol 1, No 2, 155-171, 2011.

[8] K.-Y. Chen, K.-A. Feng, Y. Kim and M.-C. Lai, A note on pressure accuracy in immersed boundary method for Stokes flow, Journal of Computational Physics, vol 230, 4377-4383, 2011.

[9] Y. Kim, Y. Seol, M.-C. Lai and C. S. Peskin, The immersed boundary method for two-dimensional foam with topological changes, Communications in Computational Physics, to appear, 2011.

[10] C.-H. Teng, I .-L. Chern and M.-C. Lai, Simulating binary fluid-surfactant dynamics by a phase field model, Discrete and Continuous Dynamical Systems - Series B, Special issue for FAN2010 in honor of J. Thomas Beale, to appear, 2011.

[11] P. Constantin, M.-C. Lai, R. Sharma, Y.-H. Tseng and J. Wu, New Numerical Results for the Surface Quasi-Geostrophic Equation, Journal of Scientific Computing, to appear, 2011.

[12] T. Li, E. K. W. Chu, J. Juang and W. W. Lin, Solution of a Nonsymmetric Algebraic Riccati Equation from a Two-Dimensional Transport Model, Lin. Alg. Appl., Vol. 434, 201-214, 2011.

[13] S. H. Chou, T. M. Huang, W. Q. Huang and W. W. Lin, Efficient Arnoldi-Type Algorithms for Rational Eigenvalue Problems Arising in Fluid-Solid Systems, J. Comp. Physics, Vol. 230, No. 5, 2189-2206, 2011.

[14] Y. C. Kuo, W. W. Lin, S. F. Shieh and W. Wang, Exploring Bistability in Rotating Bose-Einstein Condensates by a Quotient Transformation Invariant Continuation Method, Physica D, Vol. 240, 78-88, 2011.

[15] T. Li, C. Y. Chiang, E. K. W. Chu and W. W. Lin, The Palindromic Generalized Eigenvalue Problem A*x= λAx : Numerical Solution and Applications, Lin. Alg. Appl., Vol. 434, 2269-2284, 2011.

[16] E. K. W. Chu, H. Y. Fan, Z. Jia, T. Li and W. W. Lin, The Rayleigh-Ritz Method Re nement and Arnoldi Process for Periodic Matrix Pairs, J. Comp. Appl. Math., to appear, 2011.

[17] T. Li, E. K. W. Chu, J. Juang and W. W. Lin, Solution of a Nonsymmetric Algebraic Riccati Equation from a One-Dimensional Multi-State Transport Model, IMA J. Num. Anal., to appear, 2011.

[18] T. M. Huang, W. W. Lin and W. S. Su, Parlindromic Quadratization and Structure-Preserving Algorithm for Palindromic Matrix Polynomials of Even Degree, Numer. Math., to appear, 2011.

[19] C. H. Guo, Y.C. Kuo and W. W. Lin, Complex Symmetric Stabilizing Solution of the Matrix Equation $X + X^{\top}X^{-1}A = Q$, Lin. Alg. Appl., to appear, 2011.

[20] Yin-Liang Huang, Jian-Guo Liu and Wei-Cheng Wang, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy., Vol. 9, 649-667, 2011.

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‹‹-Highlights of the Regional Programs 58

Coordinators: H. Wang (National Chiao-Tung University), N.-J. Hsu (National Tsing-Hua University), S.-T. Tseng (National Tsing-Hua University), C.-D. Fuh (National Central Univ. and Academia Sinica)

E.1 Regional Programs on Statistics at Hsinchu

Highlights of the Regional Programs

his is the third year of this statistics program and we have a signif icant

progress on developing the research group. First of all, we had a very successful short course on experimental design given by C.-S. Cheng. He is an international well-known expert in the area of design of experiments (DOE) and his speech inspires young researchers (P-W, Tsai, S-W Chang and C-Y Peng) to generate actual collaborations. In the winter, we also run a small workshop on statistical process control (SPC) and invited Dr. Changliang Zou to give a series of lectures which focused on profile monitoring and fault detection and classification (FDC). Currently, these two are highly used techniques for monitoring the manufacturing process of high-tech industry, especially in IC industry. More than 50 peoples (included industrial engineers) participated in this event and it was a very successful workshop. Stimulating with a real industrial data, we had some joint with Dr. Zou which turned out to be a good starting point for international collaborations. Regarding the research group, the Industrial Statistics Research Group (ISRG) operated by S.-T. Tseng is well developed and functioned in this year. The primary goal of ISRG is to promote frontier research of statistical methods that can be efficiently applied to improve the quality and productivity of high-tech industry. In this year, ISRG had held monthly seminars and discussions to generate interactions between academic researchers and industr ial engineers. It usually takes time for collaborations among multi-disciplines. We satisfy the current

accomplishment and we are very confident on the enhancement and improvement of the program in the future. The activities held by the statistics program this year are summarized in the following:

Regular Seminars Industrial Statistics Research Group (ISRG)

The ISRG runs a one-day regular seminar monthly. This year (up to October), we have invited 17 speakers to introduce contemporary research topics in industrial statistics. The topics include run to run (R2R) process control, Bayesian inference in screening experiment, degradation modeling and inference, profile monitoring, fault detection and classification (FDC). The seminar activities are listed below and more information can be found at the website: http://stat.web.nthu.edu.tw/files/11-1017-428.php.

(1) Speaker: Prof. Yu-Shan Shih 史玉山 (National Chung Cheng University)

Title: Statistical Decision Trees Time: Sep. 30, 2011(2) Spearker: Prof. Yi-Kuei Lin 林義貴 (National

Taiwan University of Science andTechnology)Title: System Reliability Evaluation for Stochastic Flow Networks Time: Sep. 30, 2011

(3) Spearker: Prof. Ching-Shui Cheng 鄭清水 (University of California, Berkeley)

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‹‹- Highlights of the Regional Programs 59

Title: Factorial Designs with Multiple Processing Stages

Time: May. 27, 2011(4) Spearker: Prof. Shou-Jye Wu 吳碩傑 (Tamkang

University) Title: Reliability Sampling Plans and Optimal

Warranty under Progressive Censoring Time: May. 27, 2011(5) Spearker: Prof. Smiley W. Cheng 鄭惟孝

(University of Manitoba, Manitoba, Canada and National Chengchi University, Taipei, Taiwan)

Title: A New Simple Chart to Monitor the Process Mean

Time: Apr, 29, 2011(6) Spearker: Prof. Miin-Shen Yang 楊敏生 (Chung

Yuan Christian University, Taiwan) Title: Robust Fuzzy Clustering and Validity

Indexes Time: Apr, 29, 2011(7) Spearker: Prof. Ray-Bing Chen 陳瑞彬 ( National

Cheng-Kung University) Title: Efficient Bayesian Variable Selection

Algorithms with an Application in Analysis of Supersaturated Designs

Time: Mar, 25, 2011(8) Spearker: Mr. Chih-Chun Tsai 蔡志群 ( National

Tsing-Hua University) Ti t le: D e s ig n a nd A n a lys i s of G a m m a

Degradation Process Time: Mar, 25, 2011(9) Spearker: Prof. William Q. Meeker (Iowa State

University, USA ) Title: Warranty Prediction Based on Auxiliary

Use-rate Information Time: Dec. 21, 2010(10) Spearker: Prof. Loon-ChingTang (National

University of Singapore, Singapore ) Title: Planning and Inference of a 2-Stage

Accelerated Life Testing Time: Dec. 21, 2010(11) Spearker: Prof. FugeeTsung (HK Univ. Sci. and

Tech., , HK) Title: Likelihood Ratio-Based Distribution-Free

EWMA Control Charts

Time: Dec. 21, 2010(12) Spearker: Prof. N. Balakrishnan (McMaster

University, Canada) Title: It's all BS ! Time: Nov. 26, 2010(13) Spearker: Prof. N. Balakrishnan (McMaster

University, Canada) Title: More BS ! Time: Nov. 26, 2010(14) Spearker: Prof. Shu-Kai S. Fan 范書愷 (Yuan Ze

University) Ti t le: En ha nce d d EW M A a nd R LS -LT

Controllers to Compensate for Time-varying Metrology Delays Time: Oct. 22, 2010(15) Spearker: Dr. Kevin Tu 凃凱文 ( 旺宏電子工程

資料分析處副處長 ) Title: 以統計在旺宏的經驗，談統計工程

Time: Oct. 22, 2010(16) Spearker: Prof. I. -T. Yu 俞一唐 (Tung Hai

University) Title: A Bayesian Approach to Identifying the

Active Factors in a Screening Experiment Time: Sep. 24, 2010(17) Spearker: Prof. Chien-Yu Peng 彭健育 (Institute of Statistical Science, Academia Sinica)

Title: Statistical Lifetime Inference with Skew- Wiener Linear Degradation Models Time: Sep. 24, 2010

Conference and Course

Topic: Factorial Designs with Multiple Processing StagesSpeaker: Prof. Ching-Shui Cheng 鄭清水 (University of California, Berkeley)Dates: May 27, 2011 13:30~15:00 Course Description: In factorial experiments with multiple processing stages, the levels of treatment factors are assigned at different stages. At each stage the experimental units are partitioned into disjoint classes, and for each of the treatment factors whose levels are assigned at that stage, the same level is assigned to all the units in the same class. I will

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review recent developments, and discuss some issues on the design and analysis of such experiments.

A Series of Lectures on SPC

Speaker: Dr. Chiangliang Zou 鄒長亮 (Naikai University, China)Talk 1: Multivariate Categorical Control ChartAbstract: In the literature, there is a scarcity of research focusing on multivariate categorical data, and most existing methods lack in robustness for some deficiency. We employ the log-linear model for characterizing the relationship among the categorical factors. Based on this and the exponentially weighted moving average control scheme, novel Phase II control charts are suggested, which incorporate the monitoring of multivariate categorical processes into the unified framework of multivariate binomial and multivariate multinomial distributions. This proposed method is robust to detect various shifts efficiently, especially the shifts in interaction effects which represent the dependence among factors. Numerical simulations and a real-data example demonstrate its effectiveness.Talk 2: Empirical-Likel ihood-Based High-Dimensional EWMA Control SchemesAbstract: In this talk, I will address the issue on calibration of the empirical likelihood (EL) for high-dimensional data in which the data dimension depends on the sample size. Recently, Chen et al. (2009) improve the dimension growth rates of Hjort et al. (2009) for the asymptotic normality of the empirical likelihood ratio (ELR) under a specific multivariate model. We analyze the asymptotic behavior of the EL under a general multivariate model and provide less restrictive conditions under which the best rate for the asymptotic normality of the ELR is achieved. By examining the connection between the ELR and the classical Hotelling's T-square statistic, we propose a new multivariate SPC methodology for monitoring location parameter based on adapting EL to on-line sequential monitoring. The weighted version of EL ratio test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA.

Talk 3: Spatial-Signs-Based High-Dimensional Test s for Spher ic i t y w ith Appl icat ion to Multivariate Statistical Process ControlAbstract: This talk is concerned with the monitoring of shape matrix for high-dimensional data streams. We find that the existing spatial-sign-based procedure (Hallin and Paindaveine, 2006) for sphericity is not robust against high dimensionality, producing tests with type I errors much larger than nominal levels. This is mainly due to additional biases yielded by using the estimation of location parameter to replace the true one. We develop a new correction to the existing test statistic that makes it robust against high dimensionality. We show that the proposed test is asymptotically normal under elliptical distributions and allows dimensionality to increase in the rate of square of sample size. By incorporating the proposed test with classical SPC charting techniques, we suggest a simple but quite efficient monitoring system to tackle high-dimensional monitoring of shape matrices which is of practical needs come from several specific domains of application.Talk 4: Multiple Change-Points Detection by Using Forward RegressionAbstract: Conventional multiple change-points detection methods, such as recursive use of binary segmentation and dynamic programming algorithm, are often computationally expensive when the sample size or variable dimension is large. In this work, we propose a practical procedure which combines extended BIC with the classical forward regression method. Given the simple algorithm, the test and estimation results can be obtained easily and quickly with a similar computational effort as least-squares regression. Under mild conditions, we show that this method provides consistent estimators of the change points with an almost optimal rate. Simulation studies show that our procedure has better performance than existing approaches from both testing and estimating viewpoints in most situations.

Publications

[1] Fan, T. H. and Wang, Y. F. (2011) “An Empirical Bayesian Forecast in the Threshold Stochastic Volatility Models.” (Accepted by J. Statistical Computation and Simulation.)

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[2] Jeng, S.-L. and Huang, B.-Y., and Meeker, W. Q. (2011), Accelerated Destructive Degradation Tests Robust to Distribution Misspecification. (Accepted by IEEE Transactions on Reliability).

[3] Lee, S. P., Chao A. K. , Tsung, F., Wong, DSH, Tseng, S. T. and Jang S. S. (2011), “Monitoring batch process with multiple on-off steps in semiconductor manufacturing.” Journal of Quality Technology, 43(2), 142-157.

[4] Tsai, C. C., Tseng, S. T. and N. Balakrishnan (2011), “Mis-specification analyses of gamma and Wiener degradation processes.” Journal of Statistical Planning and Inference, 141, 3725-3735.

[5] Tsai, C. C., Tseng, S. T. and N. Balakrishnan (2011), “Optimal burn-in policy for highly reliable products using Gamma degradation process.” IEEE Transactions on Reliability, 60(1), 234-245.

[6] Wang, W. L. and Fan, T. H. (2011). “Bayesian Analysis of Multivariate t Linear Mixed Models Using the IBF-Gibbs Sampler.” (Accepted by J. of Multivariate Statistics.)

[7] Yang, S.-F. and Yang, C.-C. (2011), “Optimal Variable Sample Size and Sampling Interval MSE Chart.” (Accepted by Service Industry Journal).

[8] Yang, S.-F., Cheng, T-C. , Huang, T.-M., and Cheng, S. (2011),” A New Chart for Monitoring Service Process Mean.” Quality and Reliability Engineering International..

[9] Yang, S.-F., and Cheng, S. (2011),” A New Nonparametric CUSUM Mean Chart.” Quality and Reliability Engineering International, to appear.

[10] Hsieh, W.J. and Wang, H. (2011). Human MicroRNA Target Identification by RRSM. Journal of Theoretical Biology, 286, 79-84.

[11.] Cheng, C. S. and Tsai P. W. (2011). Multi-stratum fractional factorial design. Statistica Sinica. 21, 1001-1021.

[12] Chueh, T.-H., and Lu, H. H.-S. (2011). Boolean networks. Handbook of Computational Statistics: Statistical Bioinformatics.

[13] Lu , H . H . - S . , a nd Wu , H .-M. (2011) . Visualization, screening, and classification of cel l cycle-regulated genes in yeast”. International Journal of Systems and Synthetic Biology, in press.

[14] Wang, H., Lu, H. HS. and Chueh, TH. (2011). Constructing Biological Pathways by a Two-step Counting Approach. PLoS ONE, 6(6): e20074. doi: 10.1371/journal.pone.0020074

[15] Wang, H. (2011). Confidence Intervals for the Substitution Number in the Nucleotide Substitution Models. Molecular Phylogenetics and Evolution, 60, 472–479.

[16] Wa n g , H . , Wa n g , Y H . a n d Wu , WS . (2011). Yeast cell cycle transcription factors identification by variable selection criteria. Gene, 485, 172-176 .

[17] Wang, H. and Hung, S. L. (2011). Phylogenetic Tree Selection by the Adjusted K-means Approach. Journal of Applied Statistics, to appear.

[18] Deng, L.-Y., Shiau, J.-J. H., Lu, H. H.-S., Large-order multiple recursive generators with modulus $2^{31}-1$. INFORMS Journal on Computing, 2011, Accepted.

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E.2 Regional Programs on Multiscale Modeling, Analysis and Computation at Taipei

E.2.1 Background and Description

he rapid growth of high performance c o m p u t e r s h a s t r a n s f o r m e d t h e

methodology of scientific investigation. Computing is nowadays joined experiment and theory as one of the fundamental tools of investigation. It is safe and cheap. Further, in many cases, it can go beyond experiments or observation, as those in astrophysics or meteorology, etc. The development of computational science needs integration of researchers from different disciplines: mathematics, physics, chemistry, biology, geoscience, engineering, computer science, etc. The funding of NCTS provided opportunities to bring researchers from different disciplines together. In the year 2010/8-2011/7, we focus on three interdisciplinary topics: (1) multi-scale analysis and computation, (2) GPU and matrix computation, (3) computational mechanics. Multi-scale analysis and computation focuses on Schrodinger systems such as Bose-Einstein condensates and interface problems.1. Multi-scale analysis and Computation: Fu r t he r s t udy on spi nor Bose -Ei n s t e i n

condensation and interface problems2. GPU and matrix computation: Large-scale parallel eigenvalue and linear system

solvers and its applications in nano and photonics sciences Fast medical image reconstruction on GPU Optimization and its applications in image and

computer experiments3. Computational mechanics, multi-phase f lows,

symplectic algorithms

E.2.2 Local focus group

I-Liang Chern, Chien-Cheng Chang, Tony W. H. Sheu, Keh-Ming Shyue,Wei-Chung Wang

E.2.3 Short Term Visitors

Nagata Masato (Kyoto University), Chiu-Yen Kao(Ohio State University), Phillip Colella (US National Academy of Sciences,La), John A.Strain (University of California), Runborg Olof (Royal Institute of Technology (KTH), Sweden), Tsai Yen-Hsi Richard (The University of Texas at Austin, USA), Zhao Hongkai(University of California, Irvine)

E.2.4 Seminars, Short courses and workshops

I. Activities: We hold several regular seminars, short courses, summer schools,

workshops and international conference.

II. Short courses and schools(1) NCTC/TPE Short Course on Transition to

turbulence for flows without linear criticality Speaker: Nagata Masato (Kyoto University) Abstract: Instability of fluid flows and their transition

to turbulence are widespread phenomena in engineering and natural environment. Yet, the transition to turbulence in canonical unidirectional shear flows is still an unsolved problem in f luid mechanics. The difficulty consists in extracting relevant information f rom the Nav ie r-Stokes equat ions to understand what is observed in real life

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Coordinators: I-Liang Chern (National Taiwan University), Chien-Cheng Chang (National Taiwan University), Tony W. H. Sheu (National Taiwan University), Keh-Ming Shyue (National Taiwan University), Wei-Chung Wang (National Taiwan University)

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turbulence. It is well known that plane Couette f low and pipe f low are linearly stable against arbitrary three-dimensional perturbations at any finite Reynolds number, so that transitions from the basic laminar states, if they exist, must be abrupt. Due to this lack of linear criticality, weakly nonlinear analysis does not work in general and numerical approaches must be resorted to. The absence of a l inear instabil ity mechanism has previously prevented the discovery of nonlinear solutions to these linearly stable canonical f lows. However, Nagata (1990) found, for the first time, time-independent three-dimensional solutions to plane Couette flow by first focusing on Taylor-Couette flow between co-rotating cylinders. The solutions to plane Couette f low were obtained by bringing the rotation rate to zero. In the first part of the present lecture series we describe how the bifurcation theory was applied to the Taylor-Couette flow in order to obtain Nagata’s solution. Recently, nonlinear solutions have been obtained for pipe flow by Faisst & Eckhardt (2003) and independently by Wedin & Kerswell (2004) using the idea of a self-sustaining process (SSP) of turbulence proposed by Waleffe (1998). In the second part of the lecture series we plan to briefly introduce this SSP, which was used successfully to obtain nonlinear solutions for other flow without linear criticality, namely the pressure-driven flow in a square duct (Wedin, Bottaro & Nagata, 2009). Then, we proceed to seek a different type of nonlinear states in a square duct by introducing an internal heat source to make the system unstable. We explore the nonlinear solution branch, which originates due to the resulting instability, in the physical parameter space (Okino & Nagata, 2010). We introduce yet another flow that, in a similar way to plane Couette flow, pipe flow and square duct flow, exhibit no linear critical point for the laminar states, namely sliding Couette f low in an annulus with a certain range of gap ratio. We shall show our recent numerical investigations on these flows where nonlinear travelling wave states are found

for the first time (Deguchi & Nagata, 2011). Non-trivial nonlinear states for these f lows at finite Reynolds number as solutions in the background of the stable basic state bifurcate from infinity. The onset of turbulence in a subcritical transition is believed to be related to the appearance of steady/travelling wave states, called exact coherent structures, caused by disturbances of finite amplitude that take the flows out of the basin of attraction of the laminar state in phase space. We believe that these states constitute the skeleton around which a time-dependent trajectory in the phase space is organized and help in understanding non-equilibrium turbulent processes. The last part of the lecture series shall concentrate on a new class of travelling wave solutions with a Λ-vortex pattern found in plane Poiseuille flow. The solutions are obtained by continuing the traveling hairpin-shaped f luid vortices found in plane Couette f low by Deguchi & Nagata (2010) to plane Poiseuille f low. The solutions arise from a saddle-node bifurcation at a Reynolds number that is smaller than the critical value known to date (Waleffe, 2003). We believe that the new travelling wave with a Λ-vortex pattern plays an important role to understand the observed onset of a near wall turbulence.

(2) NCTS/TPE Short Course on Dispersive Wave Theory

Speaker: 林琦焜 ( 國立交通大學應用數學系 ) Time: 2011 年 1 月 3 日

Title: Variational approach of the modulation theory , I Variational approach of the modulation theory, II(3) NCTS/TPE Summer Research Program on

Applied Mathematics Aims and scope This summer school will provide research

opportunities to those senior or graduate students who are interested in applied mathematics. Guest speakers will give short lectures on some specific subjects on applied mathematics and will help students to work on

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some research projects. The topics will include optimization, signal and image analysis, and inverse problems. The students are required to attend lectures and submit a final report. A certificate will be granted by NCTS after fulfilling all requirement.

Invited Speakers① Prof. Phillip Colella, Members of the US

National Academy of Sciences (Lawrence Berkeley National Laboratory)

a. Volume-of-Fluid Methods for Partial Differential Equations in Irregular Domains

b. High-Order Finite-Volume Methods for Partial Differential Equations

② Prof. Chiu-Yen Kao (Ohio State University) Int roduction to Shape and Topology

Optimization Involving Eigenvalues and Eigenfunctions

③ Professor John A. Strain (University of California)

a. Moving Interfaces b. Elliptic Systems ④ Prof. Richard Yen-Hsi Tsai (The University

of Texas at Austin) T BA ( N u m e r i c a l PDE S c i e n t i f i c

Computing)⑤ Dr. Hau-Tieng Wu (Princeton University) Adaptive analysis of complex data sets Time: Session 1: June 21-July 15, 2011 (Prof.

Chiu-Yen Kao & Dr. Hau-Tieng Wu) Session 2: August 01, 2011 (Profs. Phillip

Collela and John Strain) Session 3: August 8~12 (Prof. Richard

Yen-Hsi Tsai) Venue: Session 2: Room 202 , Ast ro -Math .

Building, National Taiwan University Organizers I - L i a n g C h e r n ( Na t i o n a l Ta i w a n

University)

III. WorkshopsWorkshop: Topics in Computat ional High Frequency Wave PropagationAims and scopeHigh frequency wave propagation is a classical example of applied mathematics dating back to the development of geometrical optics. Today it is a rich field with a variety of applications in electromagnetic scattering, seismology, photonics, quantum physics and medical imaging. The computational challenges originate in the need of resolving short wave length signals over large domains. The mathematical theory is linked to micro-local analysis, nonlinear partial differential equations, Wigner transforms, semi-classical analysis and analysis of fast algorithms in numerical analysis. In this mini-workshop we will present some recent development in the computational treatment of high frequency waves, including fast wavefront methods, source discovery using high frequency asymptotics and Gaussian beam based methods.Invited SpeakersOlof Runborg (Royal Institute of Technology (KTH), Sweden)Yen-Hsi Richard Tsai (The University of Texas at Austin, USA)Program:10:00~ 11:00 Speaker: Prof. Olof Runborg (Royal Institute of Technology (KTH), Sweden)Title: A Fast Multiresolution Based Wavefront Tracking MethodAbstract:Wavefront tracking can be an attractive alternative for simulating high-frequency waves. It captures multivalued solutions naturally and, although it is a Lagrangian method, it is reasonably easy to interpolate results onto a Eulerian grid. In this talk we consider a wavefront tracking method where the front is desribed in a multiresolution fashion; the representation of the wavefront is in terms of a set of wavelet vectors. Instead of tracking marker points on the wavefront we track the wavelet vectors, which like the markers satisfy ordinary differential equations. We show that the finer the spatial scale, the slower the wavelet vectors evolve. By designing a

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numerical method which takes longer time steps for finer spatial scales we are able to track the front with the same overall accuracy as when directly tracking the markers, but at a computational cost of O(log N/Delta t) rather than O(N/Delta t) for N markers and timestep Delta t. We sketch the proof of this and show numerical examples supporting the theory. We also consider extensions to higher dimensions.11:00~ 12:00 Speaker: Prof. Yen-Hsi Richard Tsai (The University of Texas at Austin, USA)Title: Source discovery for Helmholtz equations14:00~15:00Speaker: Prof. Olof Runborg (Royal Institute of Technology (KTH), Sweden)Title: Error Estimates for Gaussian Beam SuperpositionAbstract:Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as the Schrodinger equation. Superposit ions of Gaussian beams provide a powerful tool to generate more general high frequency solutions that are not necessarily concentrated on a single curve. In contrast to the standard geometrical optics, the Gaussian beam approximation does not break down at caustics. In this talk we discuss the construction of Gaussian beam superpositions and show error estimates in terms of the small wavelength.15:00~16:00Speaker: Prof. Yen-Hsi Richard Tsai (The University of Texas at Austin, USA)Title: Gaussian beam decomposit ion of high frequency wave fieldsOrganizersI -Liang Chern (National Taiwan University)

IV. Regular seminars:(1) N C T S / T P E S e m i n a r o n A p p l i e d

Mathematics • 朱家杰博士 (The University of Texas at

Austin) 2011 年 1 月 6 日

Mult iscale Methods for Ell ipt ic Par t ial Differential Equations and Related Applications

• Chang Lo-Bin 博士 (Brown University) 2011年 1 月 25 日

Generative Models for Image Analysis • Zhao Hongkai 教授 (University of California,

Irvine) 2011 年 5 月 24 日

Level set method for moving interface and free boundary problem

• Zhao Hongkai 教授 (University of California, Irvine) 2011 年 5 月 25 日

A n e w a p p r ox i m a t i o n f o r e f f e c t i v e Hamiltonians for homogenization of a class of Hamilton-Jacobi equations

• 李瑞光教授 ( 清華大學光電工程 )2011 年 5 月

30 日

Spontaneous pattern formations for soliton, vortex, and crescent waves

• Miao-Jung Yvonne Ou 教授 (University of Delaware) 2011 年 6 月10 日

Inverse problems for composite materials and wave propagation in cancellous bone

• Long Lee 教授 (University of Wyoming) 2011年 6 月10 日

Cartesian grid embedded boundary algorithms for solid-fluid interaction

• Todd Arbogast 教授 (University of Texas at Austin) 2011 年 6 月 24 日

Comput at ional Simulat ion of F low in Heterogeneous Porous Media using Multiscale Mortar Methods

• Wong Weng Kee 教授 (UCLA) 2011 年 7月 20 日

A Web-based Tool for Generating Optimal Experimental Designs

• 應文俊教授 ( 上海交通大學 ) 2011 年 7月 29 日

Kernel-free boundary integral method for elliptic PDEs

(2) Seminar on Bose-Einstein condensates • 陳人豪教授 ( 新竹教育大學 ) 2011 年 10月18 日

Continiation Method for Spin-1 BEC and Zeeman effect

• 葉崇傑教授 ( 中央研究院物理研究所 ) 2011年 10 月18 日

Bose -Ei ns te i n Condensates and othe r

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superfluids with internal degrees of freedom • 葉崇傑教授 ( 中央研究院物理研究所 ) 2011

年 11 月 22 日

Bose -Ei ns te i n Condensates and othe r superfluids with internal degrees of freedom: part II

E.2.5 Select publications of the local focus group

[1] Ren-Hao Chen, I-Liang Chern, Weichung Wang, `Èxploring Ground States andExcited States of Spin-1 Bose-Einstein Condensates by Continuation Methods,"Journal of Computational Physics, Vol. 230, (2011), 2226-2236.(SCI)

[2] Teng, Chun-Hao, I-Liang Chern and Ming-Chih Lai, “Simulating binary fluid surfactant dynamics by a phase field model,” Discrete and Continuous Dynamical System, B, (accepted).

[3] Ren-Hao Chen, I-Liang Chern, Weichung Wang, “Exploring Ground States and Excited States of Spin-1 Bose-Einstein Condensates by Continuation Methods,” Journal of Computational Physics, Vol. 230, (2011), 2226-2236.(SCI)

[4] Daomin Cao, I-Liang Chern, Jun-Cheng Wei, “On Ground State of Spinor Bose-Einstein Condensates ,”NOEDA-Nonl inear Par t ia l Differential Equations and Applications Vol. 18, No. 1, (2011), 427-445.(SCI)

[5] I-Liang Chern and Chun-Hsiung Hsia, “Dynamic phase transition for Cahn- Hilliard equations in cylindrial geometry,” Discrete and Continuous Dynamical System, B, Vol. 16, No. 1 (2011), 173-188.(SCI)

[6] Yukai Hung and Weichung Wang* (Accepted). "Ac cele r a t i ng Pa r a l le l Pa r t ic le Swa r m Optimization via GPU." Optimization Methods and Software. http://dx.doi.org/10.1080/10556788.2010.509435

Chenhan D. Yu, Weichung Wang*, and Dan'l Pierce. (2011) "A CPU-GPU Hybrid Approach for the Unsymmetric Multifrontal Method." Parallel Computing, 37:759-770. http://dx.doi.org/10.1016/j.parco.2011.09.002

[8] Cheng-Ying Chou, Yi-Yan Chuo, Yukai Hung, and Weichung Wang*. (2011)

"A Fast Forward Projection Using Multithreads for Mult i rays on GPUs in Medical Image Reconstruction." Medical Physics, 38(7):4052-4065.http://dx.doi.org/10.1118/1.3591994

[9] Tsung-Ming Huang, Feng-Nan Hwang*, Sheng-Hong Lai, Weichung Wang, and Zih-Hao Wei (2011). "A Parallel Polynomial Jacobi-Davidson Approach for Dissipative Acoustic Eigenvalue Problems." Computers and Fluids,45:207-214. http://dx.doi.org/10.1016/j.compfluid.2010.11.020

[10] Weichung Wang, Ray-Bing Chen*, and Chia-Lung Hsu (2011). "Using Adaptive Multi-Accurate Function Evaluations in a Surrogate-Assisted Method for Computer Experiments." Jou r na l of Comput at ional and Appl ied Mathematics, 235:3151-3162.ht tp://dx.doi.org/10.1016/j.cam.2010.12.021

[11] Jen-Hao Chen, I-Liang Chern*, and Weichung Wang* (2011). "Explor ing Ground States and Excited States of Spin-1 Bose-Einstein Condensates by Continuation Methods." Journal of Computational Physics,230:2222-2236. http://dx.doi.org/10.1016/j.jcp.2010.11.048

[12] Ray-Bing Chen, Weichung Wang*, and C. F. Jeff Wu (2011). "Building Surrogates with Overcomplete Bases in Computer Experiments with Applications to Bistable Laser Diodes." IIE Transactions (Quality and Reliability Engineering), 43(1):39-53. (SCI)http://dx.doi.org/10.1080/0740817X.2010.504686

[13] Yueh- Cheng Kuo, Wen-Wei Li n , Sh i h-Feng Shieh, and Weichung Wang*(2011). "Exploring Bistability in Rotating Bose-Einstein Condensates by a Quotient Transformation Invariant Continuation Method." Physica D: Nonlinear Phenomena, 240:78-88.http://dx.doi.org/10.1016/j.physd.2010.08.008 (SCI)

[14] Tony W. H. Sheu, C. H. Yu, P. H. Chiu (2011) , Development of a level set method with good area preservation to predict interface in two phase flows, International Journal for Numerical Methods in Fluids, Vol. 67, pp.109-134.

[15] Roberto Camassa, P. H. Chiu, Long Lee, Tony W. H. Sheu (2011), A particle method and numerical study of a quasilinear partial differential equation, Discrete and Continuous Dynamics Systems-Series S, Vol. 10, pp. 1503-1512.

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[16] Tony W. H. Sheu, C. H. Yu (2010), Development of an incompressible Navier-Stokes solver involving symplectic and non-symplectic time integrators, Numerical Heat Transfer, Part A: Fundamentals, Vol. 58(4), pp.262-286.

[17] Tony W. H. Sheu, S. H. Kuo, Prediction of temperature-dependent electroosmotically driven

microchannel flows with the Joule heating effect, International Journal of Numerical Methods for Heat & Fluid Flow (accepted)

[18] Tony W. H. Sheu, R. K. Lin (2011), Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection, Int. J. Heat and Mass Transfer, Vol. 54, pp. 447-467.

We state our activities in several different focus areas (I-III below):

I. Probabi l ity/Stat ist ics Methods Program Coordinator: Wen-Jang Huang/Tiee-Jian Wu

he main goal is to generate some common research interest among members and to

learn some new topics.The activities from Jan., 2011 to the present time

are as follows: 1. Seminar 高雄大學應用數學系黃士峰教授 gave a

talk entitled: ”Moment Bounds and Multistep Prediction of Linear Processes” on 9/22/2011 at NCKU. 江其衽博士 of Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC gave a talk entitled: ”Covariate Adjusted Functional Principal Component Analysis” on 1/6/2011 at NCKU. Professor P-Y. Chen ( 陳平雲 ) of Syracuse University gave a talk: “Selection Procedures in Identifying EM Fields following Log-normal Distributions“ on 8/11/2011 at NCKU. Professor潘光明 of Division of Mathematical Sciences, Nan yang Technological University gave a talk: ”Testing cross-sectional independence by empirical spectral distribution functions” on 1/13/2011 at NSYSU.

2. Visitor Professor P-Y. Chen ( 陳平雲 ) of Syracuse

University visited NCTS (South) from 7/30/2011 to 8/14/2011 and gave a talk (see above). He has also discussed a joint research work with T-J Wu on applying multivariate regression model selection criteria to signal processing. A paper on this subject has been submitted to Signal Processing (under revision). Professor 潘光明 of Division of Mathematical Sciences, Nan yang Technological University visited NCTS (South) and NSYSU from 1/5/2011 to 1/19/2011. He gave a talk (see above) and discussed joint work with M-H Guo (NSYSU).

II. Industrial Statistics/ Biostatistics and Bioinformatics Coordinator: S.-L. Jeng/ Tiee-Jian Wu

The activities from Jan., 2011 to the present time are as follows:1. Seminar

中興大學統計學研究所 Prof. Wen-Han Hwang ( 黃文瀚 ) gave a talk entitled: “Improving on Semiparametric Approach for Joint Modeling of Survival and Longitudinal Data” on 10/6/2011. 交通大學統計學研究所 Prof. Henry Horng-Shing Lu ( 盧鴻興 ) gave a seminar lecture in the general area of bioinformatics on 11/10/2011 at NCKU. 臺灣科技大學資訊工程系 Prof. Yuh-Jye Lee ( 李

育杰 ) gave a seminar talk entitled: “Combine the Passive and Aggressive Algorithm with a Proximal Model” on 9/29/2011 at NCKU. 中央研究院統計科學研究所 Prof. Chih-Hsin Tsai

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Coordinators: Tiee-Jian Wu (National Cheng-Kung University)

E.3 Regional Programs on Statistics at Tainan

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( 蔡志鑫 ) gave a talk in the area of Functional MRI data analysis/Human Learning and Memory/Artificial Neural Network Models on 10/13/2011 at NCKU. 台灣大學數學系 Prof. Chin-Tsang Chiang ( 江金倉 ) gave a talk in the area of Recurrent Event Data Analysis on 11/3/2011 at NCKU. Prof. and chair D. Simpson of Dept. of Statistics, University of Illinois gave a talk entitled: ”Ultrasound Image Segmentation and Classification using Texture Features” on 2/24/2011 at NSYSU. Professor Ying Chen of Department of Statistics & Applied Probability, National University of Singapore will give a talk in high frequency data analysis/machine learning on 12/15/2011 at NCKU. Professor Sam Kou ( 寇星昌 ) of Department of Statistics, Harvard University will give a talk on statistical analysis of protein sequence on 12/26/2011.

2. VisitorsProf. and chair D. Simpson of Dept. of Statist ics, University of Illinois visited NCTS (South) and NSYSU from 2/17/2011 to 3/08/2011 and gave a talk on statistical methodology (see above) that can be applied to detect tumor images. He discussed research project with M-N Lo and M-H Guo, both of NSYSU. A joint paper has been completed out of his visitation. Professor Ying Chen of Department of Statistics & Applied Probability, National University of Singapore will visit our center from 12/12/2011-12/16/2011, give a talk (see above) and discuss research ideas in high frequency data analysis/financial statistics/machine learning with R-B Chen and S-L Jeng, both at NCKU.

I I I . Financial Stat ist ics and Time Ser ies Coordinator: Mei-Hui Guo

The activities from Jan., 2011 to to the present time are as follows:

1. Seminar 李相烈教授 of Dept. of Statistics, Seoul National University, Korea gave a lecture: ”Maximum entropy type test of f it” on 1/25/2011 at NSYSU. 陳毅恆教授 of Dept. of Statistics, Chinese University of Hong-Kong

will give a talk in the area of high-dimensional t ime-ser ies data analysis on 12/16/2011 (tentative) at NSYSU.

2. Visitor 李相烈教授 of Dept. of Statistics, Seoul national University, Korea visited our center from 1/23/2011-1/30/2011 and gave a lecture (see above). He discussed research ideas in time series and statistics with M-H Guo. Also, 陳毅恆教授 of Dept. of Statistics, Chinese University of Hong-Kong will visit our center from 12/16/2011 to 12/19/2011. He will give talks at NSYSU and NUK, and discuss research topics with M-H Guo in high-dimensional time-series model.

Research Results:From Jan, 2011 to Dec. 2011, our program has

already invited or will invite totally 6 visiting scholars; and hold 9 seminar talks. Furthermore, under the (partial) support of our program, 7 papers (6 in SCI-journals) have been published or accepted (in press), and 6 papers have been submitted to good SCI-journals for review. All of them have acknowledged the support of NCTS (South).

Publications:[1] R-B Chen, C-H Chu, T-Y Lai and Y-N Wu (2011).

Stochastic matching pursuit for Bayesian variable selection. Statistics and Computing, 21, 247-259. SCI

[2] M.-R. Chen (2011). Two-person red-and-black game with Lower Limit. Probability in the Engineering and Informational Sciences 25, 119-133. SCI

[3] W. Wang, R-B Chen and C-L Hsu (2011). Using Adaptive Multi-Accurate Function Evaluations in a Surrogate-Assisted Method for Computer Experiments. J. Computational and Applied Mathematics 235, 3151–3162. SCI

[4] S.-C. Chen, M S. Rosenberg and B Lindsay (2011). MixtureTree: a program for constructing phylogeny. BMC Bioinformatics (an open access journal) 2011, 12:111 http://www.biomedcentral.com/1471-2105/12/111 SCI

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[5] S. Lee and M-H Guo (2011) Test for dispersion constancy in stochastic differential equation models. Applied Stochastic Models in Business and Industry. (accepted, in press, DOI: 10.1002/asmb.908) SCI

[6] S-L Jeng, B-Y Huang and W.Q. Meeker (2011). Accelerated Destructive Degradation Tests Robust to Distribution Misspecification. IEEE Transactions on Reliability (accepted, in press) SCI

[7] S.-C. Chen, L-A Li, S. Li and J. He (2011). Influence of choices of statistical models on neural spike trend. J. of Data Science, 9, (accepted, in press, 19 pages).

[8] C-K Wen, G Pan, K-K Wong, Meihui Guo and J-C Chen. (2011). A Deterministic Equivalent for the Analysis of Non-Gaussian Correlated MIMO Multiple Access Channels. (Conditionally accepted by IEEE Transactions on Information Theory).

Preprints submitted[1] W-J Huang, Nan-Cheng Su and A. K. Gupta

(2011). A study of generalized skew-normal distribution. (submitted)

[2] T-J Wu, P. Chen and Y. Yan. (2011). The weighted average information criterion for multivariate regression model selection (Signal Processing, under revision).

[3] T-J Wu, H-Y Chen and H-C Yu (2011). Root n estimates of integrated squared density partial derivatives (submitted).

[4] R-B Chen, C-H Chu and J-Z Weng (2011). A Stochastic Matching Pursuit (SMP) MATLAB Toolbox for Bayesian Var iable Select ion (submitted)

[5] R-B Chen, J-Z Weng and C-H Chu (2011). Screening Procedure for Supersaturated Designs using a Bayesian Variable Selection Method (submitted)

[6] M-N Lo Huang , M-H Guo, J-M Chen , L-W Kao, D. Simpson, K-S Hsieh. (2011) Discriminant analysis and classification of heart function with cardiology ultrasound in left ventricle (submitted)

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E.4.1 Important Results, Breakthrough

ocal l inear reg ression has become a popular technique for est imat ing

reg ression f u nc t ions nonpa ramet r ica l ly i n applications and has been implemented in the open access software R and others. Theoretically, it enjoys many nice properties such as automatic boundary correction and linear minimax optimality. However, in finite sample cases the local least squares problem in local linear estimation becomes ill-posed when the design is sparse i.e. locally the point of estimation is far from the center of design points or the design points are lumped in one cluster. As a result, the local linear estimator either does not exist or exhibits drastic roughness in the sparse design regions. Many methods have been proposed to address this serious problem in the univariate case with some of which can be extended to the multivariate case. However, all of the existing remedies involve some additional tuning parameters, which have to be decided by the researchers or by the data. In the univariate case, we propose two approaches to cope with the design sparsity problem, both of which possess nice finite sample and asymptotic theoretical results. One of them does not involve any additional tuning parameters and has superior numerical performance. However, i mplement a t ion of t he d i rec t ion generalization to the multivariate case becomes complicated although the computation time can be controlled. The other method requires an additional tuning parameter, and the numerical performance depends choice of the tuning parameter, which is under investigation. On the other hand, this method can be directly extended to general multivariate case without any compensation on the implementation or the theoretical justifications. Our theoretical investigation shed some light on how to set the order of this tuning parameter. We plan to write up a paper based on this work and submit it to a top tier statistical journal in December 2011 or early 2012.

Multiparameter local likelihood models specify the parametric form of the conditional distribution of the response variable (which can be univariate or multivariate and discrete or continuous) on the independent variables (which can be discrete or continuous) and allow the parameters in the conditional distribution to vary with values of the independent variables. This kind of models have been accepted as a f lexible tool for modeling the relationship between responses and covariates, and the corresponding methodology has been used to analyze data arising from climatology, environmetrics, finance, medicine, and so on. Although both point estimation and interval estimation for the unknown parameter functions in these models have been investigated in the literature, how to formally test goodness-of-fit of the specified form of the conditional density function remains an unsolved problem. Testing the specification of the conditional density is an important issue, the inference becomes inclusive or misleading and the estimated parameter functions become meaningless if the form of the true conditional density is different from the specified one. We propose bootstrap tests based on two new test statistics constructed using transformation of the data and local likelihood estimation of the unknown parameter functions. We obtained the asymptotic null distributions of the proposed test statistics. We also conducted an extensive simulation study to assess numerical performance of the tests in terms of both level accuracy and power. The tests were applied to an environmental dataset, which consists of annual largest sea levels in Venice. Our analysis provides scientific justification for previous studies on the dataset that use generalized extreme value distribution as the conditional distribution. We plan to write up a paper based on this work and submit it to a top tier statistical journal in December 2011.

High d imensional dat a a r ise f rom many fields of research including finance, economy, climatology, medicine, and so on. In analysis of

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Coordinator: Ming-Yen Cheng (National Taiwan University)

E.4 Regional Programs on Statistics at Taipei

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high dimensional data, the main challenge is how to identify low dimensional features are hidden from the high dimensional data. In the recent decade this important and emerging topic has been extensive studied by researchers in different fields, including applied mathematics, computer science, electrical engineering, statistics, and others. For example, statistical methods LASSO, SCAD and other variable selection and dimension reduction techniques have been found useful in applications, and manifold learning methods leads to understanding of the unknown manifolds. We develop a new method to nonparametrically estimate the regression function on an unknown manifold and to select the smoothing parameter in the nonparametric regression. We have obtained the asymptotic mean squared error of the regression estimator and developed an automatic bandwidth selector for the estimator using ideas of generalized cross validation, empirical bias and robust variance estimation. Numerical results indicate that our estimator outperforms existing methods. We plan to write up a paper based on this work and submit it to a top tier statistical journal by end of 2011.

E.4.2 Accomplishments

[1] Cheng, M.-Y., Kang, K.H. and Peng, L. (2011). Nonparametric tests for distribution specification in multiparameter local likelihood models. Manuscript.

[2] Cheng, M.-Y., Wu, J.-S., Yang, Y.-H., and Chen, L.-H. (2011). Adapting to sparse design in multivariate local linear regression. Manuscript.

[3] Cheng, M.-Y., and Wu H.-T. (2011) Regression on manifolds and its geometric interpretation. Manuscript.

[4] Chen, L.-H., Yang, Y.-H., Chen, C.-S., and Cheng, M.-Y. (2011). Illumination invariant feature extraction based on natural images statistics -- taking face images as an example. Proceedings of the 2011 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 681--688.

[5] Cheng, M.-Y. (2010). Discussion on the paper ``Maximum likelihood estimation of a multi-dimensional log-concave density' ' by Cule,

Samworth and Stewart, Journal of the Royal Statistical Society Series B, 72, 585--586.

[6] Xue, S. and Cheng, M.-Y. (2010). Nonparametric change-point analysis of gold andpetroleum prices and US dollar index. Journal of the Chinese Statistical Association, 48, 45--73.

[7] Cheng, M.-Y., Paige, R.L., Sun, S. and Yan, K. (2010). Variance reduction for kernel estimators in clustered/longitudinal data analysis. Journal of Statistical Planning and Inference, 140, 1389--1397.

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‹‹-Activities of Onsite Scientists

Activities of Onsite Scientists

Title Name Field Period

Center Scientists(Chern Fellow)

Kuo-Chang Chen(Chern Fellow)

Dynamical Systems 2009/08/01-2012/07/31

Guan-Yu Chen Probability 2010/08/01-2011/07/31

Sze-Bi Hsu Mathematical Biology 2010/08/01-2012/07/31

Ming-Chih Lai Scientific Computation 2010/08/01-2012/07/31

Wen-Ching Winnie Li Number Theory 2009/05/14-2012/07/31

Ming-Chia Li Dynamical Systems 2010/08/01-2011/07/31

Duy-Minh Nhieu Differential Geometry 2009/08/01-2011/07/31

Shuenn-Jyi Sheu Probability 2010/08/01-2012/07/31

Chih-Wen Shih Dynamical Systems 2009/08/01-2012/07/31

Honorary FellowshipDong-Ho Tsai Differential Geometry 2011/01/01-2012/12/31

Yi-Fan Yang(Center Scientists)

Number Theory 2011/01/01-2012/12/31

Young Theory Award

Jung Chao Ban Dynamical System 2010/01/01-2011/12/31

Jiun-Cheng Chen Algebraic Geometry 2010/01/01-2011/12/31

Nan Kuo Ho Differential Geometry 2009/01/01-2011/12/31

Ching-Lung Lin PDE 2010/01/01-2011/12/31

Jeng-Daw Yu Number Theory 2010/01/01-2011/12/31

Postdoctoral Fellow

Chieh-Yu Chang Number Theory 2010/08/01-2011/10/21

Chi-Hua Chan Applied Mathematics 2011/02/01-2011/07/31

Jiangwei Xue Number Theory 2010/08/01-2012/07/31

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‹‹- Activities of Onsite Scientists 73

F .1 Center Scientists

I. CHEN, KUO-CHANG

National Tsing Hua University, Professor

Conferences and Workshops 1. The Fifth International Congresses of Chinese

Mathematicians, Dec. 17-22, 2010. Tsing Hua University, Beijing, China. (40 min

talk)2. International Conference on Diff.Geometry and

Diff. Equations, April 11-16, 2011. Yangzhou University, Yangzhou, China. (1 hour

talk)3. Symposium on Celestial Mechanics, September 1-2,

2011. Osaka University, Osaka, Japan. (1 hour talk)

Visits1. Yonsei University, Seoul, Korea, January 22-31,

2010. 2. Nanjing University, Nanjing, China, April 7-9,

2011. 3. Nanjing University, Nanjing, China, August 21-28,

2011.

NCTS Activities1. NCTS Summer Course on Dynamical Systems,

July–August, 2010. (co-organizer)2. NCTS Workshop on Dynamical Systems, National

Tsing Hua Univeristy, Hsinchu, Taiwan, May 12-14, 2011. (co-organizer)

3. NCTS Dynamical systems seminar.4. NCTS Short Course on Analysis, March 17-April

21, 2011. (organizer)5. NCTS Topic Course on the N-body Problem, May

5-June 16, 2011. (speaker)6. NCTS Summer Course on Dynamical Systems,

July–August, 2011. (speaker and organizer)

Recent Publications

1. On action-minimizing retrograde and prograde orbits of the three-body problem (with Y.-C.Lin). Comm. Math. Phys., 291, 403-441 (2009).

2. Variational constructions for some satellite orbits in periodic gravitational force fields. Amer. J. Math., 132, 681-709 (2010).

3. On the barycenter of the tent map (with Xun Dong). Proc. Amer. Math. Soc., 138, 4025-4035 (2010).

4. Convex central configurations of the n-body problem which are not strictly convex (with J.S. Hsiao), J. Dyn. Diff. Equations, to appear.

II. Guan-Yu Chen

National Chiao Tung University, Assistant ProfessorNational Center for Theoretic Sciences, Center Scientist

NCTS Activities1. NCTS 2011 Summer course in probability

Research Works1. Guan-Yu Chen, Yang-Jen Fang and Yuan-Chung

Sheu, The cutoff phenomenon for Ehrenfest chains, Submitted (2011)

2. Guan-Yu Chen, A comparison of random walks and Markovian semigroups, in preparation.

III. Sze-Bi Hsu

National Tsing Hua University, ProfessorDirector, National Center for Theoretical Sciences (beginning August 1, 2011)

Activities Organized1. I organized a weekly student and post doctor

seminar titled "Application of Partial Differential Equations to Mathematical Biology", from fall 2010 to spring 2011.

2. I hosted the visit by Prof. Liang Xin, China Technology University, April 1-April 28 ,2011. We worked together on Spreading speed of two species competition with two stages.

3. I hosted the visit by Professor Horst Thieme,

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‹‹-Activities of Onsite Scientists 74

Arizona State University, May 19-June 3, 2011. We discuss some problems on the mathematical models in Epidemics

4. I hosted the visit by Professor Ruan Shigui, University of Miami, May 9-May 23, 2011. We worked on the problems of two predators competing for one prey with Beddington-DeAngelis functional responses.

Conferences/WorkshopsNCTS Workshop on PDE Models of Biological Process, Dec. 13-17,2010, co-organizer.

Colloquium/Seminar Talks1. Canada C o l l o q u i u m , M e m o r i a l U n i v e r s i t y o f

Newfoundland, July 15,2011, Invited speaker, title: Single Phytoplankton growth for light with Diffusion and advection in a water column.

Participate the workshop “ Emerging Challenge of the Interface of Mathematics and Environmental Science: Spatial Ecology”

2. China Invited talk, 5th ICCM at Beijing, Dec. 26, 2010,

Title:Lotka-Volterra two species competition model with season succession.

3. Spain(1) Colloquium, Carol III Universidad, Madrid,

June 9, Invited speaker, Title: Mathematical Models of Microbial

Competition in a chemostat.(2) Colloquium , Universidad Seville, June 27,

Invited Speaker, Title : Single Phytoplankton growth for light

with Diffusion and advection in a water column.

(3) Invited talk, Complutense Universidad, Madrid, June 15, in the workshop “ Application of Nonlinear PDE”, Title: Competition and coexistence in flowing habitat with a hydraulic storage zone.

4. Taiwan Invited speaker, 19th Annual DE workshop. Title

:Lotka-Volterra two species Competition Model with season succession.

PublicationsNCTS affiliated1. Sze-Bi Hsu and Xiaoqiang Zhao , A Lotka-

Volterra Competition Model with Seasonal Succession, Journal of Mathematical Biology (2011).

2. S.B.Hsu and Y.Y.Chen, Synchronized reproduction promoting species coexistence th rough reproductive facilitation,, Journal of Theoretical Biology274 (2011) 130-144

3. S.B.Hsu,F.B.Wang and X.Q.Zhao, Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, Journal of Dynamics and Differential Differential Equations(2011)

4. S.B.Hsu,F.B.Wang and Jifa Jiang, Reaction-diffusion equation of two species competing for two complementary resources with internal storage, Journal of Differential Equations (2011)

5. J.Grover, S.B.Hsu,and F.B.Wang, Competition between micro-organism for a single limiting resource with cell quota structure and spatial variation, Journal of Mathematical Biology (2011)

6. S.B.Hsu and F.B.Wang, On a mathematical model arising from competition of phytoplankton species for a single nutrient with internal storage: Steady state analysis, Commu. Appl. Analysis 10(2011)no.5,1479-1501

IV. Ming-Chih Lai

Department of Applied Mathematics, National Chiao Tung University, Professor

Invited Conferences and Workshops • Inter nat ional Conference on Front iers of

Numerical PDEs (invited speaker, 35 mins talk) Guangzhou, China, August 2-4, 2011

• EASIAM 2011 conference and business meeting, Kitakyushu, Japan, June 27-29, 2011

• 2011 International Conference on Applied Mathematics and Interdisciplinary Research (invited speaker, 35 mins talk), Chern Institute of Mathematics, Nankai University, Tianjin, June 13-15, 2011

• Workshop on Kinetic Theory and Computation

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(invited speaker), University of Kyoto, Japan, March 21-24, 2011 (cancelled due to earthquake)

• International Congress of Chinese Mathematicians ICCM2010 (invited speaker, 45 mins talk), Beijing, December 17-22, 2010

• Workshop on Fluid Motion Driven by Immersed Structures (tutorial speaker on the immersed boundary method, one hour talk), Fields Institute, Canada, August 9-13, 2010

International Activities1. Elected to the Vice President of SIAM East Asia

Section (EASIAM) since 2011/012. Served as Editorial Board of two journals; East

Asian Journal of Applied Mathematics, (since 2010) and International Journal of Numerical Analysis and Modeling- Series B, (since 2011) -

NCTS Activities1. Organized NCTS Workshop on Fluid-Structure

Interact ion Problems, National Tsing Hua Univeristy, Hsinchu, Taiwan, May 26-29, 2011. Jointly sponsored by NCTS (Organizer: Ming-Chih Lai) and NSF-US (USD$25,000, PI: Zhilin Li)

2. Organized NCTS Spring Course on Computational Science and Engineering, 2011/02/23-2011/06/22, every Wednesday 1:30-4:30pm. Speakers include Chin-Tien Wu (NCTU), Chun-Hao Teng (NCTU), Ming-Chih Lai (NCTU), I-Liang Chern (NTU) and Wen-Wei Lin (NTU).

3. Organized NCTS Summer Course on Scientific Computation, September 7-9, 2011, two hours per day. Speaker : Ming-Cheng Shiue (NCTU)

Recent Publications1. Z. Li, M.-C. Lai, G. He and H. Zhao, An

augmented method for free boundary problems with moving contact lines, Computers and Fluids , Vol 39, 1033-1040 (2010).

2. Y. Kim, M.-C. Lai and C. S. Peskin, Numerical simulat ions of two-d imensional foam by the immersed boundary method, Journal of Computational Physics, Vol 229, 5194-5207 (2010).

3. M.-C. Lai, Y.-H. Tseng and H. Huang, Numerical

simulation of moving contact lines with surfactant by immersed boundary method , Communications in Computational Physics , Vol 8, 735-757 (2010).

4. Y. Kim and M.-C. Lai, Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method , Journal of Computational Physics, Vol 229, 4840-4853 (2010).

5. C.-T. Wu, Z. Li and M.-C. Lai, Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method , International Journal of Numerical Analysis and Modeling, Vol 8, No 3, 466-483 (2011).

6. M.-C. Lai, C.-Y. Huang and Y.-M. Huang, Simulating the axisymmetric interfacial flows with insoluble surfactant by immered boundary method , International Journal of Numerical Analysis and Modeling, Vol 8, No 1, 105-117, (2011).

7. Z. Li and M.-C. Lai, New f inite difference methods based on IIM for inextensible interfaces in incompressible flows , East Asian Journal of Applied Mathematics, Vol 1, No 2, 155-171 (2011).

8. P. Constantin, M.-C. Lai, R. Sharma, Y.-H. Tseng and J. Wu, New Numerical Results for the Surface Quasi-Geostrophic Equation, Journal of Scientific Computing, in press (2011).

9. K.-Y. Chen, K.-A. Feng, Y. Kim and M.-C. Lai, A note on pressure accuracy in immersed boundary method for Stokes flow, Journal of Computational Physics, vol 230, 4377-4383 (2011).

10. Y. Kim, Y. Seol, M.-C. Lai and C. S. Peskin, The immersed boundary method for two-dimensional foam with topological changes, Communications in Computational Physics , accepted.

11. C.-H. Teng, I.-L. Chern and M.-C. Lai, Simulating binary fluid-surfactant dynamics by a phase field model, Discrete and Continuous Dynamical Systems - Series B , Special issue for FAN2010 in honor of J. Thomas Beale, accepted.

V. Wen-Ching Winnie Li

Professor of Mathematics, Pennsylvania State UniversityDirector, National center for Theoretical Sciences (2009.6.1-2011.7.31)

Activities Organized

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1. Invited and hosted Prof. Don Zagier, Director of MaxPlanck Mathematics Institute, Germany and Professor of College de France, France, Aug 1-10, 2010. Prof. Zagier delivered 4 two-hour Distinguished Lecture Series titled “Modular Forms, Mock Theta Functions, and Black Holes”.

2. Invited and hosted the visit by Prof. Gebhard Boeckle, University Heidelberg, Germany. Prof. Boeckle visited NCTS for three weeks in September, 2010, and gave a 12 hour short course on “Cohomological Theory of Crystals over Function Fields and Applications”.

3. Invited and hosted the visit by Prof. Dale Brownawell, Penn State University, who visited NCTS Sept 28-Oct 26, 2010. During this period, Prof. Brownawell gave a 10 hour short course titled “Topics in the Theory of Transcendental Numbers Related to the Function Field Setting”.

4. Invited NCTS postdoctoral fellow Dr. Chieh-Yu Chang to offer a fall course on ”Fontaine's theorem in equal characteristic” from Oct 1 to Dec. 6, 2010.

5. “NCTS special day on Serre's conjecture”, talks presented by graduate students, Feb. 24, 2011.

6. Shor t course on “Deligne's work on Weil conjectures”, lectured by NCTS post doctoral fellow Dr. Jiangwei Xue, March 21-31, 2011.

7. 4 intensive lectures in March, 2011 to prepare students for Serre's special lecture series in April.

8. Invited and hosted the visit by Prof. Rene Schoof from University of Roma II, Italy, for 3 weeks in April. Prof. Schoof gave a 16 hour short course on “Finite group schemes over rings of integers of number fields”, April 7 to April 22, 2011.

9. Invited and hosted the visit by Prof. Jean-Pierre Serre, College de France, France, April 10-17, 2011. Prof. Serre gave 8 hour lectures on”Introduction to the Sato-Tate conjecture for algebraic varieties”. Prof. Serre wrote a book titled “Lectures on NX(p)” based on his lecture series given at NCTS in 2009 and 2011. This book, currently posted on NCTS website, will be published by AK Peters.

10. Co-organized (with Prof. Ramin Takloo-Bighash, University of Illinois at Chicago, U.S.A.) Atkin Memorial Lecture and Workshop on Galois Representations and Noncongruence Modular Forms, Chicago, U.S.A., April 29-May 1, 2011.

11. Invited and hosted the visit by Prof. Henri Darmon, McGill University, Canada, June 10-24, 2011. Prof. Darmon gave a 6 hour short course on “Algebraic cycles and p-adic deformations”.

12. Invited and hosted the visit by Prof. Ravi Ramakrishna, Cornell University, U.S.A., who gave a 6 hour short course on “A survey on Serre's conjecture and its generalizations”, June 16-17, 2011.

13. Co-organized (with Prof. King-Fai Lai of National Sun Yet Sen University) the conference “Galois representations, automorphic forms and Shimura varieties”, June 20-23, 2011. This conference is jointly sponsored by NCTS and NSF through a conference grant from NSF granted to me. Among the audience were 4 graduate students from universities in the US.

14. "NCTS special day on noncongruence subgroups", June 27, 2011. This is a one day conference with 5 international speakers.

15. Hosted the visit by Prof. YoungJu Choie, Pohang Institute for Science and Technology, Korea, July 4-15, 2011. Prof. Choie gave one seminar talk on ”Weakly holomorphic modular forms”. We worked together to seek connections between weakly modular forms and noncongruence forms.

16. Hosted the visit by Prof. Jiu-Kang Yu, Purdue University, U.S.A., July 5-8, 2011. Prof. Yu gave a seminar talk on “Zeta functions of graphs and complexes from buildings”.

17. Hosted the visit by Prof. Ling Long and Prof. Richard Ng, Iowa State University, U.S.A., June 14-28, July 10-21, 2011. Prof. Long and Prof. Ng lectured in the Galois representations conference and the one day workshop on noncongruence modular forms. Prof. Long and I worked on our joint research project.

18. Invited and hosted the visit by Prof. Alexey Zykin, State University-Higher School of Economics, Russia, July 17-26, 2011. Prof. Zykin gave a seminar talk on "Asymptotic properties of zeta functions" and discussed math research with me.

19. Co-organized (with Prof. YoungJu Choie, POSTECH, Korea) 2011 Taiwan-Korea workshop - number theory, held in POSTECH, Pohang, Korea, July 24-26, 2011. I led a group of 8 number theorists from Taiwan to attend this

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conference.20. Invited Prof. S-T. Yau, Harvard University, U.S.A.

to give a special lecture on “Mass and momentum in general relativity”, July 29, 2011.

Conferences / Workshop Talks- China -1. International Congress of Chinese Mathematicians,

Beijing, Dec. 17-22, 2010, invited plenary speaker, title: ”The arithmetic of noncongruence modular forms”.

2. Mathamatics Forum, Sanya, Dec. 23-26, 2010, invited panelist.

3. Number Theory and Related Topics- conference in honor of Prof. Keqin Feng's 70th birthday, Hefei and Huangshan, June 6-12, 2011, invited speaker, title: “Zeta functions in combinatorics and number theory”.

- Korea -1. 2011 Korea- Taiwan Workshop - Number Theory,

July 24-26, 2011, Pohang,Korea, invited speaker, title: Modularity of Scholl representations of low degree.

- United States -1. Elliptic Curves and Crypto Workshop 2010,

Microsoft Research, Redmond,WA, Oct 18-22, 2010, invited speaker, title: “Atkin-Swinnerton-Dyer congruences on noncongruence modular forms”.

2. Atkin Memorial Lecture and Workshop on Galois Representations and Non-congruence Modular Forms, Chicago, U.S.A., April 29-May 1, 2011, invited Atkin Memorial Lecturer, title: The arithmetic of noncongruence modular forms.

Colloquium/Seminar Talks- China -1. Number Theory Seminar, Shandong University,

Jinan, May 31, 2011, title:"The arithmetic of noncongruence modular forms".

2. Number Theory Seminar, Shandong University, Jinan, June 2, 2011, title:"Modularity of low degree Scholl representations".

- United States -

1. Distinguished Women Lecture, University of Texas, Austin, March 7, 2011,title: "Zeta functions in combinatorics and number theory".

2. Number Theory seminar, University of Texas, Austin, March 8, 2011, title:"The arithmetic of noncongruence modular forms".

3. Colloquium, Ohio State University, Columbus, OH, April 29, 2011, title:"Zeta functions in combinatorics and number theory".

4. Number Theory seminar, University of Wisconsin, Madison, May 2, 2011,title: "Modularity Scholl representations of low degree".

- Taiwan -1. Colloquium, Providence University, November

23, 2010, title: "Applicationsof number theory to network constructions".

2. Colloquium, National Chang-Hua Normal University, December 2, 2010, title:"Applications of number theory to network constructions".

3. Colloquium, Tamkang University, March 22, 2011, title: "Zeta functions incombinatorics and number theory".

4. Colloquium, Academia Sinica, May 12, 2011, title: "Zeta functions in combi-natorics and number theory".

5. Number Theory Seminar, NCTS, May 25, 2011, title: "Recent progress on Sato-Tate conjecture".

6. Number Theory Seminar, National Chung-Cheng University, June 30, 2011,title: "Zeta functions in combinatorics and number theory".

PublicationsA. NCTS affiliated1. Zeta functions in combinatorics and number

theory, Proceedings of the Fourth International Congress of Chinese Mathematicians, Hangzhou, China, 2007, AMS/IP Studies in Advanced Mathematics, vol. 48 (2010), 351-366.

2. Modular curves and coding theory: A survey. Proceedings of 9th International Conference on Finite Fields and Their Applications, Dublin, July, 2009, Contemporary Math., vol 518, 301-313 (2010), Amer. Math. Soc., Providence.

3. Zeta functions of group based graphs and complexes. Fields Institute Communications, vol

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60, 2011, Volume WIN - Women In Numbers, 225-236.

4. ( joint with Oliver Atkin, Ling Long and Tong Liu) Galois representations with quaternion multiplications associated to noncongruence modular forms, submitted.

5. (w ith Li ng Long) Fou r ie r coe_cient s of noncongruence cuspforms, Bulletin London Math. Soc., to appear.

6. (joint with Maosheng Xiong) Statistics of zeros of families of L-functions over function fields: a survey, submitted.

7. The arithmetic of noncongruence modular forms. Proceedings of the Fifth International Congress of Chinese Mathematicians, Beijing, China, 2010, preprint, 2011, submitted.

8. (joint with Yang Fang and Chian-Jen Wang) The zeta functions of complexes from Sp(4), submitted.

B. Acknowledging NCTS1. (with Ming-Hsuan Kang) Zeta functions of

complexes arising from PGL(3), submitted.

VI. Ming-Chia Li

National Chiao-Tung UniversityNational Center for Theoretic Sciences, Center Scientist (08/2010-07/2011)

NCTS Activities- 2011 NCTS Workshop on Dynamical Systems, May, 2011 (one of the organizers)

Visitors• Professor Leonid Bunimovich, Georgia Tech, USA (May. 1-15, 2011)

Research works1. S. Kiriki, M.-C. Li and T. Soma, 2010, Coexistence

of invariant sets with and without SRB measures in Henon family, Nonlinearity, 23, 2253-2269

2. H.-J. Chen and M.-C. Li, 2011, Environmental tax policy, habit formation and nonlinear dynamics, Nonlinear Analysis-Real World Applications, 12, 246-253.

3. M.-C. Li and M.-J. Lyu, 2011, Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition, Journal of Differential Equations, 250, 799-812.

4. M.-C. Li and M.-J. Lyu, 2011, Positive topological entropy for multidimensional perturbations of topologically crossing homoclinicity, Discrete and Continuous Dynamical Systems, ser. A, 20, 243-252.

VII. Duy-Minh Nhieu

National Central University, ProfessorNational Center for Theoretic Sciences, Center Scientist

Conferences: First Taiwan Geomet r y Symposium, NCTS-South(NCKU), Nov 20, 2010. Invited speaker.

Workshop on Mean Cu r vat u re Equat ion in Heisenberg Geometry, Academia SinicaDec 18-19, 2010. Invited speaker.

Workshop/Seminar/Minicourse:NCTS Summer Course in Geometric and Analysis: "The Heat Equation on Riemannian manifolds", NCTS, July 11-15, 2011, Instructor.

RefereeIEEE transaction on signal processing.

Publicationsjoint with D. Danielli, N. Garofalo and S. PaulsThe Bernstein problem for embedded surfaces in the Heisenberg group H^1,Indiana Univ. Math. J. 59 (2010), no. 2, 563–594.

joint with D. Danielli, N. GarofaloIntegrability of the Sub-Riemannian Mean Curvature of Surfaces in the Heisenberg Group,Proceedings of the AMS, (to appear)

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VIII. Shuenn-Jyi Sheu

National Central UniversityAcademia Sinica

Activities Organized:1. Organize two series of study seminars. Stochastic Control in Insurance Advanced Stochastic Calculus

For the first topic, we want to learn basic knowledge of insurance and some interesting mathematical problems from insurance. We also learn the applications of stochastic control to insurance. This is a research area with many chances for mathematician.

For the second topic, we learn theory of stochastic calculus. The topic is important and has broad applications.

The participants include students, research assistants, post docs and colleagues f rom Academia Sinica, National Central University.

2. Organize a one day workshop jointly with Chii-Ruey Hwang (Academia Sinca, Yuan-Chung Sheu (NCTU):

Probability One Day Workshop, 2011.2.23, at Academia Sinica, TaipeiSpeakers include: Prof. Hideo Nagai, Prof. Makoto Maejima and Dr. Yusuke Watanabe from Japan and Prof. Chii-Ruey Hwang, Prof. Yuan-Chung Sheu, Prof. Sean Han, Prof. Guan-Yu Chen from Taiwan. The workshop provides a chance for us to meet and discuss.

3. Organ ize reg u la r probabi l i t y semina r at Department of Mathematics, National Central University. We have a small group working on probability theory and statistics. We invite people to give talks. This also provides chance for our group to learn and to meet each other regularly.

VisitorsDaniel Hernandez-Hernandez(Center for Research in Mathematics (CIMAT), Mexico)Sep 16-Oct 2, 2010Hideo Nagai (Osaka Univ.), Feb 21-24Naoyuki Ichihara(Hiroshima Univ.), Sep 21-Nov 21, 2010

Hidehiro Kaise (Nagoya Univ.), March 10-March 17, 2011Yasushi Ishikawa (Ehime Univ.), April 30-May 8, 2011Yusuke Watanabe (Osaka Univ.), April 1-July 31, 2011

Conference/Invited talk/Organizer1. On Accelerating the diffusions to the equilibrium,

Stochastic Analysis and Its Applications (SAA), Osaka, Japan, Aug.30-Sep3, 2010

2. On the Hamilton-Jacobi-Bellman equation for an optimal Consumption Problem,Mathematical Finance and Related Issues, Kyoto, Japan, Sep 12-Sep 15, 2010.

3. On HJB for Some Portfolio Optimization Problem: Some Recent Results,International Research Forum: What Can The Academia Community Learn

From The Global Crisis? Models , Methods and Transfer, Hong Kong, Hong Kong Polytechnic University, Dec 14-18, 2010.

4. On a Consumpt ion Problem with Part ial Information, SIAM Conference on Control and Its Applications, Hyatt Regency Baltimore, USA, July 25-27, 2011.

5. OSAKA SPA Conference (Stochastic Processes and Their Applications)

Organize the session on Mathematical Finance and Stochastic Control. Sep .6-10, 2010.

Publications1. (with H. Hata) An optimal consumption and

investment problem with Partial information, to appear in Risk and Decision Analysis.

2. (with H. Hata) On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: I. Existence of solution, submitted and under revision.

3. (with H. Hata) On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: II. Verification Theorem, submitted and under revision.

4. (with Naoyuki Ichihara) Large time behavior of solutions of Hamilton- Jacobi- Bellman

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equations with quadratic nonlinearity in gradients, submitted.

IX. Chih-Wen Shih

National Chiao-Tung UniversityNational Center for Theoretic Sciences, Center Scientist (08/2010-07/2011)

Conferences and Visiting- Annual Meeting, Taiwan Mathematical Society- AMMCS 2011, Waterloo, Canada, 7/25-7/29• MBI, Ohio State University, USA, 3/20-4/1,• Department of Mathematics UBC (Professor Yue-

Xian Li), Canada

NCTS Activities- 2011 NCTS Workshop on Dynamical Systems,

May, 2011 (organizing committee)- Dynamics Systems summer school, July-Aug. 2011

(organizing committee)

Research worksCh i h-Wen Sh i h , Ju i -P i n Tseng, Globa l

synchronization and asymptotic phases for a ring of identical cells with delayed coupling, SIAM J. Math. Anal., Vol. 43, 4(2011), 1667-1697.

Kang-Ling Liao, Chih-Wen Shih, Snapback repellers and homoclinic orbits for multi-dimensional maps, J. Math. Anal. Appl., 386(2011), 387-400.

Avner Friedman, Chiu-Yen Kao, Chih-Wen Shih, Transcriptional control in cell differentiation: asymptotic limit, submitted.

Kang-Ling Liao, Chih-Wen Shih, Jui-Pin Tseng, Synchronized oscillations in a mathematical model of segmentation in zebrafish, Nonlinearity, under revision

Kang-Ling Liao, Chih-Wen Shih, A lattice model on somitogenesis of zebrafish, submitted.

F.2 Honorary Fellowship

I. Dong-Ho Tsai

National Tsing Hua University, Professor

Visit during the year 2011:• Department of Mathematics, East China Normal

University, March 16-29, 2011.NCTS activities during the year 2011:• NCTS various seminars.• 2011 NCTS Distinguished Lecture Series.• Organizer of the conference "NCTS Taiwan-Japan

Joint Workshop on PDEs and Geometric Analysis, December 19-21, 2011".

Publications during the year 2011:• Y.-C. Lin, C.-C. Poon, D.-H. Tsai (2011) Contracting

convex immersed closed plane curves with slow speed of curvature, to appear in Transactions of the AMS, 2011.

• Y.-C. Lin, D.-H. Tsai (2011) Application of Andrews and Green-Osher inequalities to nonlocal flow of convex plane curves, submitted.

• Y.-C. Lin, D.-H. Tsai (2011) Refined entropy estimate for expanding convex closed plane curves, submitted.

• Y.-C. Lin, D.-H. Tsai (2011) Remarks on some isoperimetric properties of the k -1 flow, submitted.

• Y.-C. Lin, D.-H. Tsai (2011) On a general nonlocal linear curvature f low of convex plane curves, preprint.

II. Yifan Yang

National Chiao Tung University, ProfessorNational Center for Theoretic Sciences, Center Scientist

Conference talks (2010—2011)1. Modular forms of half-integral weights on SL(2,Z),

Automorphic forms and related topics, NCTS, Hsinchu, Taiwan, July 7—9, 2010.

2. Apery limits and special values of L-functions, Tokyo Metropolitan University workshop, August 24, 2010.

3. Jacobsthal identity for Q(sqrt(-2)), Workshop on number theory, geometry, and physics at the crossroads, Tsuda College, Japan, August 30—31, 2010.

4. Algebraic transformations of hypergeometric functions, Annual meeting of the Taiwanese Mathematical Society, December 10—12, 2010.

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5. Cuspidal rational torsion subgroups of J_1(N), Algebraic number theory and related topics, Kyoto University, December 6—10, 2010.

6. Cu spidal ra t ional tors ion subg roups o f J_1(N), 5th International Congress of Chinese Mathematicians, Beijing, December 17—22, 2010.

7. S c h wa r z i a n d i f f e r e n t i a l e q u a t i o n s a n d a u tomor ph ic for m s on S h imura c ur ve s , International conference on Galois representations, automorphic forms, and Shimura varieties, NCTS, June 20—23, 2011.

8. S c h wa r z i a n d i f f e r e n t i a l e q u a t i o n s a n d automorphic forms on Shimura curves, NCTS, Taiwan – PMI, Korea workshop – number theory, Postech, July 24—26, 2011.

9. S c h wa r z i a n d i f f e r e n t i a l e q u a t i o n s a n d automorphic forms on Shimura curves, workshop on arithmetic geometry, October 10—13, 2011.

Visits (2010—2011)1. Waseda Universit y, Japan , visit Ki-Ichiro

Hashimoto from January 20 to February 10, 2010.2. Tsuda College, Japan, visit Shinji Fukuhara from

August 21 to September 4, 2010.3. Waseda Universit y, Japan , visit Ki-Ichiro

Hashimoto from June 29 to July 21, 2011.4. Tohoku University, visit Takao Yamazaki from

November 6 to 13, 2011.

NCTS Activities1. NCTS number theory seminar.2. NCTS Shimura curve seminar (organizer).

Research Works (2010—2011)1. A r is t ides Kontogeorg is and Yifan Yang,

automorphism groups of hyperelliptic modular curves, LMS J. Comp. Math. 13 (2010), 144—163.

2. Yifan Yang and Jeng-Daw Yu, structure of the cuspidal rational torsion subgroups of J_1(p^n), J. London Math. Soc 82 (2010), 203—228.

3. **Shinji Fukuhara and Yifan Yang, twisted Hecke L-values and period polynomials, J. Number Theory 130 (2010), 976—999.

4. Yifan Yang and Wadim Zudil in, an Sp _ 4

modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds, Contemporar y Mathematics 517, 381—413.

5. **Yifan Yang, congruences of the partition function, Int. Math. Res. Not., 2011, 3261—3288.

6. **Heng Huat Chan, Ling Long, and Yifan Yang, a cubic analogue of the Jacobsthal identity, Amer. Math. Monthly 118:4 (2011), 316—326.

7. **Ki-Ichiro Hashimoto, Ling Long, and Yifan Yang, Jacobsthal identity for Q(sqrt(-2)), Forum Math., in press.

8. **Heng Huat Chan, Yoshio Tanigawa, Yifan Yang, and Wadim Zudilin, new analogues of Clausen’s identities arising from the theory of modular forms, Adv. Math, in press.

9. **Shinji Fukuhara and Yifan Yang, a basis for and representations of integers as

sums of squares, accepted for publication by the Ramanujan Journal.

10. **Fang-Ting Tu and Yifan Yang, la t t ice packing from quaternion algebras, accepted for publication, RIMS Kokyuroku Bessatsu.

11.**Fang-Ting Tu and Yifan Yang, algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves, submitted.

12. **Yifan Yang, modular forms of half-integral weights on SL(2,Z), submitted.

13. **Yifan Yang, Schwarzian differential equations and Hecke eigenforms on Shimura curves, submitted.

打 ** 為以 NCTS 名義發表

Summary of research worksYang is a specialist in the theory of modular forms

and modular curves. In [2], he and Jeng-Daw Yu of the National Taiwan University studied the structure of cuspidal Q-rational torsion subgroups of the Jacobians associated to the modular curves X_1(N). In a series of joint works with Fukuhara (References [3,9] above), Yang studied the periods of cusp forms. By combining Rankin’s methods, explicit evaluation of Hankel determinants, and so on, they obtained bases for the space of modular forms on congruence subgroups of levels 2 and 4 in terms of Eisenstein series. As applications, they found new formulas for the number of ways to write a positive integer as

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sums of squares and new methods to determine the special values of L-function of cusp forms twisted by Dirichlet characters.

In [7], using the theories of Hecke characters, CM modular forms, Galois representations, and algebraic curves, Yang and his coauthors obtained an beautiful analogue of the classical Jacobsthal identity for the case Q(sqrt(-2)). A simpler version for the case Q(sqrt(-3)) was treated in a separate paper [6], which involves only elementary properties of the Legendre symbols and Jacobi sums.

Yang [5] also worked on the classical problem of congruences for the par tition function. He demonstrated that it is possible to obtain new congruences for the partition function using only modular forms of half-integral weights without the use of the Shimura correspondence and Galois representations, which were key ingredients in Ken Ono’s treatment of the problem. While he was working on this problem, he also discovered an explicit Shimura correspondence between modular forms of half-integral weights on SL(2,Z) and certain newform subspace of cusp forms of level 6. A paper [11] has recently been submitted for publication.

Finally, Since the second half of the last year, he focused his research on automorphic forms on Shimura curves. He showed that if a Shimura curve has genus zero, then automorphic forms on it can be expressed in terms of solutions of the Schwarzian differential equations. He then devised a method to compute Hecke operators on these functions. By interpreting hypergeometr ic functions as automorphic forms on Shimura curves, he and F.-T. Tu established some elegant identities among hypergeometric functions. Moreover, he and Ki-Ichiro Hashimoto have obtained several new explicit families of hyperelliptic curves of genus 2 with quaternionic multiplication. In addition, he continued his collaboration with Shinji Fukuhara on periods of cusp forms and obtained new formulas for the number of ways to write a positive integer as sums of squares.

F.3 Young Theory Award

I. Jung Chao Ban

Department of Applied Mathematics,

Nat ional Dong Hwa University, Associate Professor

Conferences and Visiting–Portugal –1. Inter nat ional Conference on Dif ferent ial

& Difference Equations and Applications, Conference in honour of Professor Ravi P. Agarwal

Department of Mathematics, Azores University, Ponta Delgada, Portugal July 4 - 8, 2011

NCTS Activities1. 2011 CTS Workshop on Dynamical Systems -

invited speaker and organizer (May 12~14, 2011)

Publications1. Zeta functions for two-dimensional shifts of finite

type, Memoirs of the Amer. Math. Soc. (2011) (SCI), to appear (with Wen-Guei Hu, Song-Sun Lin and Yin-Heng Lin).

2. Factor, Diamond and Density of Pressure, Proc. Amer. Math. Soc. vol. 139, No 11, 3985-3997 (2011) (SCI) (with Chih-Hung Chang)

3. The complexity of Permutive Cellular Automata, Journal of Cellular Automata. (2011) (with Chih-Hung Chang, Ting-Ju Chen and Mei-Shao Lin)

4. Diamond in multi-layer cellular neural networks, International Journal of Circuit Theory and Applications, (2011) to appear. (with Chih-Hung Chang and Song-Sun Lin)

II. Chen, Jiun-Cheng

National Tsing Hua University, Associate Professor

Conferences and visiting• Algebraic Geometry in East Asia (Nov, 2011):

Invited Speaker.• Visiting RIMS (July-August, 2011)

NCTS Activities• NCTS Algebraic Geometry Seminar• NCTS Student Complex geometry Seminar

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Submitted• Jiun-Cheng Chen, Hsian-Hua Tseng, On the

Bogomolov-Miyaoka-Yau inequality for Deligne-Mumford surfaces

III. Nan-Kuo Ho

National Tsing Hua University, Associate Professor

Conferences (invited speaker)The 2nd East Asian Symplectic Geometry Conference, KIAS, Seoul, South Korea, June 21-25, 2011.

Visits1. Newton Institute, Cambridge. Attend Moduli

Space program from March 1, 2011 to March 13, 2011, Gave a talk at the Institute on March 8.

2. Oxford University, Oxford. Attend Representations of Surface groups and Higgs bundles workshop from March 13, 2011 to March 18, 2011.

3. The University of Hong Kong, Hong Kong. Visit Prof. Siye Wu from April 24, 2011 to May 8, 2011.

4. KIAS, Seoul, Attend the 2nd East Asian Symplectic Geometry Conference from June 21, 2011 to June 25, 2011.

5. Newton Institute, Cambridge. Attend Moduli space closing conference from July 27, 2010 to July 1, 2011.

6. University of Toronto, Toronto, Visit Prof. Lisa Jeffrey from July 11, 2011 to August 26, 2011.

NCTS Activities1. Organizing the NCTS and NTHU joint Geometry

and Topology Seminar 2011 Fall. Website to the seminar:http://www.math.nthu.edu.tw/~nankuo/seminar.html

2. Invite Prof. Graeme Wilkin (National University of Singapore) for a visit, September 17-25, 2011.

3. Invite Prof. Siye Wu (University of Hong Kong) for a visit, May 20-June 17, 2011.

4. Organizing the NCTS(Taiwan)-CPT(France) joint workshop which was held on February 21-25, 2011.

Research Works1. (Joint with C.C. Melissa Liu) Anti-perfect Morse

Stratification, Selecta Mathematica 17 (2011), no.2 , 505-532

IV. Ching-Lung Lin

National Cheng-Kung University,Professor of National Cheng-Kung University.

I do the qualitative and quantitative uniqueness for some equations and elasticity systems.These results are quite useful in studying the nodal sets of eigenfunctions or localization in the Anderson-Bernoulli model.

It is an important tool for stability estimates in inverse boundary value problems.It also connected with volume bounds of unknown inclusions in terms of boundary measurements.

VisitingsUniversity of Florence, Italy, July 23- August 1,2011Dept. of Math., Hokkaido Univ, August 11-25 2011.

NCTS Activities第 19 屆微分方程研討會

Research Works• Ching-Lung Lin, Gen Nakamura, Gunther

Uhlmann and Jenn-Nan Wang (2011), Quantitative strong unique continuation for the Lame system with less regular coeff icients, Methods and Applications of Analysis, (18), No.1, 85-92.

• Ching-Lung Lin, Gen Nakamura and Jenn-Nan Wang (2011), Quantitative uniqueness for second order elliptic operators with strongly singular coeff icients, Revista Mathematica Iberoamericana.(27), No.2, 475-491.

• Ching-Lung Lin, Sei Nagayasu and Jenn-Nan Wang (2011), Quantitative uniqueness for the power of Laplacian with singular coefficients, To appear in Ann. Scuola Norm. Sup. Pisa Cl.Sci.(5) , NO.3.

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V. Jeng-Daw Yu

National Taiwan University, Assistant Professor

Conferences, Workshops and Visiting- Canada -Visiting: Queen’s University, Kingston, July 2 – 12. [Hosted by Prof. Noriko Yui]Workshop: Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds. Fields Institute, Toronto, July 16 – 25. [Invited speaker]

- Germany -(Long Term) Visiting: Universität Duisberg – Essen, Essen, September 12, 2011 – June 30, 2012 (expected). [Hosted by Prof. Hélène Esnault]

- Taiwan -School: TIMS 2011 Winter School on Number Theory. TIMS, National Taiwan University, February 8 – 11. [Speaker]

Publications• Special l i f t s of ordinar y K3 sur faces and

applications. To appear in Pure Appl. Math. Q.• Ordinary crystals with logarithmic poles. Preprint

(submitted).

F.4 Report of Post Doctors

I. Chieh-Yu Chang

National Center for Theoretical Sciences

Research:My current research is a continuation of my

previous work on transcendence theory in positive characteristic. In the past year, I spent much time on revising the papers [8, 9] and finally they were accepted. In [9], we have shown the Brownawell-Yu conjecture on the algebraic independence of Drinfeld logartihms of algebraic points (note that the case of rank 2, non-CM, odd characteristic was proved in [6]). So I have been working on a natural generalization: algebraic independence of the logarithms of algebraic

points for pair-wise non-isogenous Drinfeld modules. It would have the following two important consequences.

Assuming the validity of the generalization mentioned above, then we would obtain the algebraic independence of the non-zero values of arithmetic Drinfeld modular forms (of positive weight) at pair-wise non-isogenous algebraic points on the Drinfeld upper half plane. The case concerning the CM points was carried out in [8]. On the other hand, I have made a conjecture as follows: two Drinfeld modules (defined over an algebraic function field) are isogenous if and only if their special L-values (at 1) are linearly dependent. This interesting classification via special L-values should follow by combining the generalization of [9] and Taelman's work on the analogue of class number formula for Drinfeld modules (to appear in Ann. Math.).

Carlitz polylogarithms are analogues of the classical polylogarithms. In [1], we have shown that all the algebraic relations among the Carlitz polylogarithms of algebraic points are generated by linear relations over the base field (the rational function field over a given finite field). In [12], we give a necessary and sufficient criterion for the n-th polylogarithms of algebraic points being linearly dependent in terms of the given algebraic points (note that the classical situation is still an open problem).

Invited talks at Seminars/Workshops/Conferences• TIMS Seminar on Arithmetic Geometry, Oct. 2010.• Colloquium of Applied Math. Dept of NCTU, Dec.

2010.• Colloquium of Math. Dept of NCKU, Dec. 2010.• 5th ICCM 2010, Dec. 2010.• Workshop on the Arithmetic of Function Fields,

London, June 2011.• NCTS Internat ional Conference on Galois

representations, Automorphic Forms and Shimura Varieties, June 2011.

• TIMS Summer School on Number Theory, July 2011.

Conferences attended:• The 3rd MSJ-SI Conference: Development of

Galois-Teichmuller Theory and Anabelian

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Geometry, Oct. 25-30 2010 (Kyoto).• 5th ICCM 2010, Beijing, Dec. 17-22 2010.• Workshop on the Arithmetic of Function Fields,

London, June 13-17 2011.• NCTS Internat ional Conference on Galois

representations, Automorphic Forms and Shimura Varieties, Hsinchu, June 20-23, 2011.

Publications and Preprints:[1] C.-Y. Chang and J. Yu, Determination of algebraic

relations among special zeta values in positive characteristic, Adv. Math. 216 (2007), 321-345.

[2] C.-Y Chang, A note on a refined version of Anderson-Brownawell-Papanikolas criterion, J. of Number Theory 129 (2009), 729-738.

[3] C.-Y. Chang, M. A. Papanikolas, D. S. Thakur and J. Yu, Algebraic independence of arithmetic gamma values and Carlitz zeta values, Adv. Math. 223 (2010), 1137-1154.

[4] C.-Y. Chang, M. A. Papanikolas and J. Yu, Geometric gamma values and zeta values in positive characteristic, Int. Math. Res. Notices (2010) vol. 8, 1432-1455.

[5] C.-Y. Chang, Transcendence of special values of quasi-modular forms, to appear in Forum Math.(DOI 10.1515/FORM. 2011. 072)

[6] C.-Y. Chang and M. A. Papanikolas, Algebraic relations among periods and logarithms of rank 2 Drinfeld modules, Amer. J. Math.133 (2011), 359-391.

[7] C.-Y. Chang, M. A. Papanikolas and J. Yu, Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic, Algebra & Number Theory 5 (2011), 111-129.

[8] C.-Y. Chang, Special values of Drinfeld modular forms and algebraic independence, to appear in Math. Ann. (DOI 10.1007/s00208-011-0633-8)

[9] C.-Y. Chang and M. A. Papanikolas, Algebraic independence of periods and logarithms of Drinfeld modules. With an appendix by B. Conrad, to appear in J. Amer. Math. Soc. 25 (2012), 123-150.

[10] C.-Y. Chang, Frobenius difference equations and difference Galois groups, submitted 2010.

[11] C.-Y. Chang, On periods of the third kind for rank 2 Drinfeld modules, preprint 2011.

[12] C.-Y. Chang and M.A. Papanikolas, On Carlitz tensor powers and polylogarithms, preprint 2011.

II. Chi-Hua Chan


Research:Sturm-Liouville eigenvalue problem:

In this year, I keep researching a special type of Strum-Liouville eigenvalue problem and its inverse problem, based on the previous work collaborated with Professor Chao-Liang Shen in National Tsing-Hua University. We Study the distribution and the property of the nodal points of this special type of Strum-Liouville eigenvalue problem. We find that the distribution of nodal points of this type is similar to the classical type and prove the interlacing property of the nodal points with two different boundary conditions of this type.

Additionally, collaborating with Professor Kuo-Chang Chen in National Tsing-Hua University, we try to study some problems in celestial mechanics by eigenvalue problem version.

Seminar:2011 NCTS Short Course on Analysis (2011/3/17-2011/4/21)

Title:Introduction to Dirichlet series and the zeta function

Abstract:Dirichlet series is a "discrete" transform of

frequent occurence in analysis. In this course, we want to introduce the theory of Dirichlet series. The theory involved will be simple in the sense that much of it could be conjectured from the theory of power series. And yet this "discrete" transform will provide a sort of model for the more complicated integral transforms to follow.

As a special type of Dirichlet series, some properties of the zeta function will of course confirm

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and illustrate the results of Dirichlet series, but in addition it will have specific properties resulting from its special definition.

Publication and Preprint:1.Chi-Hua Chan “Some eigenvalue problems

for vectorial Sturm-Liouville equations with eigenparameter dependent boundary conditions” Trans. Amer. Math. Soc. 364 (2012), 119-136

2. Chi-Hua Chacn “ On the eigenvalues and the nodal points of the eigenfunctions of some eigenvalue problems with eigenparameter dependent boundary conditions”(2011) Submitted

III. Jiangwei Xue


Research:1. Hodge group of Jacobians of superelliptic curves

Continuing from my Ph.D work, I study [1] a certain subvariety of the jacobian variety of superelliptic curves defined by the equation yq = f(x).Under certain mild conditions, we determine the Hodge group (also knownas special Mumford-Tate group) and show that it is, in a sense, “as large aspossible”. This work is useful for the study of ranks of Mordell-Weil groups in infinite towers of function fields. A key improvement from earlier work is that we study a deeper arithmetic property of the multiplicities related to the differential forms of the first kind.2. Long Exact Sequence of the Chinese reminder

theoremWe use the philosophy of cohomology to give a

generalized form of the Chinese reminder theorem[2]. In particular, given a ring R and a list of ideals I0; : : : ; In, we build a chain complex of quotient rings and show that this complex is a long exact sequence if R is an arithmetic ring. In particular, it holds for all Dedekind domains. The main ingredient in the proof is the Koszul complex, which is an important tool for the study of commutative algebras.Short Course:Deligne's work on Weil ConjecturesMar. 21-31, 2011

Summary: The Weil conjecture concerns with the number of the solutions of polynomial equations over finite fields. It has motivated significant development of algebraic geometry and culminated in Deligne's proof of the analogue of the “Riemann Hypothesis” using l-adic cohomology. In this short course, we present a part of the Deligne's work (commonly known as“Weil II”). This result is a corner stone of the contemporary number theory,which has numerous implications.

Visiting:2011/1/26 Visit Chulalongkorn University Thailand for 5 days. Host: Prof. Yotsanan Meemark2011/1/31 Visit Hong Kong University of Science and Technology for a week. Host: Prof. Maosheng Xiong

Talks:• Hodge Groups of certain superelliptic Jacobians,

Academia Sinica, Taipei, Aug 21st, 2010.• p-adic Analysis and the Zeta functions of a

Hypersurface, NCTS, Aug 24th, 2010.• Introduction to étale fundamental group, NCTS,

Feb 23, 2011.• Etale fundamental groups, lisse sheaves, and

L-functions, NCTS, Mar 9, 2011.

Publication and Preprint1. Hodge groups of certain superelliptic Jacobians II,

Mathematical Research Letters (MRL) Vol. 18.4, 2011.

2. Long Exact Sequence of Chinese reminder theorem for Arithmetic rings, preprint.

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Preprints 87 ‹‹-

Preprints

Series I Title and Author

2011-1-01Structure-Preserving Arnoldi-type Algorithms for Solving Palindromic Quadratic Eigenvalue Problems in Leaky Surface Wave Propagation Tsung-Ming Huang, Wen-Wei Lin, Chin-Tien Wu

2011-1-02 The Cutoff Phenomenon for Ehrenfest Processes Guan-Yu Chen, Yang-Jen Fang, and Yuan-Chung Sheu

2011-1-03 A Study to the 3n+1 Problem with State Transition Model Shu-Ming Chang, Lung-Lung Liu

2011-1-04 Applying Snapback Repellers in Resource Budget Models Shu-Ming Chang, Hsun-Hui Chen

2011-1-05Optimal burn-in policy for highly reliable products using Gamma degradation process.Tsai, C. C., Tseng, S. T.* and N. Balakrishnan

2011-1-06Dynamics of A Periodically Pulsed Bio-reactor Model with A Hydraulic Storage Zone Sze-Bi Hsu, Feng-Bin Wang, Xiao-Qiang Zhao

2011-1-07Monitoring batch process with multiple on-off steps in semiconductor manufacturing.Lee, S. P., Chao A. K. , Tsung, F., Wong, DSH, Tseng, S. T. and Jang S. S.

2011-1-08Sub-Riemannian Geodesics and Heat Operatoron Odd Dimensional SpheresMauricio Godoy Molina, Irina Markina

2011-1-09 Deconvolution for the Pompeiu Problem on the Heisenberg Group, I Der-Chen Chang, Wayne Eby, and Eric Grinberg

2011-1-10A Semiorthogonal Generalized Arnoldi Method and Its Variations for Quadratic Eigenvalue Problems Wei-Qiang Huang, Tiexiang Li, Yung-Ta Li and Wen-Wei Lin

2011-1-11 Factorization of Lipschitz Quaternions Cherng-tiao Perng

2011-1-12 Periods of the Third Kind for Rank 2 Drinfeld Modules Chien-Yu Chang


2011-1-28 Error Analysis of The Generalized MAC Scheme Yin-Liang Huang, Jian-Guo Liu, and Wei-Cheng Wang

2011-1-29Regression-adjusted multivariate functional profiles monitoring and diagnosis. Tseng, S. T. and Zou, C. L.

2011-1-30Existence of Traveling Wave Front Solutions of Predator Prey System with Holling Type III Functional Response Chi-Ru Yang and Ting-Hui Yang

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Preprints 88‹‹-


2011-1-13 On the Solutions to a Liouville-type System Involving Singularity Zhi-You Chen, Jann-Long Cherny, Yong-Li Tang

2011-1-14 A Refuge-Mediated Apparent Competitoin Model Sze-Bi Hsu and Lih-Ing Wu Roeger

2011-1-15Subfunctionalization Reduces the Fitness Cost of Gene Duplication in Humans by Buffering Dosage Imbalances Ariel Fernández, Yun-Huei Tzeng, and Sze-Bi Hsu

2011-1-16Algebraic Transformations of Hypergeometric Functions and Auomorphic Forms on Shimura Curves Fang-Ting Tu and Yifan Yang

2011-1-17Schwarzian Differential Equations and Hecke Eigenforms on Shimura Curves Yifan Yang

2011-1-18 Modular Forms of Half-Integral Weights on SL(2,Z) Yifan Yang

2011-1-19 Improvement of the Shortest Path Problem with Geodesic-Like Method Wen-Haw Chen

2011-1-20 Residual Bounds of the Stochastic Algebraic Riccati Equation Chun-Yueh Chiang and Hung-Yuan Fan

2011-1-21 Preperiodic Points for Families of Polynomials D. Ghioca, L.-C. Hsia, and T. J. Tucker

2011-1-22 The Multifractal Spectra for the Recurrence Rates of Beta-Transformations Jung-Chao Ban and Bing Li

2011-1-23 On the Entropies of the Linear Cellular Automata Hasan Akin, Jung-Chao Ban, and Chih-Hung Chang

2011-1-24 On the Structure of Multi-Layer Cellular Neural Networks Jung-Chao Ban, Chih-Hung Chang, Song-Sun Lin

2011-1-25 Mis-specification Analyses of Gamma and Wiener Degradation Processes. Tsai, C. C., Tseng, S. T.* and N. Balakrishnan

2011-1-26A Conservative Scheme for Solving Coupled Surface-Bulk Convection-Diffusion Equations with an Application to Interfacial Flows with Soluble Surfactant Kuan-Yu Chen, Ming-Chih Lai

2011-1-27 Partially Implicit Motion of a Sharp Interface in Navier-Stokes Flow J. Thomas Beale

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2011-1-28 Error Analysis of The Generalized MAC Scheme Yin-Liang Huang, Jian-Guo Liu, and Wei-Cheng Wang

2011-1-29Regression-adjusted Multivariate Functional Profiles Monitoring and Diagnosis. Tseng, S. T. and Zou, C. L.

2011-1-30Existence of Traveling Wave Front Solutions of Predator Prey System with Holling Type III Functional Response Chi-Ru Yang and Ting-Hui Yang

Series II Title and Author

2011-2-01Generalization of Field Embeddings into Simple Algebras and the Noether-Skolem Theorem Chia-Fu Yu

2011-2-02 Embeddings of Fields in Simple Algebras over Global Fields Sheng-Chi Shih, Tse-Chung Yang and Chia-Fu Yu

2011-2-03 Which Polynomials are Characteristic? Chia-Fu Yu

Series III Title and Author

2011-3-01 The Hamiltonian Numbers of Möbius Double Loop Networks G. J. Chang, T.-P. Chang and L.-D. Tong

2011-3-02 Reconstructing Potentials from Zeros of One Eigenfunction X. Chen, Y.H. Cheng and C.K. Law

2011-3-03Optimal Upper Bounds for the Eigenvalue Ratios of One-Dimensional P-LaplacianC.Z. Chen, C.K. Law, W.C. Lian and W.C. Wang

2011-3-04 The Hamiltonian Numbers of Graphs T.-P. Chang and L.-D. Tong

2011-3-05 On a Bilinear Estimate of Schrödinger WavesYung-fu Fang

2011-3-06 Ergodicity of Mapping Class Group Actions on SU(2)-Character VarietiesWilliam M. Goldman, Eugene Z. Xia

2011-3-07 Action of the Johnson-Torelli group on Representation VarietiesWilliam M. Goldman, Eugene Z. Xia

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Preprints 90‹‹-


2011-3-08Quantitative Strong Unique Continuation for the Lame System with Less Regular Coefficients Ching-Lung Lin*, Gen Nakamura, Gunther Uhlmann and Jenn-Nan Wang

2011-3-09 When is the Direct Product of Generalized Mycielski Graphs a Cover Graph Hsin-Hao Lai, K. W. Lih, C.-Y. Lin, and L.-D. Tong

2011-3-10A Generalized Semi-Infinite Programming Method for Solving Optimal Power Flow with Transient Stability and Variable Clearing Time of Faults X. J. Tong, C. Ling, S. Y. Wu and L. Qi

2011-3-11A Smoothing SQP Method for Nonlinear Programs with Stability Constraints Arising from Power Systems X. J. Tong, L. Qi and S. Y. Wu

2011-3-12 Dehn Twists and Invariant Classes Eugene Z. Xia

2011-3-13An Entropy-Based Central Cutting Plane Algorithm for Convex Min-Max Problems with Infinite Constraints L. P. Zhang and S. Y. Wu and S.-C. Fang

2011-3-14A New Approach To the Weighted Peak-Constrained Least-Square Error FIR Digital Filter Optimal Design Problem L. P. Zhang and S. Y. Wu

2011-3-15 Self-Similar Solutions of the Euler Equations with Spherical Symmetry C.-C. Peng, W.-C. Lien

2011-3-16Nonlinear Stability Of Spherical Self-Similar Flows to the Compressible Euler Equations Ha, S.-Y., Huang, H.-C., Lien, W.-C.

2011-3-17Counting the Regularly Distributed Potential Resonances In Odd Dimensional Euclidean Spaces Lung-Hui Chen

2011-3-18An Elementary Proof for Bilinear Estimates of Homogeneous Wave Equations Tsai-Jung Chen, Yung-Fu Fang, Chung-Chou Jiang and Chi-Hua Liu

2011-3-19On the Constructions Holomorphic Vertex Operator Algebras of Central Charge 24 C.H. Lam

2011-3-20 Dade’s Invariant Conjecture for the Ree Groups 2F4(Q2) S.-C. Huang and F. Himstedt

2011-3-21 Generalized Shalika Models and Classification for SO4n Over P-Adic Local Fields Chufeng Nien, Dihua Jiang and Yujun Qin

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2011-3-22Twisted Gamma Factor of Cuspidal Representations of GL(N) Over A Finite FieldChufeng Nien

2011-3-23On the Equation Axm + Bym - Czm = 1 and Cyclotomic Numbers Over Finite FieldsWen-Fong Ke, Hubert Kiechle

2011-3-24 Matrix Near-Rings and 0-PrimitivityWen-Fong Ke and Johan H. Meyer

2011-3-25Contracting Convex Immersed Closed Plane Curves with Slow Speed of CurvatureYu-Chu Lin, Chi-Cheung Poon and Dong-Ho Tsai

2011-3-26 Stochastic Matching Pursuit for Bayesian Variable SelectionR-B Chen, C-H Chu, T-Y Lai and Y-N Wu

2011-3-27 Two-Person Red-and-Black Game with Lower LimitM.-R. Chen

2011-3-28Using Adaptive Multi-Accurate Function Evaluations in A Surrogate-Assisted Method for Computer ExperimentsW. Wang, R-B Chen and C-L Hsu

2011-3-29 Mixturetree: A Program for Constructing PhylogenyS.-C. Chen, M S. Rosenberg and B Lindsay

2011-3-30 Test for Dispersion Constancy in Stochastic Differential Equation ModelsS. Lee and M-H Guo

2011-3-31Accelerated Destructive Degradation Tests Robust to Distribution MisspecificationS-L Jeng, B-Y Huang and W.Q. Meeker

2011-3-32 Influence of Choices of Statistical Models on Neural Spike TrendS.-C. Chen, L-A Li, S. Li and J. He

2011-3-33A Deterministic Equivalent for the Analysis of Non-Gaussian Correlated MIMO Multiple Access ChannelsC-K Wen, G Pan, K-K Wong, Meihui Guo and J-C Chen.

2011-3-34A Stochastic Matching Pursuit (SMP) MATLAB Toolbox for Bayesian Variable SelectionR-B Chen, C-H Chu and J-Z Weng

2011-3-35Screening Procedure for Supersaturated Designs Using A Bayesian Variable Selection MethodR-B Chen, J-Z Weng and C-H Chu

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Preprints 92‹‹-


2011-3-36Discriminant Analysis and Classification of Heart Function with Cardiology Ultrasound in Left VentricleM-N Lo Huang , M-H Guo, J-M Chen , L-W Kao, D. Simpson and K-S Hsieh.

2011-3-37 A Moonshine Path for 5A and Associated Lattices of Ranks 8 and 16R.L. Griess Jr. and C.H. Lam

2011-3-38 Diagonal Lattices and Rootless EE8 PairsR.L. Griess Jr. and C.H. Lam

2011-3-39 Mckay's E6 Observation on the Largest Fischer GroupG. Hoehn, C.H. Lam, H. Yamauchi

2011-3-40Quadratic Spaces and Holomorphic Framed Vertex Operator Algebras of Central Charge 24C.H. Lam and H. Shimakura

2011-3-41 A New Existence Proof of the Monster by VOA TheoryR.L. Griess Jr. and C.H. Lam

‹‹- Appendix I

Appendix I

93

Name Field Duration

PEI-YU TSAI(Harvard University, Department of Mathematics)

Number Theory and Representation Theory 2011-01-01 ~2011-01-31

Jay Chu(The University of Texas at Austin)

Scientific Computation 2011-01-01 ~ 2011-01-07

Huseyin Kocak(University of Miami)

Computer ScienceR.L. Griess Jr. and C.H. Lam 2011-01-04 ~2011-01-12

Jean-Pierre Puel(University of Tokyo, Japan) PDE 2011-01-05 ~2011-01-12

Guangming Pan (Nanyang Technological University )

Statistics 2011-01-05 ~2011-01-19

Shui-Nee Chow(School of Mathematics George Institute of Technolo)

Dynamical Systems and Nonlinear Studies 2011-01-06 ~2011-01-14

Sergei Pilyugin(St. Peterburg State University) differential equation 2011-01-06 ~2011-01-16

Tzyy-Leng Horng(Feng Chia University) Differential Equation 2011-01-10 ~2011-01-15

Takayoshi Ogawa(Tohoku University)

Nonlinear partial differential equations 2011-01-13 ~2011-01-17

Kenji Nakanishi (Kyoto University ) Applied Mathematics 2011-01-13 ~2011-01-17

Nobu Kishimoto (Kyoto University ) Applied mathematics 2011-01-13 ~2011-01-20

Tsorng-Whay Pan (University of Houston ) Applied Mathematics 2011-01-14 ~2011-01-16

Maosheng Xiong(The Hong Kong University of Science and Technology)

Mathematical Biology 2011-01-15 ~ 2011-01-30

Sangyeol Lee (Seoul national University ) Statistics 2011-01-23 ~2011-01-30

Appendix I. Visiting Mathematicians 2011

‹‹-Appendix I

Appendix I

94

Name Field Duration

Ching-Long Lin(The University of Iowa)

Multiscale simulation of gas flow and particle transport in the human lungs 2011-02-01 ~2011-04-30

Otto Van Koert(Seoul National University) contact topology 2011-02-06 ~2011-02-13

Olof Runborg(NADA, KTH) Computational Sciences 2011-02-12 ~2011-02-26

Yen-Hsi Richard Tsai(The University of Texas at Austin)

Multiscale modeling and computations 2011-02-12 ~2011-02-26

Makoto MAEJIMA(Keio University) Levy process 2011-02-14 ~2011-02-22

Douglas Simpson (University of Illinois at Urbana-Champaign )

Statistics 2011-02-17 ~2011-03-08

Valentin Ovsienko(Univ-Lyon-1)

Group Representations Mathematical Physics 2011-02-19 ~ 2011-02-24

Otto Van Koert(Seoul National University) contact topology 2011-02-20 ~2011-02-26

Oleg Ogievetsky(CPT and Laboratoire Poncelet)


Yasuyuki Kawahigashi(University of Tokyo)


Jean-Phlippe Michel(Univ. Luxembourg)


Patrick Iglesias-Zemmour(ENS-Lyon)


Christian Duval(CPT)


Robert COQUEREAUX(CPT)


Siye Wu(University of Hong Kong)


‹‹- Appendix I

Appendix I

95

Name Field Duration

Yusuke Watanabe(Osaka University) Probability Theory and Statistics 2011-02-21 ~ 2011-02-24

Martin Schlichenmaier(Univ. Luxembourg)


Ping Xu(The Pennsylvania State University)


Patrick Iglesias-Zemmour (Laboratoire d’Analyse Topologie et Probabilité, CNRS )

Geometry 2011-02-25 ~2011-03-04

Mickael Montassier(Universite Bordeaux) Graph theory 2011-02-26 ~2011-03-14

Andre Raspaud(Universite Bordeaux 1) Graph theory 2011-02-26 ~2011-03-14

Koichiro Harada (Ohio State University ) Algebra 2011-02-26 ~2011-03-14

Federico Pellarin(University of Saint-Etienne) Number Theory 2011-02-27 ~ 2011-03-09

Arnaud Pecher(Universite Bordeaux 1) Graph theory 2011-03-01 ~2011-03-12

Weizhe Gu(Tianjin University)

Optimization Theory, Algorithms and Applications 2011-03-01 ~2011-05-31

Nathann COHEN(INRIA Sophia Antipolis) Graph tutorial 2011-03-09 ~2011-03-18

Frédéric HAVET (INRIA Sophia Antipolis) Graph theory 2011-03-09 ~2011-03-18

Li-Da Tong(National Sun Yat-sen University)

Graph theory 2011-03-10 ~2011-03-12

Hong-Gwa Yeh (National Central University) Graph theory 2011-03-10 ~2011-03-12

Xuding Zhu(National Sun Yat-sen University)

Graph theory 2011-03-10 ~2011-03-19

‹‹-Appendix I

Appendix I

96

Name Field Duration

Masanobu Taniguchi(Waseda University) Statistics 2011-03-15 ~2011-03-19

Alex PETKOVIC(Waseda University) Statistics 2011-03-15 ~2011-03-19

Tomoyuki AMANO(WASEDA University) Statistics 2011-03-15 ~2011-03-19

Ka-Fai Cedric Yiu (The Hong Kong Polytechnic University )

Applied Mathematics 2011-3-20 ~2011-03-22

Mark L. Lewis (Kent State University ) Algebra 2011-3-26 ~2011-04-03

Masato NAGATA(Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University)

Hydrodynamic instabilitie 2011-03-27 ~2011-04-10

Viktor Ginzburg (UC Santa Cruz ) Geometry 2011-03-27 ~2011-04-04

Satoshi Shinohara(Meisei University) Optical Orthogonal Code 2011-04-01 ~2011-04-04

Miwako Mishima (Gifu University) combinatorial approach 2011-04-01 ~2011-04-05

Shinji Kuriki (Osaka Prefecture University) Statistics 2011-04-01 ~2011-04-05

Kazuhiko Ushio(Kinki University) Combinatorial Design Theory 2011-04-01 ~2011-04-05

Nobuko Miyamoto(Tokyo University of Science) Probability Theory 2011-04-01 ~2011-04-05

Masahide Kuwada (International Institute for Natural Sciences)

Factorial Design 2011-04-01 ~2011-04-05

Ryoh Fuji-Hara(University of Tsukuba) geometry 2011-04-01 ~2011-04-06

‹‹- Appendix I

Appendix I

97

Name Field Duration

Ying Miao(University of Tsukuba) Design theory 2011-04-01 ~2011-04-06

Martin Guest(Tokyo Metropolitan University)

Geometry 2011-04-01 ~2011-04-30

Masakazu Jimbo(Nagoya Universitry) Discrete Mathematics 2011-04-02 ~2011-04-04

Frank Himstedt (Zentrum Mathematik ) Algebra 2011-04-03 ~2011-04-09

Xing Liang(University of Science and Technology of China)

Differential Equations and Dynamical Systems 2011-04-03 ~ 2011-04-30

René Schoof(Universita di Roma II) Number Theory 2011-04-04 ~ 2011-04-26

Hironori Sakai (Mathematics Division, National Center for Theoretical Sciences (south))

Integrable Systems & Frobenius Manifolds 2011-04-05 ~2011-04-28

Makoto Yamashita (Tokyo Institute of Technology )

Applied Mathematics 2011-04-10 ~2011-04-16

Jean-Pierre Serre(College de France)

Number Theory, Algebra and Geometry 2011-04-10 ~ 2011-04-17

Takao Yamazaki(Tohoku University) Number Theory 2011-04-10 ~ 2011-04-20

Ping-Chen Lin(Institute of Finance and Information, National Kaohsiung University of Applied Sciences)

Optimization 2011-04-12 ~2011-04-19

Jeremy Wong(University of Georgia)

Diameter and integral curvature of hypersurfaces in Euclidean space 2011-04-14 ~2011-04-20

Lixing Zhu(Hong Kong Baptist University)

Multivariate Data analysis 2011-04-17 ~2011-04-24

‹‹-Appendix I

Appendix I

98

Name Field Duration

Vincent Maillot(Institut de Mathématiques de Jussieu )

Arakelov Geometry 2011-04-21 ~2011-05-11

Toshihiro Uemura(Kansai University)

60—Probability theory and stochastic processes 2011-04-29 ~2011-05-06

Bogdan Kazmierczak(Polish Academy of Science) PDE 2011-05-01 ~2011-05-14

Hironori Sakai(National Cheng Kung University)

Geometry 2011-05-01 ~2011-05-31

Leonid Bunimovich(Georgia Institute of Technology)

Dynamical System 2011-05-01 ~ 2011-05-15

Shin Kiriki(Kyoto University of Education)


Xingfu Zou(University of Western Ontario)


Xiong-Ping Dai(Nanjing University) Dynamical System 2011-05-08 ~ 2011-05-15

Wang, Chang-Pian(Peking University) Differential geometry 2011-05-09 ~2011-05-14

Robert Lie(Peking University)

Theory and Algorithm to Optimal Control Problem 2011-05-09 ~2011-05-14

Wang, Jia-Jun(Peking University) Differential geometry 2011-05-09 ~2011-05-14

Ma, Xiang(Peking University) Partial differential equation 2011-05-09 ~2011-05-14

Jhang, Jhih-Fei(Peking University) Partial differential equation 2011-05-09 ~2011-05-14

Liou, Yong(Peking University) Partial differential equation 2011-05-09 ~2011-05-14

‹‹- Appendix I

Appendix I

99

Name Field Duration

Liou, Hua-Rong(Peking University) Partial differential equation 2011-05-09 ~2011-05-14

Bin Liu(Peking University) differential equation 2011-05-09 ~2011-05-14

Alexander R. Its(Indiana University-Purdue University, Indianapolis)

theory of integrable systems 2011-05-10 ~2011-05-24

Wei-Xiao Shen(National University of Singapore)



geometry 2011-05-11 ~2011-05-21

Wei-Yann Tsai(Columbia University) Biostatistics 2011-05-11 ~2011-05-24

Yuan-Pin Lee(University of Utah)

Gromov-Witten theory and related fields 2011-05-11 ~2011-05-31

Bao-Jun Huang(Huaibei Normal University) Dynamical System 2011-05-11 ~ 2011-05-17

Han-Feng Li(SUNY at Buffalo) Dynamical System 2011-05-11 ~ 2011-05-22

Shigui Ruan(The University of Miami) Dynamical System 2011-05-11 ~ 2011-05-26

Michel GROS(Institute de recherche mathematique de Rennes)

D-modules, Representation theory 2011-05-15 ~2011-06-04

Ching-Jui Lai(University of Utah) higher dimensional geometry 2011-05-16 ~2011-08-05

Ping-chen Lin(National Kaohsiung University of applied Science)

financial information management theory 2011-05-20 ~2011-05-20

Yih-Lon Lin(I-shou University) Soft Computing 2011-05-20 ~2011-05-20

‹‹-Appendix I

Appendix I

100

Name Field Duration

Chun-Syu Ke(I-shou University)

Fuzzy control Microelectromechanical Systems 2011-05-20 ~2011-05-20

Jyh-Horng Jeng(I-shou University) Digital Application Soft Computing 2011-05-20 ~2011-05-20

Shu-Ling Cheng(Far East University) Strategic Group 2011-05-20 ~2011-05-20

Che-kuang Hsieh(I-shou University) Nonlinear Control 2011-05-20 ~2011-05-20

Xianjin Chen(University of Science and Technology of China)

critical point 2011-05-20 ~2011-06-17

Horst R. Thieme(Arizona State University)

Geometric Analysis and Applied Analysis 2011-05-20 ~ 2011-06-03

Siye Wu(University of Hong Kong) Differential Geometry Others 2011-05-20 ~ 2011-06-15

Hongkai Zhao(University of California Irvine)

Applied Mathematics Scientific Computation 2011-5-23 ~ 2011-05-29

Philippe Angot(University of Marselle France)


Christine Noot-Huyghe (Universite de Strasbourg ) Algebra 2011-05-23 ~2011-06-04

Hong Kai Zhao(University of California, Irvine)

The Level Set Method 2011-05-24 ~2011-05-26


geometry 2011-05-24 ~2011-06-24

Qiang Du(Penn State University) Scientific Computation 2011-05-24 ~ 2011-05-29

Michael Siegel(New Jersey Institute of Technology)


‹‹- Appendix I

Appendix I

101

Name Field Duration

Zhonghua Qiao(Hong Kong Baptist University)


Tien-Yien Li(Michigan State University)

Dynamical System Numerical Analysis Others

2011-05-24 ~ 2011-05-31

Gretar Tryggvason(University of Norte Dame) Scientific Computation 2011-05-24 ~ 2011-05-31

Aaron Fogelson(University of Utah) Scientific Computation 2011-05-24 ~ 2011-06-02

J. Thomas Beale(Duke University) Scientific Computation 2011-05-24 ~ 2011-06-02

Anna-Karin Tornberg(KTH Sweden) Scientific Computation 2011-05-25 ~ 2011-05-28

Boo Cheong KHOO(National University of Singapore)


Zhilin Li(North Carolina State University)


Yongsam Kim(Chung-ng University Korea)


Zhiming Chen(Chinese Academy of Sciences)


Mark Sussman(Florida State University) Scientific Computation 2011-05-25 ~ 2011-05-31

Georges-Henri Cottet(Univ. de Grenoble and CNRS France)


Chaouqi Misbah(Univ. Joseph Fourier and CNRS France)


Lisa Fauci(Tulane University) Scientific Computation 2011-05-26 ~ 2011-06-02

‹‹-Appendix I

Appendix I

102

Name Field Duration

Albert Jeu-Liang Sheu(University of Kansas) Rings and Related Algebras 2011-05-27 ~2011-08-10

JIN Xiao Qing(University of Marcau) Scientific computing 2011-05-28 ~2011-06-05

Galia Dafni(Concordia University) Number Theory 2011-06-01 ~ 2011-06-16

Xiaojun Chen(University of Michigan) Algebraic Geometry 2011-06-01 ~ 2011-07-31

Alex Vasiliev(University of Bergen)

Differential Geometry and Geometric Analysis Others Harmonic Analysis

2011-06-05 ~ 2011-06-11

Irina Markina(University of Bergen)

Differential Geometry and Geometric Analysis Others Harmonic Analysis

2011-06-05 ~ 2011-06-11

Wei Wang(Zhejiang University)

Differential Geometry and Geometric Analysis 2011-06-05 ~ 2011-06-15

Erlend Grong(University of Bergen)


Mauricio Godoy Molina(University of Bergen)


Georgy Ivanov(University of Bergen)


Yuan-Pin Li(University of Utah)

Gromov-Witten theory and related fields 2011-06-06 ~2011-06-30

Po Lam Yung(Rutgers University)


Po-Ning Chen (Harvard University) Dierential geometry: general relativity 2011-06-07 ~2011-07-04

Shinobu Hosono(School of Science, The University of Tokyo)

Mathematical Physics 2011-06-08 ~2011-06-11

William Messing(The University of Minnesota) Algebraic Geometry 2011-06-09 ~2011-06-29

‹‹- Appendix I

Appendix I

103

Name Field Duration

Hsin-Yuan Huang(University of Minnesota) Dynamical Systems 2011-06-09 ~2011-07-31

Henri Darmon(McGill University) Number Theory 2011-06-09 ~ 2011-06-24

Chiu-Yen Kao(Ohio State University, USA) Computational and Applied Math 2011-06-13 ~2011-07-14

Ravi Ramakrishna(Cornell University) Number Theory 2011-06-13 ~ 2011-06-26

John Voight(University of Vermont) Number Theory 2011-06-15 ~ 2011-06-25

Richard Siu Hung Ng (Iowa State Univerity ) Algebra 2011-06-15 ~2011-06-26

Jung-Ying Tzeng(Bioinformatics Research Center)

Statistical methods for studying susceptibility genes for complex traits 2011-06-16 ~2011-06-30

Jerome William Hoffman(University of Minnesota) Number Theory 2011-06-18 ~ 2011-06-28

Kai-Wen Lan(Princeton University) Number Theory 2011-06-19 ~ 2011-06-23

Suh-Hyun Choi(KAIST Korea) Number Theory 2011-06-19 ~ 2011-06-23

Ulrich Gortz(U Duisburg-Essen Germany) Number Theory 2011-06-19 ~ 2011-06-24

Ching-Li Chai(University of Pennsylvania) Number Theory 2011-06-19 ~ 2011-06-25

Tong Liu(Purdue University) Number Theory 2011-06-19 ~ 2011-06-25

Tonghai Yang(University of Wisconsin) Number Theory 2011-06-19 ~ 2011-06-26

Ye Tian(Academia Sinica China) Number Theory 2011-06-19 ~ 2011-06-26

Matija Kazalicki(University of Zagreb) Number Theory 2011-06-19 ~ 2011-06-28

‹‹-Appendix I

Appendix I

104

Name Field Duration

Chang Hong Lu(East China Normal University)

Combinatorics, graph algorithms discussed 2011-06-22 ~2011-06-26

Zhi-An Wang(Hong Kong Polytechnic University)

Traveling waves of chemotaxis and applications 2011-06-22 ~2011-07-05

Wing Hung Wong(Stanford University) Probability Theory and Statistics 2011-06-22 ~ 2011-06-22

Jinpeng An (Peking University ) Geometry 2011-06-25 ~2011-07-01

Tommaso Pacini(Scuola Normale Superiore, Pisa)

Differential geometry 2011-06-26 ~2011-07-08

Johannes Nordström(Imperial College) geometry group 2011-06-27 ~2011-07-09

Mao-Pei Tsui(The University of Toledo) Geometric analysis 2011-06-27 ~2011-07-29

Yusheng Li(Tongji University) Graph Theory 2011-06-27 ~ 2011-06-30

Baogang Xu(Nanjing Normal University) Graph Theory 2011-06-27 ~ 2011-06-30

Hau-Tieng Wu(Princeton University) Adaptive analysis for complex data 2011-06-30 ~2011-08-29

Jiu-Kang Yu(Purdue University) Number Theory 2011-07-01 ~ 2011-07-05

Jinpeng An(Peking University) Number Theory 2011-07-01 ~ 2011-07-07

Knut Smoczyk(Leibniz University) Geometry 2011-07-02 ~2011-07-08

Yiqiang Zhou(Memorial University) theory of rings and modules 2011-07-02 ~2011-08-01

Yong-Geun Oh(Univeristy of Wisconsin) Symplectic geometry 2011-07-03 ~2011-07-08

‹‹- Appendix I

Appendix I

105

Name Field Duration

Dominic Joyce(University of Oxford) Differential Geometry 2011-07-03 ~2011-07-09

Ian McIntosh(University of York) Pure Mathematics 2011-07-03 ~2011-07-10

Mohammed Abouzaid (MIT & Clay Mathematics Institute)

Geometry 2011-07-04 ~2011-07-08

Ildefonso Castro Lóp(Universidad de Jaén)

Compact hypersurfaces with constant mean curvature 2011-07-04 ~2011-07-08

Kenji Fukaya(Kyoto University)

Special Lagrangians and Related Topics 2011-07-04 ~2011-07-08

Mark Haskins(Imperial College)


Mu-Tao Wang(Columbia University) Differential Geometry 2011-07-04 ~2011-07-08

Tom Ilmanen(ETH Zürich)


Nicolaos Kapouleas(Brown University)

Differential Geometry Partial Differential Equation 2011-07-04 ~2011-07-08

William P. Minicozzi II (Johns Hopkins University) Geometric analysis 2011-07-04 ~2011-07-08

Pascal Romon(Université de Marne-la-Vallée)

Geometry 2011-07-04 ~2011-07-08

Richard M. Schoen(Stanford University) Differential Geometry 2011-07-04 ~2011-07-14

YoungJu Choie(POSTECH) Number Theory 2011-07-04 ~ 2011-07-15

Xi-Ping Zhu(Sun Yat-sen University) Geometry & Geometric Analysis 2011-07-07 ~2011-07-09

Neil Trudinger(Australian National University)

Nonlinear elliptic partial differential equations and applications 2011-07-07 ~2011-07-10

‹‹-Appendix I

Appendix I

106

Name Field Duration

Eiji Yanagida(Tokyo Institute of Technology)

Nonlinear elliptic and parabolic equations 2011-07-07 ~2011-07-10

Nassif Ghoussoub(University of British Columbia)

Announcement 2011-07-07 ~2011-07-12

Gabriella Tarantello(Università di Roma "Tor Vergata")

Nonlinear Differential Equation 2011-07-07 ~2011-07-13

Pengfei Guan(McGill University)

Geometric Analysis, Several Complex Variables. 2011-07-07 ~2011-07-17

Shing-Tung Yau(Harvard University) Differential geometry 2011-07-08 ~2011-07-09

Horng-Tzer Yau(Harvard University) Probability theory 2011-07-08 ~2011-07-09

Fang-Hua Lin(New York University) nonlinear partial differential equation 2011-07-08 ~2011-07-12

Edmund Puczylowski(University of Warsaw) Ring Theory 2011-07-09 ~2011-08-08

Leon Van Wyk (Universiteit Stellenbosch ) Algebra 2011-07-09 ~2011-07-23

Mikhail Chebotar(Kent State University) Linear Algebra 2011-07-10 ~2011-07-23

Wenjun Ying(Shanghai Jiao Tong University)


Richard Ng(Iowa State University) Number Theory 2011-07-12 ~ 2011-07-21

Ling Long(Iowa State University) Number Theory 2011-07-12 ~ 2011-07-21

Robert Wisbauer (Universität Düsseldorf ) Algebra 2011-07-15 ~2011-07-19

Leonid Makar-Lemanov (Wayne State University ) Algebra 2011-07-15 ~2011-07-19

‹‹- Appendix I

Appendix I

107

Name Field Duration

Edmund Puczylowski (Warsaw University) Algebra 2011-07-15 ~2011-07-22

Mikhail Chebotar (Kent State University) Algebra 2011-07-15 ~2011-07-22

Alexey Zykin(State University - Higher School of Economics)

Number Theory 2011-07-16 ~ 2011-07-27

Eric King-wah Chu (Monash University) Applied Mathematics 2011-07-25 ~2011-08-17

Shing-Tung Yau(Harvard University) Differential Geometry 2011-07-29 ~ 2011-07-29

Phillip Colella(Lawrence Berkeley National Laboratory)

Applied Numerical Algorithms 2011-07-30 ~2011-08-08

John A. Strain (University of California) Applied Numerical Mathematics 2011-07-30 ~2011-08-13

Pinyuen Chen (Syracuse University) Statistics 2011-07-30 ~2011-08-14

Muneya Matsui (Keio University) Statistical science 2011-07-31 ~2011-08-015

Muneya Matsui (Nanzan University) Statistical science 2011-07-31 ~2011-08-15

Yen-Hsi Richard Tsai (The University of Texas at Austin)

Multiscale modeling and computations Computational interface problems Computational inverse problems Image processing

2011-08-01 ~ 2011-08-20

Shunsuke Hayashi (Kyoto University ) Applied Mathematics 2011-08-10 ~2011-08-25

Akinari Hoshi(Rikkyo University)

Rationality problem under finite group actions Family of Thue equations Constructive aspects of the inverse Galois problem Field isomorphism problem of generic polynomials Multiplicative quadratic forms on algebraic varieties Gaussian period polynomials

2011-08-11 ~ 2011-09-22

‹‹-Appendix I

Appendix I

108

Name Field Duration

Gerard Freixas(CNRS,Institut de Mathematiques de Jussieu)

Arithemetic Geometry,Arakelov Geometry 2011-08-14 ~ 2011-09-04

Hidetaka Kitayama(Osaka University) Algebra 2011-08-15 ~ 2011-09-02

Shunsuke Hayashi (Kyoto University) Applied Mathematics 2011-09-05 ~2011-09-22

Hubert Kiechle (Universität Hamburg, and Technische Universität München )

Algebra 2011-09-08 ~2011-09-24

Graeme Wilkin(National University of Singapore)

Differential Geometry 2011-09-17 ~ 2011-09-25

Ajda Fosner(University of Primorska) Ring Theory 2011-09-18 ~2011-09-22

Tomoo Matsumura (KAIST) Geometry 2011-09-27 ~2011-10-02

Li Chi-Kwong(College of William and Mary)

Matrix theory 2011-09-28 ~ 2011-10-01

Gerard Besson(Université Grenoble 1, Institut Fourier)


Mont Mickael (Université Bordeaux 1)

Information Processing Letters Journal of Graph Theory Discrete Mathematics Discrete Applied Mathematics

2011-10-16 ~ 2011-10-27

Andre Raspaud(Université Bordeaux 1)

Discrete Mathematics, Algorithms & Theory, Probability 2011-10-16 ~ 2011-10-27

Arnaud Pêcher (Université Bordeaux 1)

graph theory: graph colorings, polyedral graph theory, perfect graph theory, algebraic graph theory mathematical programming : mixed integer linear programming

2011-10-16 ~ 2011-10-27

‹‹- Appendix I

Appendix I

109

Name Field Duration

Gerhard Huisken(Max Planck Institute for Gravitational Physics)


susan wilson(University of Melbourne) Biostatistics 2011-11-11 ~ 2011-11-18

Yujiro Kawamata(University of Tokyo, Komaba)

Algebraic Geometry 2011-11-16 ~ 2011-11-20

JongHae Keum(Korea Institute for Advanced Study )

Algebraic Geometry, Algebra 2011-11-16 ~ 2011-11-20

Baohua Fu(AMSS-CAS) Algebraic Geometry, Algebra 2011-11-16 ~ 2011-11-20

Xiaotao Sun(Institute of Mathematics, Chinese Academy of Science)


Jilong Tong(Tsinghua University) Geometry 2011-11-16 ~ 2011-11-20

Shigeharu Takayama(University of Tokyo) Geometry 2011-11-16 ~ 2011-11-20

Shunsuke Takagi(Kyushu University) Algebraic Geometry 2011-11-16 ~ 2011-11-20

Keiji Oguiso(Osaka University) Algebraic Geometry 2011-11-16 ~ 2011-11-20

Yoshinori Gongyo(University of Tokyo) Algebraic Geometry 2011-11-16 ~ 2011-11-20

Shinnosuke Okawa(University of Tokyo) Algebraic Geometry 2011-11-16 ~ 2011-11-20

Jun-Muk Hwang(Korea Institute for Advanced Study)

Algebraic Geometry Geometry of minimal rational curves on Fano manifolds Hermitian locally symmetric manifolds

2011-11-16 ~ 2011-11-20

Yongnam Lee(Sogang University) Algebraic Geometry 2011-11-16 ~ 2011-11-20

‹‹-Appendix I

Appendix I

110

Name Field Duration

Jihun Park(Postech) Algebraic Geometry 2011-11-16 ~ 2011-11-20

Dano Kim(University of Chicago)

Algebraic Geometry, Algebraic Topology 2011-11-16 ~ 2011-11-20

Sijong Kwak(Korea Advanced Institute of Science and Technology)


Wan-Keng Cheong(National Cheng Kung University)

Algebraic geometry and related fields 2011-11-16 ~ 2011-11-20

Jiun-Cheng Chen(National Tsing Hua University)

Algebraic geometry 2011-11-16 ~ 2011-11-20

Hai Phung Ho (University Duisburg-Essen)

Tensor categories, Tannaka duality Quantum groups, Hopf algebras Fundamental groupschemes

2011-11-16 ~ 2011-11-20

Bernold Fiedler(Free University Berlin) Dynamical System 2011-11-20 ~ 2011-11-27

Ariel Fernández(Rice University) Mathematical Biology 2011-11-25 ~ 2011-12-01

Yasuhiro Goto(Hokkaido University of Education)

Number Theory 2011-11-29 ~ 2011-11-30

Yihong Du(University of New England)

Dynamical System Mathematical Biology Nonlinear PDE

2011-11-29 ~ 2011-12-19

Der-Chen Chang(Georgetown University) Geometric Analysis 2011-12-08 ~ 2011-12-27

Lih-Yuan Deng (鄧利源 )(University of Memphis) Statistics 2011-12-08 ~ 2011-12-31

Yoshihiro Tonegawa(Department of Math. Hokkaido University)

Partial differential equations of elliptic and parabolic Partial differential equations of elliptic and parabolic types Geometric measure theory and its applications Calculus of variations

2011-12-09 ~ 2011-12-11

‹‹- Appendix I

Appendix I

111

Name Field Duration Ying Chen (National University of Singapore )

Statistics 2011-12-10 ~2011-12-15

Goong Chen(Texas A&M University) Mathematical Biology 2011-12-11 ~ 2012-1-11

Nader Tajvidi(Lund Institute of Technology)

Statistics 2011-12-12 ~ 2011-12-27

Wolfram Bauer(Universität Göttingen) Geometric Analysis 2011-12-14 ~ 2011-12-23

Chisato Iwasaki(University of Hyogo) Geometric Analysis 2011-12-15 ~ 2011-12-22

Kenro Furutani(Tokyo University of Science) Geometric Analysis 2011-12-15 ~ 2011-12-22

Tatsuo Nishitani(Osaka University) Geometric Analysis 2011-12-15 ~ 2011-12-22

Toshiyuki Abe(Ehime University) Algebra 2011-12-17 ~ 2011-12-23

Tomoyuki Arakawa(RIMS, Kyoto University) Representation Theory 2011-12-17 ~ 2011-12-23

Chongying Dong(University of California, Santa Cruz)

Vertex operator algebras 2011-12-17 ~ 2011-12-23

Terry Gannon(University of Alberta)

algebra, number theory, and mathematical physics 2011-12-17 ~ 2011-12-23

Robert Jr.Griess(University of Michigan) Vertex operator algebras 2011-12-17 ~ 2011-12-23

Gerald Hohn(Kansas State University) Algebra 2011-12-17 ~ 2011-12-23

YiZhi Huang(Rutgers University) quantum field theory 2011-12-17 ~ 2011-12-23

Alexander A.Ivanov(Imperial College , London)

1.Sporadic groups and their geometries 2.Distance-regular and distance- transitive graphs 3.Monstrous moonshine, Monster

2011-12-17 ~ 2011-12-23

‹‹-Appendix I

Appendix I

112

Name Field Duration

Cui Bo Jiang(Shanghai Jiao Tong University)

Algebra 2011-12-17 ~ 2011-12-23

Haisheng Li(Rutgers University, Camden) Mathematics / Statistics 2011-12-17 ~ 2011-12-23

Geoffrey Mason(University of California , Santa Cruz)

conformal field theory 2011-12-17 ~ 2011-12-23

Masahiko Miyamoto(University of Tsukuba) Group Theory 2011-12-17 ~ 2011-12-23

Hiroki Shimakura(Aichi University of Education)

Algebraic Combinatorics 2011-12-17 ~ 2011-12-23

Qing Wang (Xia men University) Algebra 2011-12-17 ~ 2011-12-23

Feng Xu (University of California , Riversides)

Operator Algebras 2011-12-17 ~ 2011-12-23

Hiromichi Yamada(Hitotsubashi University) Mathematics 2011-12-17 ~ 2011-12-23

Hiroshi Yamauchi(Tokyo Woman's christian University)

Mathematics related to Moonshine 2011-12-17 ~ 2011-12-23

Naoyuki Ishimura(Hitotsubashi University) Geometric Analysis 2011-12-18 ~ 2011-12-20

Yohei Tsutsui(Osaka University) Geometric Analysis 2011-12-18 ~ 2011-12-22

Mitsuro Sugimoto(Nagoya University) Geometric Analysis 2011-12-18 ~ 2011-12-22

Yoshitsugu Kabeya(Osaka Prefecture University) Geometric Analysis 2011-12-18 ~ 2011-12-22

Shinya Okabe(Tohoku University) Geometric Analysis 2011-12-18 ~ 2011-12-22

‹‹- Appendix I

Appendix I

113

Name Field Duration

Yutian LI(City University of Hong Kong)

Geometric Analysis 2011-12-18 ~ 2011-12-22

Michiaki Onodera(Mittag-Leffler Institute Sweden)

Geometric Analysis 2011-12-19 ~ 2011-12-22

Sheng-Chi Liu (劉昇吉 )(Texas A&M University) Number Theory 2011-12-19 ~ 2011-12-23

Changliang Zou(Nankai University) Probability Theory and Statistics 2011-12-20 ~ 2012-01-04

‹‹-Appendix II

Appendix II

114

NCTS 2011 Conference, Workshop & School, Special Lecture

Time Conference & Workshop School & Special Lecture Place

January 7 , 2011

Conference in Dynamical Systems: A Celebration in honor of Kenneth James Palmer on his RetirementSpeakersJung-Chao Ban (National Dong Hwa University)Yi-Chiuan Chen (Academia Sinica)Shui-Nee Chow (Georgia Institute of Technology)Peter Kloeden (Goethe Universitaet)Huseyin Kocak (University of Miami)Ming-Chia Li (National Chiao Tung)Chen-Chang Peng (National Chiayi University)Sergei Pilyugin (St. Petersburg State University)Organizers:Chiun-Chuan Chen (National Taiwan University)I-Liang Chern (National Taiwan University)Chun-Hsiung Hsia (National Taiwan University)Song-Sun Lin (National Chiao Tung University)

The International Cnference Hall, Astro-Math. Building, National Taiwan University

January 11-14, 2011

Miniworkshop of AlgebraSpeakersMeng Chen (Fudan University)Meng-Kiat Chuah (Tsinghua University) Osamu Fujino (Kyoto University)Shigeru Kuroda (Tokyo Metropolitan University)Mingyao Xu (Peking University)Chia-Fu Yu(Academia Sinica)

Astro-Math. Building 440, National Taiwan University

January 14-17, 2011

The 19th(2011) Workshop On Differential EquationsOrganizers:Min-Hung Chen (National Cheng Kung University)Yung-Fu Fang (National Cheng Kung University)Jong-Shenq Guo (Tamkang University)Suchung Hou (National Cheng Kung University)Kuo-Ming Lee (National Cheng Kung University)Wen-Ching Lien(National Cheng Kung University)Ching-Lung Lin(National Cheng Kung University)Yoshio Tsutsumi (Kyoto Univ., Japan)Chern-Shuh Wang (National Cheng Kung University)

International Conference Rooms, NCKU

February 18, 2011

Topics in Computational High Frequency Wave PropagationSpeakersOlof Runborg (KTH) Yen-Hsi Richard Tsai (The University of Texas at Austin)Organizers:I -Liang Chern (National Taiwan University)

Room 440, Astro-Math. Building, National Taiwan University

‹‹- Appendix II

Appendix II

115


February 21-25, 2011

NCTS (Taiwan)-CPT(France) Joint Workshop on Symplectic Geometry and Quantum Symmetries in Mathematical PhysicsOrganizers: Nan-Kuo Ho (Nat’l Tsing Hua University)Robert Coquereaux (CPT, Marseille, France)

Lecture Room of NCTS, National Tsing Hua Univ.

February 23, 2011

2011 Probability One Day WorkshopOrganizers:Chii-Ruey Hwang (Academia Sinica)Shuen-Jyi Sheu (Nat’l Central University)Yuan-Chung Sheu (Nat’l Chiao Tung University)

The Auditorium, Institute of Mathematics,Academia Sinica

February 23 - June 22, 2011

NCTS Spring Course on Computational Science and EngineeringOrganizer:Ming-Chih Lai (Nat’l Chiao Tung University)

National Chiao Tung University

February 24, 20112011 NCTS Special Day on Serre’s ConjectureOrganizer:Wen-Ching Winnie Li (NCTS)


February 26, 2011

2011 South Taiwan Workshop on Scientific computing and ApplicationsSpeakers:Prof. Li-Ming Yeh (National Chiao Tung University)Prof. Yung-Ta Li(National Chiao Tung University)Prof. Chun-Yueh Chiang (National Formosa University)Prof. Min-Hsiung Lin (National Chung Cheng University)Prof. Yin‐Liang Huang(National University of Tainan)Prof. Shing-Lin Chang (Southern Taiwan University)Prof. Tsung-fang Wu (National University of Kaohsiung)Prof. Yueh-Cheng Kuo (National University of Kaohsiung)Prof. Chin-Yueh Liu (National University of Kaohsiung)Prof. Tsung-Lin Lee (National Sun Yat-sen University)Prof. Tzon-Tzer Lu (National Sun Yat-sen University)Prof. Chung‐Chien Hong (National Pingtung University of Science and Technology )

R204, 2F, NCTS, NCKU

March 11-12, 2011

Workshop on Graph TheorySpeakersGerard Jennhwa Chang ( National Taiwan University) Nathann Cohen (INRIA Sophia Antipolis) Frederic Havet (INRIA Sophia Antipolis) Mickael Montassier (Universite Bordeaux 1) Zhi-Shi Pan (Tamkang University) Arnaud Pecher (Universite Bordeaux 1) Andre Rauspaud (Universite Bordeaux 1) Li-Da Tong (National Sun Yat-sen University) Hong-Gwa Yeh (National Central University) Xuding Zhu (National Sun Yat-sen University)

Department of Mathematics, National Taiwan University

‹‹-Appendix II

Appendix II

116


March 16, 2011

Workshop on Time Series Analysis and ApplicationsSpeakersMasanobu Taniguchi (Waseda University) Hwai-Chung Ho (Academia Sinica) Feng Yao (Kagawa University) Tomoyuki Amano (Waseda University) Henghsiu Tsai (Academia Sinica) Alexandre Petkovic (Waseda University)

Room 440, Astrophysics-Mathematics Building, National Taiwan University

March 17, 2011

NCTS/TPE PDE SEMINAR:MINI-WORKSHOP ON APPLIED ANALYSISSpeakersNarn-Rueih Shieh (National Taiwan University)Jui-Tang Chen (National Taiwan Normal University)Je-Chiang Tsai (National Chung Cheng University)Tsung-Ming Hwang (National Taiwan Normal University)Shyan-Shiou Chen (National Taiwan Normal University)Shih-Feng Shieh (National Taiwan Normal University)

Rm S433, Science Hall, Tamkang University, Tamsui

March 17-April 21, 2011

2011 NCTS Short Course on AnalysisInstructor:Chi-Hua Chan (NCTS)


March 21-31, 20112011 NCTS Short Course on Deligne's work on Weil ConjecturesInstructor:Jiangwei Xue (NCTS)


April 2- 4, 2011

2011 Taiwan-Japan Conference of Combinatorics and its ApplicationsSpeakersMiwako Mishima (Gifu University) Ryoh Fuji-Hara (University of Tsukuba) Masakazu Jimbo 神保雅一 (Nagoya Universitry) Shinji Kuriki (Osaka Prefecture University) Kazuhiko Ushio (Kinki University)Ying Miao (University of Tsukuba) Satoshi Shinohara (Meisei University) Nobuko Miyamoto (Tokyo University of Science)Masahide Kuwada (International Institute for Natural Sciences) Yeong-Nan Yeh( 中央研究院數學研究所 ) Hong-Gwa Yeh( 中央大學數學系 ) Chiang Lin ( 中央大學數學系 ) Kuo-Ching Huang ( 靜宜大學財務與計算數

學系 ) Hong-Bin Chen ( 中央研究院數學研究所 ) Chih-Hung Yen 嘉義大學應用數學系 Ming-Hway Huang 元培科技大學資訊工程系

Yao-Tsu Chang 義守大學應用數學系

Hsun-Wen Chang 大同大學應用數學系

Hung-Lin Fu 交通大學應用數學系

Bit-shun Tam 淡江大學數學系

Zhi-Shi Pan 淡江大學數學系

Li-Da Tong 中山大學應用數學系

Tamkang University

‹‹- Appendix II

Appendix II

117


April 7-22, 20112011 NCTS Lecture Series on Number TheoryInstructor:Rene Schoof (University of Roma II, Italy)


April 11-15, 20112011 NCTS Lecture Series by Jean-Pierre SerreInstructor:Jean-Pierre Serre (College de France)


May 5-June 16, 2011

2011 NCTS Topical Program : Topics on the N-Body ProblemInstructor:Kuo-Chang Chen (Nat’l Tsing Hua University)


May 9, 2011Special Joint Math Physics Colloquium Instructor:Steve Hsu (University of Oregon)


May 10, 2011

臺灣大學─北京大學兩校交流研討會SpeakersNTU林太家余正道林文偉莊武諺張樹城

PEIKING UNIVERSITY李若马翔王家军刘勇章志飞

臺灣大學天文數學館 440 室

May 12-14, 2011

2011 NCTS Workshop on Dynamical SystemsOrganizers:Jung-Chao Ban (Nat’l Dong Hwa University)Kuo-Chang Chen (Nat’l Tsing Hua University)Cheng-Hsiung Hsu (Nat’l Central University)Ming-Chia Li (Nat’l Chiao Tung University)Chih-Wen Shih (Nat’l Chiao Tung University)


May 14, 2011

The Second Taiwan Geometry SymposiumSpeakers Jih-Hsin Cheng, (Academic Sinica) Yu-Chu Lin, (National Tsing-Hua University) Chin-Tung Wu,( National Pingtung University of Education)

Room 440 Astro-Math. Building, National Taiwan University

May 20, 2011

2011 Optimization WorkshopSpeakers林智仁教授 (NTU) 林萍珍教授 ( 高雄應用科技大學 )

林義隆教授 ( 義守大學 ) 李育杰教授 ( 台灣科技大學 ) 柯

春旭教授 ( 義守大學 ) 鄭志宏教授 ( 義守大學 ) 鄭淑玲教

授 ( 遠東科技大學 ) 謝哲光教授 ( 義守大學 )

台北市文山區汀州路四段八十八號台灣師大數學系 M210

‹‹-Appendix II

Appendix II

118


May 25-June 22, 2011

2011 NCTS Short Course– Some Combinatorial Problems in Design of ExperimentsInstructor:Ching-Shui Cheng (University of California, Berkeley)


May 26-29, 2011

NCTS Workshop on Fluid-Structure Interaction ProblemsOrganizers:Ming-Chih Lai (Nat’l Chiao Tung University)Zhilin Li (NCSU, USA)John Lowengrub (UC-Irvine, USA)


June 7-10, 2011

2011 NCTS Taiwan-Norway Joint Workshop on Analysis and Its ApplicationsOrganizers:Der-Chen Chang (Georgetown Univ., USA & NCTS)Chiung-Jue Sung (Nat’l Tsing Hua University)Alex Vasiliev (Bergen University, Norway)


June 10, 2011One-day Workshop on AlgebraOrganizerMing-Chang Kang 康明昌 (National Taiwan University)

Room 519, Astro‐Math. Building, National Taiwan University

June 13, 2011Special Day in Fourier AnalysisOrganizers:Der-Chen Chang (Georgetown Univ., USA & NCTS)Chiung-Jue Sung (Nat’l Tsing Hua University)


June 15-17, 2011NCTS Short Course on Number TheoryInstructor:Henri Darmon (McGill University, Canada)Ravi Ramakrishna (Cornell University, USA)


June 20-23, 2011

2011 NCTS International Conference on Galois Representations, Automorphic Forms and Shimura VarietiesOrganizers:KingFai Lai (National Sun Yet San University)Wen-Ching W. Li (National Center for Theoretical Sciences)


June 21-July 15, August 1-12, 2011

Summer Research Program on Applied MathematicsInvited SpeakersChiu-Yen Kao (Ohio State University)Richard Yen-Hsi Tsai (The University of Texas at Austin)Hau-Tieng Wu (Princeton University)OrganizersI-Liang Chern (National Taiwan University)


‹‹- Appendix II

Appendix II

119


June 27, 2011

2011 NCTS Special Day on Noncongruence Modular FormsOrganizer:Wen-Ching W. Li (National Center for Theoretical Sciences)


June 27-July1, 2011

2011 NCTS/TPE Summer School on GeometryInvited SpeakersMark Haskins (Imperial College, UK)Tommaso Pacini (Scuola Normale Superiore, Pisa, Italy) Mao-Pei Tsui (The University of Toledo, USA)OrganizersYng-Ing Lee (National Taiwan University)Mao-Pei Tsui (The University of Toledo, USA)

Room 101 Astro-Math. Building, National Taiwan University

July 4-August 26, 2011

NCTS Summer Program on Number TheoryInstructor:Liang -Chung Hsia (National Central University)Wei-Chen Yao (Taipei Municipal University of Education)


July 4-8, 2011

2011 Taiwan International Conference on Geometry~Special Lagrangians and Related Topics~SpeakersMohammed Abouzaid (MIT & Clay Mathematics Institute, USA) Ildefonso Castro López (Universidad de Jaén, Spain) Kenji Fukaya (Kyoto University, Japan)Mark Haskins (Imperial College, UK)Tom Ilmanen (ETH Zürich, Switzerland)*Nicolaos Kapouleas (Brown University, USA)Ian McIntosh (University of York, UK)Johannes Nordström (Imperial College, UK)Yong-Geun Oh (Univeristy of Wisconsin, Madison, USA) Tommaso Pacini (Scuola Normale Superiore, Pisa, Italy) Pascal Romon (Université de Marne-la-Vallée, France) Richard M. Schoen (Stanford University, USA) Knut Smoczyk (Leibniz University, Hannover, Germany) Brian White (Stanford University, USA)


July 5-26, 2011NCTS Summer Course in ProbabilityInstructor:Guan-Yu Chen (Nat’l Chiao Tung University)

National Chiao Tung University

July 5-28, 2011

NCTS Summer Minicourse on String Topology and Morphic CohomologyInstructor:Xiaojun Chen ((University of Michigan at Ann Arbor)Jyh-Haur The (Na’l Tsing Hua University)


‹‹-Appendix II

Appendix II

120


July 8-9, 2011

A Conference in Honor of the 60th Birthday of Chang-Shou LinSpeakersLuis A. Caffarelli (University of Texas at Austin, USA)Pengfei Guan (McGill University, Canada)Nassif Ghoussoub (University of British Columbia, Canada)Fanghua Lin (New York University, USA) Louis Nirenberg (New York University, USA) Neil Trudinger (ANU, Austria) Gabriella Tarantello (Università di Roma "Tor Vergata", Italy) Eiji Yanagida (Tokyo Institute of Technology, Japan) Shing-Tung Yau (Harvard University, USA) Xi-Ping Zhu (Sun Yat-sen University, China)


July 11-15, 20112011 NCTS Summer Course in Geometry AnalysisInstructor:Duy-Minh Nhieu (Nat’l Central University)



NCTS Summer Course in Mathematical BiologyInstructor:Je-Chiang Tsai (National Chung Cheng University)



NCTS Summer Program on Dynamical SystemsOrganizers:Kuo-Chang Chen (Nat’l Tsing Hua University)Ming-Chia Li (Nat’l Chiao Tung University)Chih-Wen Shih (Nat’l Chiao Tung University)


July 18, 2011

One Day Workshop on Rings and AlgebrasSpeakers: Prof. Mikhail Chebotar (Kent State University, USA)Prof. Edmund Puczylowski (Warsaw University, Poland)Prof. Leon van Wyk (Stellenbosch University, South Africa) Prof. Robert Wisbauer (University of Duesseldorf, Germany)Prof. Leonid Makar-Limanov (Wayne State University, USA)


July 29, 2011NCTS Special Lecture Instructor:S. T. Yau (Harvard University, USA)


August 8-25, 2011NCTS Summer Minicourse on Curve & Surface TheoryInstructor:Dong-Ho Tsai (Nat’l Tsing Hua University)


‹‹- Appendix II

Appendix II

121


August 9-18, 2011NCTS Summer Program on Maximal Principle, Moving Plane Method and ApplicationsInstructor:Jann-Long Chern ((National Central University)


August 15-19, 2011

國家理論科學中心北區數學組與物理組合辦活動「廣義相對論的物理與數學」暑期研習營主講人：

高涌泉教授（臺灣大學物理系）

王慕道教授（哥倫比亞大學數學系 / 臺灣大學數學系）

莊武諺教授（臺灣大學數學系）

王金龍教授（臺灣大學數學系）

臺灣大學

August 16, 2011

One-day workshop of algebraSpeakersHung-Jen Chiang-Hsieh(Chung Cheng University )Vincent Young(National Taiwan University)Shih-chang Huang (Cheng-Kung University) Aiichi Yamasaki (Kyoto University, Japan ) Hidetaka Kitayama (Osaka University, Japan)Akinari Hoshi (Rikkyo University, Japan)Ming-chang Kang (National Taiwan University)


September 7-9, 2011

NCTS Summer Program on Scientific ComputationInstructor:Ming-Cheng Shiue (National Chiao Tung University)


September 24, 2011

Third Taiwan Geometry Symposium Organizers: Yng-Ing Lee (Nat’l Taiwan University)River Chiang (Nat’l Cheng Kung University)Nan-Kuo Ho (Nat’l Tsing Hua University)


October 24-27, 2011

2011 NCTS Distinguished Lecture SeriesInstructor:Gerhard Huisken (Director, Max Planck Institute for Gravitational Physics, Germany)


November 5, 2011

The Second Workshop on Boundary Element Method and BoundaryOrganizers:陳正宗 (National Taiwan Ocean University)王辰樹 (National Cheng Kung University)林景隆 (National Cheng Kung University)李國明 (National Cheng Kung University)


‹‹-Appendix II

Appendix II

122


November 11-13, 2011

2011 Taiwan-Japan Joint Workshop on Numerical Analysis and Scientific ComputationSpeakers Takaaki NISHIDA (Waseda University, Japan) Hitoshi IMAI (University of Tokushima, Japan) Yuusuke ISO (Kyoto University, Japan) Toshiyuki AWAJI ( Kyoto University, Japan) Hideyuki AZEGAMI (Nagoya University, Japan ) Hitoshi YOSHIKAWA (Kyoto University, Japan) Hiroshi FUJIWARA (Kyoto University, Japan) Kazunori FUJISAWA (Okayama University, Japan ) Kosuke ITO (National Taiwan University, Japan ) Takanori KATSURA (Kyoto University, Japan ) Shugo MANABE (Kyoto University, Japan ) Jeng-Tzong Chen (National Taiwan Ocean University) I-Liang Chern (National Taiwan University) Suh-Yuh Yang (National Central University)Jinn-Liang Liu (National Hsinchu University Of Education) Lee-Wei Yang (National Tsing-Hua University) Lo-Bin Chang (National Chiao Tung University) Ming-Cheng Shiue (National Chiao Tung University) Min-Hsiung Lin (National Chung Cheng University) Chien-Sen Huang (National Sun Yat-Sen University)


November 16-20, 2011

Algebraic Geometry in East Asia, 2011SpeakersWan-Keng Cheong (National Cheng Kung University) Jiun-Cheng Chen (National Tsing Hua University) Jungkai Alfred Chen (National Taiwan University) Wu-Yen Chuang (National Taiwan University) Baohua Fu (Academy of Mathematics and System Science-Chinese Academy of Science, China) Yoshinori Gongyo (Tokyo University, Japan)Jun-Muk Hwang (Korea Institute for Advanced Study, Korea)Yujiro Kawamata (Tokyo University, Japan) JongHae Keum (Korea Institute for Advanced Study, Korea) Sijong Kwak (Korea Advanced Institute of Science and Technology, Korea) Yongnam Lee (Sogang University, Korea) Hui-Wen Lin (National Taiwan University) Keiji Oguiso (Osaka University, Japan) Shinnosuke Okawa (Tokyo University, Japan) Jihun Park (Department of Mathematics-POSTECH, Korea) Ho Hai Phung (Institute of Mathematics, Vietnamese Academy of Sciences and Technology)


‹‹- Appendix II

Appendix II

123


Miles Reid (Sogang University and University of Warwick, Korea) Xiaotao Sun (Institute of Mathematics, Chinese Academy of Science, China) Shunsuke Takagi (Kyushu University, Japan) Shigeharu Takayama (Tokyo University, Japan) Shengli Tan (East China Normal University, China) Jilong Tong (Tsinghua University, China)

November 16, 2011

2011 NCTS & CMMSC Special Lecture on Probability Theory and Related Topics Instructor:Stuart Geman (James Manning Professor of Applied Mathematics, Brown University)


December 17-18, 2011

NCTS Interdisciplinary Workshop between Mathematics and Theoretical Physics: Cold Atom System and Its Mathematical ModelsOrganizers:Tai-Chia Lin (Nat’l Taiwan University) Daw-Wei Wang (Nat’l Tsing Hua University)



Conference on Vertex Operator Algebras, Finite groups and Related topicsSpeakersToshiyuki Abe (Ehime University)Tomoyuki Arakawa (RIMS, Kyoto University) Terry Gannon (University of Alberta) Robert L., Jr. Griess (University of Michigan) Gerald Höhn (Kansas State University) Alexander A. Ivanov (Imperial College, London) Cui Bo Jiang (Shanghai JiaoTong University) Haisheng Li (Rutgers University, Camden)Masahiko Miyamoto (University of Tsukuba)Hiroki Shimakura (Aichi University of Education)Feng Xu (University of California, Riversides) Hiromichi Yamada (Hitotsubashi University)Hiroshi Yamauch (Tokyo Woman's Christian University)

Room 639, Institute of Mathematics, Academia Sinica 6F, Astronomy- Mathematics Building


2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric AnalysisOrganizers:Der-Chen Chang (Georgetown University & NCTS)Dong-Ho Tsai (Nat’l Tsing Hua University)


Physics Division

Report of the Division Head

General Remarks

We are now in the third year of 3rd phase of NCTS operation. The total time of this

phase is 6 years and will allow some flexibility in planning Center programs. In this phase, the Center continues the format established in the 2nd phase with main project located in National Tsing Hua University (NTHU), co-hosted by National Tsing Hua University, National Chiao Tung Univers i ty (NCTU) and Nat ional Central University (NCU). In addition, the subproject I is located at National Taiwan University (NTU) with Prof. Pei-Ming Ho (賀培銘) f rom NTU as Principal Investigator while the subproject II is located at National Cheng Kung University (NCKU) with Prof. Yan-Tien Lu (盧炎田) as Principal Investigator. In 2011, about 1/3 of the budget is distributed to Subproject I while 1/6 is channeled through Subproject II. The reminder of the annual budget is allocated to the main project.

In terms of research, the Division continues the operation in the form of focus groups which assemble theorists of similar interest in Taiwan to facilitate interaction and nurture collaboration. In addition, the Center maintains a good size of research staffs to carry out research of current interest and support the activities of focus groups. The Center also has very active visitor programs for international researchers. Their visits with varied length of stay will include seminars and series of lectures. This will bring up to date for the researchers in Taiwan the current research and increase the interaction and collaboration with international community.

Organizational StructureThe operation of Physics Division is conducted

by its director with the help of the Executive Committee. Division director and Principal

Investigators of Subprojects (Professors Pei-Ming Ho and Yan-Tien Lu) are ex officio members of this committee. In 2011, the other members of the committee are Profs. Chon-Saar Chu (朱仲夏, NCTU), Kin-Wang Ng (吳建宏, Academia Sinica), Chung-Yu Mou (牟中瑜, NTHU), De-Hone Lin (林德鴻, National Sun Yat Sen University), Hsien-chung Kao (高賢忠, National Taiwan Normal University). Members of the Executive Committee represent different areas of physics and different regions in Taiwan, providing opinions and suggestions based on their expertise and judgment. They also serve as second group of reviewers for personnel appointments at Center.

Scientific ActivitiesMost of the scientific activities are planned and

carried out by various focus groups in the form of workshops and seminars. The size of these meetings varies from 40 people to more than a hundred participants. These activities provide many opportunities for physicists in Taiwan to exchange ideas and to learn from each other. In addition, there are international conferences organized by focus groups in collaboration with research organizations in other countries. These will broaden the perspectives of our workers, nurture future collaboration and enhance our visibilities on the international scene. In late 2010 a special large scale workshop on LHC (Large Hadron Collider) physics has been organized by C. P. Yuan (袁簡鵬, Michigan State University) and T. C. Yuan (阮自強, Academia Sinica) of LHC focus group. This 2-month long workshop has 9 physicists from US, 7 from Japan, 3 from Korea, 2 from India, and 8 from China. This workshop is quite timely in view of the start-up of the new accelerator LHC in Geneva.

This year NCTS has put some emphasis in the training of young researchers in theoretical physics by offering advanced courses for graduate students. Ling-Fong Li (李靈峰) has been

Report of the Division Head -›› III-2

teaching a 2-semester course on “Quantum Field Theory” at Tsinghua University to provide the very basic skill for students going into high energy physics. Professor Jason Ho was brought in to visit NCTS and give lectures on cold atoms and related subjects. Jason Ho, from Ohio State University, was the recipient of 2008 Lars Onsager Prize for his contribution to quantum liquid and diluted quantum gases. Professor Miguel Cazalilla from Centro de Fisica de Materiales, Spain came to visit for 3 months and gave a month long course on one-dimensional gas. In particle astrophysics, Professor Emmanual Saridakis from Athens University in Greece has been invited to visit for 2 months. He gave a series of lectures to introduce students to the topics of dark energy and related subjects. In addition, there were numerous schools organized by various focus groups on many special topics of interest to help students to get into research fields more easily.

The physics divis ion has many formal exchange agreements with Asian organizations in Korea and Japan. These agreements enable young researchers in Taiwan to participate in conferences and workshops abroad to get more exposure and nurture any future collaboration. The exchange with China is informal but the activity is on the rise.

Highlights of ResearchesOne of the mysteries of high energy physics is

the experimental evidence for the presence of dark matter in the universe. During past few years, the data from ATIC, Pamela, and FERMI-LAT seems to yield some results which are hard to explain in terms of the usual astrophysics and could be interpreted as due to the dark matter. Members of L H C F o c u s G r o u p a n d C o s m o l o g y a n d Astrophysics Focus Group have been actively pursuing research in this area by suggesting new models to accommodate these anomalies. Chao-Qiang Geng (耿朝強), member of Cosmology and Astrophysics Focus Group, has also been very active in trying to explain the dark energy of the universe by the mechanism of modifying Einstein’s General Relativity.

Member of focus groups on strongly correlated system Ying-Jer Kao (NTU), and his coworkers study the electronic transport in a molecular

junction. Using the non-equilibrium Green's f u n c t i o n m e t h o d , t h e y o b s e r v e t h a t t h e conductance oscillates with the molecular chain.

Also in focus groups on strongly correlated system Po-Chung Chen (陳柏中, NTHU), Ming-Chiang Chung (張明強, NCTS), Sungkit Yip (葉崇傑, Academia Sinica), and their student show that the Berry’s phase depends not only on the shape of the system but also on the hopping couplings for bipartite honeycomb lattices. Using the entanglement entropy spectra obtained by diagonalizing the block Green’s function matrices, the maximal ly en tangled s ta tes wi th the eigenvalue λm = 1/2 of the reduced density matrix are shown to have 1-to-1 correspondences to the zero-energy states of the lattice with open boundaries.

M e m b e r o f f o c u s g r o u p s o n A t o m i c -Moleculan-Optical physic Daw-Wei Wang (王道維, NTHU), worked with Prof. S. Das Sarma and his postdoc in University of Maryland on the first complete quantum phase diagram for Bose-Fermi mixture of dipolar atoms/molecules in 1D optical lattice. The result shows a Bose-Fermi solid in strongly interacting regime and has a nontrivial quantum melting

Recruitment and Scientific StaffIn 2011, many of our post-doctors have found

jobs elsewhere. Dr. Eibun Senaha has joined Korean Institute for Advanced Study (KIAS) as post-doctor, Dr. Dan Tomino has taken a senior post-doctor position at Tunghai University, Dr. Jae-Sik Lee has moved to NTHU as a research scholar and Dr. Hong-Da Chen (陳鴻大) has moved to National Central University for a post-doctor position. Five new people have joined the physics division: Dr. Yu-Kuo Hsiao (蕭佑國, particle physics) from Academia Sinica, Dr. Jackson Wu (particle physics) from University of Bern, Dr. Hiroshi Yokoya (橫谷洋, particle physics) from CERN as assistant research scholar. The new post-doctors appointments are: Dr. Wen-Ming Huang (黃文敏, condensed matter physics) from NTHU, Dr. Yong Tang (湯勇, particle physics) from Institute of Physics in Beijing, Dr. Hirotaka Irie (入江広隆, string theory) from NTU.

In addition, there were several senior theorists

III-3 ‹‹- Report of the Division Head

visiting NCTS from abroad for some length of time, Professor Miguel Cazalilla from Cente de Fisics de Materiales, Spain for 3 months, Professor Emmanual Saridakis from Athens University in Greece for 2 months, Jason Ho, from Ohio State University for a week, Professor John Ng from TRIUMP for a month, Professor Wai-Yee Keung from University of Illinois at Chicago Circle for 3 weeks, Professor Tu-Nan Chang from University of Southern California for 4 weeks.

In the Center Scientists program, the new Center Scientists appointments are Prof. Cheng-Wei Chiang (蔣正偉) on the junior level and Prof. Cao-Qiang Geng (耿朝強), on the senior level. The other Center Scientists are Prof. David Lin (林及仁), Prof. Chung-Hsien Chou (周忠憲) and

Prof. Daw-Wei Wang (王道維), on the junior level and Hsuan-Yi Chen (陳宣毅), and Prof. Baruch Rosenstein (儒森斯坦) on the senior level.

Young Theorist AwardYoung Theorist Award was established in 2006

to promote excellent research work done by young theorists. This year many excellent candidates from various institutions in Taiwan have applied. The Executive Committee has selected Prof. Chyh-Hong Chern (陳智泓) of National Taiwan University, and Prof. Yueh-Nan Chen (陳岳男) of National Cheng Kung University for this awards.

Ling-Fong Li (李靈峰)

November 2011

Report of the Division Head -›› III-4

Highlights of ProgramsComplex System

Focus Group on Complexity and LifeCoordinator: Hsuan-Yi Chen (NCTS/National Central University; email: [email protected])

I. Brief Description

his focus group has ~35 PIs from various institutes in north and central Taiwan.

The coordinator is Hsuan-Yi Chen (NCU Physics) The committee members of our focus group are: Chi-Keung Chan (Academia Sinica Physics), Peilong Chen (NCU Physics), Kai-Jung Chi (NCHU Physics), Pik-Yin Lai (NCU Physics), Hoong-Chien Lee (NCU SysBiol), Watson Kuo (NCHU Physics), Jiunn-Ren Roan (NCHU Physics), Ming-Chih Shih (NCHU Physics), Sun-Chong Wang (NCU SysBiol)

Current research projects include:

1. Econophysics:　Fractal dimension analysis of time sequences

2. Nonlinear Dynamics: Evolutionary dynamics, biofilms, neural networks

3. Biophysics: Lipid rafts, interactions of lipid b i layers wi th prote ins, the mechanica l responses of spider webs, molecular motors, cell adhesion and cell movement

4. Biomechanics: Insect locomotion, f luid dynamics of biological sniffers

5. Granular Physics: The mechanism of vibrating granular system

6. Systems Biology: Evolution of genomes, sys tems b io logy of Chinese pharmacy, synchronization in biological networks, etc.

II. ActivitiesRegular meetings: 5 regular meetings are funded by our FG

1. Bio-soft matter seminars at NCU Physics: Thursday 12:00-13:00

Most of the speakers in this seminar series are graduate students and postdocs. About 25 people regularly attend this seminar series. The main topics are nonequilibrium statistical physics, biomenbranes, molecular motors, biological networks, and fluid dynamics. There are about 30 talks in a year.

2. Systems Biology Colloquium at NCU Inst of Sys Biol: Thursday 11:00-12:00

This weekly colloquium series strongly focus on the application of systems biological methods to real biological and medical problems. Most of the speakers come from different life and medical sciences research institutes and universities in Taiwan. Each year there are about 25 talks and most speakers are invited speakers around Taiwan and from abroad. The size of the audience is about 50.

3. Biophysical Journal Club at NCHU Physics: Thursday 12:00-13:00

Biophysical Journal Club (BJC) has attracted broad attendance from various disciplines. Every year more than 25 talks and ~30 people attend the Club meetings. Most of the speakers are from different research institutes and universities in Taiwan. The topics include bio-mechanics, cell biophysics, and soft matters. Details of the BJC activity subjects can be found at http://nchu-bjc.blogspot.com/

III-5 ‹‹- Highlights of Programs

4. Nonlinear phenomena seminar at NCHU Physics: Friday 15:30-18:00

Nonlinear phenomena seminar is organized by Prof. Liaw. The scope of the seminar includes granular physics, pattern formation, and fractal analysis of complex systems. About 10 to 15 people attend the seminar series.

5. Seminar series at NCTS HsinChu: Friday 12:00-13:00

This is a small scale seminar series on general aspects of complexity and physical biology. The common interests of the participants are networks, ecology and evolution, and other complex systems. Participants include PIs and students from NDHU, NTHU, NCU, and NCTS.

Workshops, conferences, and schools

1. C o m p l e x s y s t e m s s y m p o s i u m , 2011/06/21~6/23, Tamkang Unive r s i ty (Taipei).

This student symposium had about 30 student speakers from different graduate institutes around Taiwan. Talks were in the general field of complex systems including nonlinear dynamics, statistical physics, biological physics, systems biology, and biomechanics. There were about 80 attendees in which ~20 were PIs and ~60 were students. To provide more chances for the participants to discuss their research works, there was a discussion session during which the participants could discuss with the speakers about their talks in details. The total expense of this symposium is about NTD50K.

2. 6th Cross-Strait Conference on Statistical Physics (CSCSP6), 2011/7/27~2011/7/30, Sun-Moon Lake (Nantou).

This conference invited scientists working on s ta t is t ica l physic is ts f rom Taiwan and Mainland China. There were about 80 participants and 30 talks. Our FG partially supports this conference. The total expense from our FG is about NTD7K.

3. Regional Workshop for Soft Matter and Biophysics, 2011/10/27~10/29, Department of Chemistry, NTU, Taipei.

To give junior PIs in Taiwan and Japan more chances to know the research works of each other, in Dec 2005 we organized a Regional Workshop for Soft Matters and Biophysics in Taipei. A similar meeting was organized by Japanese scientists in the fall of 2009 in Tokyo. This 3-day workshop is the 3rd one of these meetings. We will invite 9 Japanese and 7 Taiwanese speakers to present their recent works on nonequilibrium statistical physics and soft matters. Student posters were arranged so that more discussions between speakers and participants were possible. According to our previous experience, we expect the number of participants will be around 70, and the total cost will be about NTD130K.

4. Bio-Soft matter days 2012: January 15-17 2012, Jia-Yi.

For our FG members, “Bio-soft matter days” has become inseparable from the annual meeting of PSROC. Since Jan. 2011, our FG organizes the biophysics/soft-matter sessions of the annual meetings of PSROC such that it becomes the place for the FG members (and other scientists working in related fields) to report their new works. Bio-soft matter days is right before the annual meeting of PSROC, during which about 15 speakers are invited to present their research in an environment that is more su i table for fur ther d iscuss ions . Therefore for our FG these two meetings are actually a combined event, while all FG members are encouraged to present their research results in PSROC soft matter/biophysics sessions, a few topics will be chosen to be discussed in details in bio-soft matter days. In this way the Bio-soft matter days helps the FG members to know each o the r ’s work i n more de t a i l s and t he d i s c u s s i o n s w i l l e n c o u r a g e f u t u r e collaborations within the FG. We expect the participants and expense to be similar to what we had in Jan 2011. About 110 people will attend this annual workshop and the total expense from our FG will be about NTD120K.

Supporting young scientists

A. International conferences and visits

Under the support of our FG, we have sent 2 g r a d u a t e s t u d e n t s , o n e a t t e n d e d a n

Highlights of Programs -›› III-6

international conferences and the other one visited the nonlinear dynamics group of the Department of Physics of Kyoto University.

B. Student Awards

�•��Fu-Lai�Wen�(NCU)�won�the�Best�Poster�Award�for Students in the 7th Joint Meeting of Chinese Physicists Worldwide (OCPA7).

�•��Wan-Jung Lin (Academia Sinica) won the Best Poster Price in 2011 annual meeting of PSROC.

�•��Shu-Han Chao (Academia Sinica) won the Best Poster Price in 2011 annual meeting of PSROC.

III. Visitors and International Collaborations

List of Foreign visitors:

name period of visit expense

====================================

劉曾榮 02/15-02/19 10365

文鐵橋 02/15-02/19 10365

Alexander Mikhailov 03/10-03/30 92724

Ramy Karam Aziz 06/20-06/15 48073

鄭波 08/06-08/14 38826

薛宇 08/13-08/27 47244

====================================

Our FG supports the following (mutual) visits for international collaborations:

1. Kai -Jung Chi (NCHU) has es tab l i shed collaboration with Prof. Stanislav Gorb from the Zoology Institute of Kiel University, Germany.

2. As a part of the long-term collaboration between Hsuan-Yi Chen (NCU) and Prof. Mikhailov (FHI Max-Planck Society, Berlin, Germany) on nonequilibrium soft matters. Mr. M-J Huang, currently a PhD student is visiting Frirz-Harber Institute at Berlin from early Sep to late Nov 2011 through the grant from FHI. Prof. Mikhailov also visited Taiwan for 2 weeks in March 2011 as a part of this collaboration, his visit was funded by NCTS. In later Nov, Prof. Mikhailov will visit Taiwan again, this time with his traveling grant from FHI.

3. Pik-Yin Lai (NCU) and CK Chan (Academia Sinica) continue their collaboration with Prof. Osipov (Nizhny Novgorod State Medical Academy, Russia) in the study of the nonlinear dynamics of cardiac tissues.

IV. Highlights of Research ResultsThe research group led by PY Lai (NCU) and

CK Chan (Academia Sinica) continued research in excitable systems. A notable breakthrough is the discovery of the mechanism for frequency enhancement in coupled noisy excitable elements. Especially, computer simulations for a coupled square la t t i ce of exc i tab le e lements can quantitatively reproduce the unexpected peak in the variation of the beating rates observed in cultured cardiac cells experiments. This work is published by Phys. Rev. Lett.

The research group led by SS Liaw (NCHU) has made progress on the segregation mechanism of granular systems. In a recent experiment, beads with two different values of restitution coefficients but otherwise identical were put between two horizontal vertically vibrating plates. Segregation of different types of beads is found under a range of oscillation amplitude and frequency. The segregation mechanism is due to an effective horizontal repulsion between different types of beads induced by bead-bead collisions. Non-horizontal collisions also play a role in stabilizing the segregation state by transferring the horizontal kinetic energy back into vertical motion

The research group led by HC Lee (NCU) has recently designed a way to analyze copy number variation (CNV) in genomes. The study of CNV is very important because it has to be with the detection of abnormal mRNA transcript levels inside a cell. HC Lee et al have designed a package that is based on statistical principles, measurement theory, and precise mathematical relations. The package’s running time scales linearly with the size of microarray, so it is very helpful in analyzing large amount of experimental data. This work is published in Nucleic Acid Res.

Together with his student, Chi-Lun Lee (NCU) studied the asymptotic dynamics of self-driven vehicles in a closed boundary. From their results they suggest that the degree of chaoticity for such


systems of self-driven particles can be defined from either integrations over unnormalized autocorrelation functions or the inverse of system relaxation times.

Hsuan-Yi Chen (NCU) in collaboration with K-t Leung (Academia Sinica) proposed a phenomenological model for the trajectories generated by moving Listeria or functionalized beads. The found that the transitions from straight to sine-wave or circular trajectories are well described by a Hopf or pitch-fork bifurcation. Experimentally observed complicated geometrical trajectories such as translating figure-eight and serpentine are also reproduced by this model.

Kai-Jung Chi (NCHU) is preparing to publish her work with colleagues Mr. Yung-Kang Chen and Dr. Ming-Huang Wu about the effects of dragline silk on spider jumping. The results suggest that during a jump the dragline silk can (1) provide significant role in decreasing spider’s velocities to reduce landing impact, and (2) allow the spider to adjust its body orientation for optimum landing posture. A mechanism is proposed to explain how silks help achieve dynamic body balance during the aerial phase of jumping.

V. Selected Publications[1] Chih-Hao Chen, Hsing-Chung Lee, Qingdong

Ling, Hsiao-Rong Chen, Yi-An Ko, Tsong-Shan Tsou, Sun-Chong Wang, Li-Ching Wu, and H.C. Lee, “An all-statistics, high-speed algorithm for the analysis of copy number var iat ion in genomes”, Nucleic Acids Research, 39, e89 (2011).

[2] Hs in -Hui L iang and Hsuan-Yi Chen , “Strength of adhesion clusters under shared linear loading”, Phys. Rev. E, 83, 061914 (2011).

[3] C h i - L u n L e e a n d C h i a - L i n g H u a n g , “Asymptotic dynamics of self-driven vehicles in a closed boundary”, J. Sat. Phys., 144, 813 (2011).

[4] E. Avalos, Pik-Yin Lai, C.K. Chan, “Spiral waves in the heterogeneous exci table Kuramoto model”, Europhys. Lett. 94, 60006 (2011).

[5] X. Zhan, PY Lai and C.K. Chan, “Effects of glial release and somatic receptors on bursting in synchronized neuronal networks”, Phys. Rev. E 84, 011907 (2011).

[6] WC Lo, H.C. Hong, H.J. Choi, PY Lai and C.K. Chan, “Stretching and migration of DNA by solvent elasticity in an oscillatory flow”, Phys. Rev. E 84, 021802 (2011).

[7] WY Ch iang , PY La i and C .K . Chan , “Frequency enhancement in coupled noisy excitable elements”, Phys. Rev. Lett. 106, 254102 (2011).

[8] S.-Y. Liaw, F.F. Chung and S.S. Liaw, “Horizontal segregation of mono-layer granules coordinated by vertical motion”, Eur. Phys. J. E 34, 59 (2011).

[9] Panupat Chaiworn, Fei Fang Chung, Cheng-Yen Want and Sy-Sang Liaw, “Brazil nut effect in annular containers’, Granular Matter 13, 379 (2011).


Focus Group on Critical Phenomena and Complex SystemsCoordinator: Chin-Kun Hu (Institute of Physics, Academia Sinica; email: [email protected])


he purpose of this FG is to develop ideas and methods in statistical and nonlinear

physics, then apply such ideas and methods to complex physical, biological, and social problems. The focus research topics include (1) Theoretical models of critical phenomena, chaos, and pattern formation, (2) Structures, folding, aggregation, and evolution of biological macromolecules, (3) Modeling and analysis of complex network and signals. The activities of this FG can be found at “Activity” of LSCP website: http://proj1.sinica.edu.tw/~statphys/.

The key researchers of this FG include (1) Shu-Chiuan Chang (張書銓) at Physics Dept. of National Cheng-Kung University, Chi-Ning Chen (陳企寧) at Physics Department of National Dong-Hwa University, Wen-Jong Ma (馬文忠) at Graduate Institute of Applied Physics, National Chengchi University, Chung-I Chou (鄒忠毅) at Department of Physics of Chinese Culture University, Ming-Chang Huang (黃敏章) at Department of Physics of Chung-Yuan Christian University, Po-han Lee (李柏翰) at The Affiliated Senior High School of National Taiwan Normal University, Chai-Yu Lin (林財鈺) at Physics Department of National Chung Cheng University, Jung-Hsin Lin (林榮信) at Research Center for Applied Sciences & Institute of Biomedical Sciences of Academia Sinica, Yu-Pin Luo (羅煜聘), Department of Electronic Engineering of National Formosa University, Chi-Tin Shih (施奇廷), Department of Physics of Tunghai University, Wen-Jer Tzeng (曾文哲) at Department of Physics of Tamkang University, Dr. Ming-Chya Wu (吳明佳) at Research Center for Adaptive Data Analysis of National Central University, Jui-Ling Yu (余瑞琳) at Department of Applied Mathematics of Providence Univ., Zicong Zhou (周子聰) at Department of Physics of Tamkang Univ.,(2)

Long term visitors: D. Y. Lando from Belarus National Academy of Sciences, BELARUS; David B. Saakian from Yerevan Physics Institute in Armenia; Sasun G. Gevorkian from Yerevan Institute of Physics, (3) Postdoctoral fellow: Shura Hayryan, Karen Petrosyanand at Inst of Phys. of AS; Chung-ke Chang at Institute of Biomedical Sciences, Academia Sinica, (4) Ph.D. students: Chun-Ling Chang at Natl Central Univ., Hsin-Ling Chiang at Natl-Hsing Hua Univ., Shi-Chieh Wang at Natl Chung Hsin Univ, Yu-Hsin Hsieh at National Taiwan University.

II. Activities A. Academic activities (see “Activities” at http://

proj1.sinica.edu.tw/~statphys/)

(1) We organized a series of four 2011 NCTS Workshops on Crit ical Phenomena and Complex Systems on 24-26 February, 29 and 30 April, 9-11 June, 12 August 2011. Two more workshops will be organized during October-December 2011.

(2) We have organized BioComplex-Taiwan 2011: 2011 Taiwan International Workshop on Biophysics and Complex Systems at Institute of Physics of Academia Sinica on 21-26 July 2011.

(3) We have helped to organize CSCSP6: The 6th Cross Strait Conference on Statistical Physics at Sun Moon Lake on 27-30 July 2011.

(4) We have helped to organize and sponsored “2011 Taipei Workshop on Econophysics Modeling and Practice of Financial Market.” on 8-11 August 2011 at National Cheng Chi University.

B. Train young-generation physicists

(1) Shu-Chiuan Chang, Chi-Ning Chen, and Jui-Ling Yu, Wen-Jer Tzeng visited NCTS (North) in the summer break of 2011.


(2) Ph.D. student Mr. Shi-Chieh Wang has been collaborating with Prof. Z. R. Struzik at University of Tokyo to work analysis of physiological signals.

(3) Ph.D. student Hsin-Ling Chiang visited Institute of Molecular Sciences, Okazaki, Japan in July 2011 to collaborate with Prof. Hisashi Okumura on aggregation of poly Q peptides related to Huntington disease.

(4) Ph.D. student Chun-Ling Chang has been collaborating with Prof. D. Y. Lando at Belarus National Academy of Sciences, BELARUS, to work on DNA melting.

C. Invited presentations

(1) Dr. Chin-Kun Hu gave two invited talks: “Neurodegenera t ive d i seases , p ro te in aggregation, and neural networks” on 18 March 2011, and “Some recent results for complex networks of nonlinear and biological s y s t e m s ” o n 2 1 M a r c h 2 0 1 1 a t “Interdisciplinary Applications of Statistical Physics & Complex Networks” at KITPC, Beijing on 28 February-1 April 2011.

(2) Dr. Chin-Kun Hu gave a plenary talk “Toward a unified theory for protein aggregation problem” at Mathematical Modeling and Computa t iona l Phys ics a t High Ta t ra Mountains, Slovakia, 4-8 July 2011.

(3) Dr. Chin-Kun Hu gave an invi ted ta lk “Relaxation and aggregation of polymer chains and their biological implications” at International Conference in Statistical Physics 2011 (Acronym: SigmaPhi2011) at Golden Bay Beach Hotel, Larnaca, Cyprus on 11-15 July 2011 (website: http://www.sigmaphi2011.org/).

(4) Drs. Chin-Kun Hu, Ming-Chya Wu and Shura Hayryan gave p lenary t a lks a t the 7 th International Conference on Structure and Stability of Biomacromolecules, Kosice, Slovakia (http://www.saske.sk/UEF/biophys/conference/index.html) on 6-9 September 2011.


Short term visitors can be found from speakers of BioComplex-Taiwan 2011 and Workshops listed in II.A. We are collaborating with visitors on following problems.

(1) Prof. Yevgeni Mamasakhlisov (Yerevan State Un iv. ) , Shura Hayryan and C . -K . Hu collaborate to study transport behavior of biopolymers in the entropy trap. A manuscript on this problem was submitted to Phys. Rev. Lett. for publication.

(2) Shura Hayryan, Ming-Chya Wu and Chin-Kun Hu in collaboration with Prof. Nikolay V. Dokholyan’s group at North Carolina are establishing database and website for three-dimensional structures of microRNA. More than 2000 3D structures of microRNA have been calculated. The draft of the manuscript is completed.

(3) Ming-Chya Wu, Yao-Chen Hung, Shi-Chieh Wang, Chin-Kun Hu, in collaboration with Z. R. Struzik and Y. Yamamoto at University of Tokyo are analyzing physiological signals to identify health problems in human subjects.

(4) Hsin-Ling Chiang, Wen-Jong Ma, Yun-Ru Chen (Genomics Res Center of AS), Rita Chen (Inst. Bio. Chem., AS), and Chin-Kun Hu in collaboration with Mai-Suan Li (Polish Academy of Sciences) and Hisashi Okumura (Institute for Molecular Science at Okazaki,) to work on protein folding and aggregation problems. A manuscript on stability of PolyQ dimer is completed.

(5) Jui-Ling Yu and Prof. Olga. S. Rozanova of Department of Math. a t Moscow State University are establishing a mathematical model for predicting the trajectory of typhoon on curved space.

(6) Chi-Ning Chen and Prof. Jonathan Dushoff (Dept. of biology, McMaster University, Canada, July-August 2011 in Taiwan) are working on the SIRS model of epidemics using stochastic partial differential equations [T. Reichenbach et al, Nature 448, 1046 (2007); PRL 99, 238105 (2007)].


IV. Highlights of Research Results (1) Molecular model for the origin of life.

D. B. Saakian, C. K. Biebricher and C.-K. Hu used methods of statistical physics to study a paradox about the origin of life by carefully analyzing the implications of neutral and lethal mutants, and truncated selection (i.e., when fitness is zero after a certain Hamming distance from the master sequence) for the critical chain length They found that lethal mutants and truncated selection together can solve the error catastrophe paradox. [Plos One, 6, e21904 (2011)].

(2) Gassy state of native collagen fibril.

This work results from collaboration between experimental and theoretical researches. Our experimental results indicate that collagen fibril has glassy behavior in room temperatures. The gassy behaviors of collagen fibril and other biopolymers are useful for understanding the mechanism for biological organisms to maintain in nonequilibrium state [EPL 95, 23001 (2011)]

(3) Exact probability distribution function for multifractal random walk models of stocks.

We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model [EPL 95, 28007 (2011)].

(4) Exact solution of a monomer-dimer problem: A single boundary monomer on a nonbipartite lattice.

F. Y. Wu, W. J. Tzeng and N. S. Izmailian solved the monomer-dimer problem on a nonbipartite lattice, a simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the nonbipartite nature of the lattice, the well-known method of solving single-monomer problems with a Temperley bijection cannot be used. In this

paper, we derive the solution by mapping the problem onto one of closed-packed dimers on a related lattice. Finite-size analysis of the solution i s ca r r ied ou t . We f ind f rom asympto t ic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value c = -2 [Phys. Rev. E 83, 011106 (2011)].

V. PublicationsPapers with NCTS as the affiliation

[1] David B. Saakian, Christof K. Biebricher, and Chin-Kun Hu, “Lethal mutants and truncated selection together solve a paradox of the origin of life”, Plos One 6, e21904.

[2] Zara Kirakosyan, David B. Saakian and C.-K. Hu, “Finite genome length corrections for the mean fitness and gene probabili t ies in evolution models”, J. Stat. Phys. 144, 198-212.

[3] D. B. Saakian, A. Martirosyan, C.-K. Hu, and Z. R. Struzik, “Exact probability distribution function for multifractal random walk models of stocks”, EPL 95, 28007.

[4] A. Martirosyan1 and David B. Saakian, “Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations”, Phys. Rev. E 84, 021122.

[5] Shu-Chiuan Chang and Lung-Chi Chen, “Hamiltonian walks on the Sierpinski gasket”, J. Math. Phys. 52, 023301 (20 pages).

Papers acknowledged NCTS supports

[1] Y. C. Hung and C.-K. Hu, “Constructive role of noise in p53 regulatory network”, Comp. Phys. Commu. 182, 249.

[2] K. G. Petrosyan* and C.-K. Hu*, “Protein-mediated Loops and Phase Transition in Nonthermal Denaturation of DNA”, J. Stat. Mech. P01005.

[3] F. Y. Wu, Wen-Jer Tzeng, and N. Sh. Izmailian, “Exact solution of a monomer-dimer problem: A single boundary monomer on a nonbipartite lattice”, Phys. Rev. E 83, 011106.


[4] K. Singh, P. E. Parham and C.-K. Hu, “Structural perturbations to population skeletons: transient dynamics”, coexistence of attractors and rarity of chaos, Plos One 6, e24200.

[5] S. G. Gevorkian, A. E. Allahverdyan*, D. S. Gevorgyan and C.-K. Hu, “Glassy state of native collagen fibril?”, EPL 95, 23001.


Highlights of ProgramsCondensed Matter Physics

Coordinators: Ming-Chiang Chung (NCTS; email: [email protected]),

Chung-Hou Chung (National Chiao Tung Univesity; email: [email protected])


he focus group is formed to promote research topics on mesoscopic physics

and strongly correlated systems and provide opportunities for condensed matter theoreticians interested in different materials and methods to increase the interaction and cooperation. In recent three years this focus group serves as a platform between NCTS in Taiwan and junior research groups in APCTP (Asian Pacific Center for Theoretical Physics) to facilitate the international collaborations, especially with young talented researchers from the asian pacific region (China, Korea, Japan and Taiwan). In addition we financially support students and young researchers to participate international conferences.

We have over 70 sing-up members in this focus group and around 1/3 of the members have been actively participating the group activities. The research topics are addressed on spintronics, topological insulators, graphenes, multiferroic materials, quantum transport, entanglement in condensed matters and nanostructures and cold atomic systems applied in condensed matter physics.

II. ActivitiesIn the past year (Oct. 2010 - Sep. 2011), our

focus group has organized (or co-organized) the following activities:

1. Miniworkshop on mesoscopic and spintronic systems

Recently, there has been growing interest in novel quantum effects on charge and spin transports in low-dimensional mesoscopic/condensed matter systems with gapless surface/edge states, such as: in two-dimensional graphene sheets, topological insulators (TI), and topological superconductors (TSc) where the spin-orbit interactions are important. The new quantum phenomena includes quantum spin-Hall effect in graphene and TI, the spin current and the existence of Majorana fermions in TSc, helical edge states and gapless chiral modes in graphene and TI, novel quantum transport properties of quantum dots in graphene and TI systems. Understanding the above new physics has great importance not only in these fundamental research but also in technological applications of these fundamental results in making new electronic devices.In this workshop, we bring domestic and international experts together to discuss recent progress in the above topics. The goals are to encourage collaborations among the experts, and to introduce this exciting new research field to students and young researchers participating in this workshop.Invited speakers:Organized by Institute of Physics, Academia Sinica (IPAS), National Center for Theoretical Sciences, Physics Division (NCTS).

Working Group on Quantum Phenomena in Condensed Matter Physics

A. Focus Group on Mesoscopic Physics and Strongly Correlated Systems


2. Quantum Condensation 2011 (04 -15 July) Hong-Kong

The idea of QC workshop was initiated by Prof. Peter Fulde (Director of APCTP) . The goal of this workshop is to intensively increase the collaboration among the condensed matter physicists working in the asian pacific countries. In this 2-week’s workshop we want to create a laid-back atmosphere for participants for building trust and long-term collaborations. In 2009 our focus group helped Prof. Xin Wan (APCTP) organize QC09 in APCTP, Pohang Korea. In 2010 QC10 was held in NCTS, Hsinchu organized by one of our coordinators (Ming-Chiang Chung). In 2011 our focus group helped QC11 held in Hong-Kong university of sciences and technology. This workshop was organized by Prof Tai-Kai Ng.

QC11 invited 34 participants from all over the asia (Taiwan, China, Hongkong, Korea, Japan and Germany). 7 Taiwanese researchers and postdocs participated this workshop. This year, QC11 had two panel topics: Majorana fermions and topology in quantum information.

Since 2009, QC 11 has been grown to one of the most important workshops in asia. More and more young talented researchers from asia and even from australia and europe would like to par t ic ipate th is workshop. The la id-back discussions in each talk has inspired a lot of collaborations among those participants. Our focus group always plays a important role in the organization of QC workshop. We bring a strong team to the international community and create the interaction among the physicists in the asian pacific region. Please see website: http://physics.ust.hk/quantcond2011/go/site/qc/home.html

QC12 will be held in APCTP, Pohang Korea again in 2012. QC13 (2013) will be held in Taiwan again.

3. Miniworkshop on topological insulator (29 - 30 July NCTS Hsinchu)

A topological insulator (TI) is a material that behaves as an insulator in its interior or bulk while permitting the movement of charges (metallic) on its surface. Topological insulators are related to fractional quantum hall effect, Majorana Fermions and different important topics of quantum physics. In this miniworkshop we invited 6 experts from

China and Hongkong to teach non-experts about topological insulators from the fundamental knowledge.

The outcome is very successful. Since each speaker had two hours to present an both educational and professional lecture, the audience learned a lot afterwards. This workshop served as a satellite workshop of OCPA (Oversea chinese physicis t associat ion) conference held in Kaoshiung this year. Therefore the audience could learn TI in this workshop and then could u n d e r s t a n d m o r e a b o u t T I i n t h e O C PA conference.

4. Summer school for numerical methods in condensed matter physics (05 - 09 Sep.)

Our focus group and FG (numerical methods in strongly correlated systems) organized together a summer school for numerical methods in condensed mat te r phys ics . We inv i ted 4 experienced physics in those field from Germany, USA and Australia. The goal of this school was to offer students at Master and PhD levels an introduction to simulation methods for quantum many body systems in condensed matter physics.

In particular the school covered the following topics: exact diagonalization (ED), classical and quantum Monte Carlo methods, density matrix renormalization group (DMRG), numerical renormalization group (NRG), and functional renormalization group (fRG). The school also focused on hands-on experience via the extensive coding sessions in the afternoon.

The topics of the summer school:

•��Exact�Diagonalization.�•��Classical�Monte�Carlo.�•��Quan tum� Monte� Car lo� (SSE� and�Worm�

Algorithm).•��Dens i ty� Matr ix� Renormal iza t ion� Group�

(DMRG).•��Numerical�Renormalization�Group�(NRG).

The students claimed that they had learned a lot in this summer school. The lecturers offered enough materials for them to start the numerical methods in physics.

5. With limited travel supports, we manage to support 6 graduate students and postdocs to attend international conferences. This channel of


supports is precious for the talented young bloods and their exposure to the international community has given them a glimpse about the outside world. In addition, we hope to attract young talents into condensed matter physics via summer school, workshops/miniprograms and journal clubs.


International visitors

1. Miniworkshop on mesoscopic and spintronic systems

Prof. Pawel Hawrylak, National Research Council, Canada Prof. Shuichi Murakami, Tokyo Institute of Technology, Japan Prof. Akira Furusaki, RIKEN, JapanDr. Stephan Rachel Yale University, U.S.A.

2. Miniworkshop on topological insulators (29. - 30. July)

Prof. Xin Wan (Zhe-Jiang university) (28. July - 2. Aug) Prof. Shun-Qing Shen (Hongkong university) (28. July - 31. July) Prof. Zhong Fang (Chinese academy of sciences) (28. July - 31. July) Prof. Xin-Chen Xie (Peking university) (28. - 31. July) Prof. Kam-Tuen Law (Hongkong university of sciences and technology) (28.- 31 July).

3. Summer school on numerical methods in condensed matter (05. -09. Sep)

Prof. Ian McColluch (Univ. of Queensland, Australia) Prof. Helmut G. Katzgraber (Texas A&M, USA) Dr. Andreas Wechselbaum (LMU, Germany) Dr. Mikhail Pletyukhov (RWTH Aachen, Germany)

International collaborators

1. Chung-Hou Chung (NCTU)+ Prof TK Ng (HKUST) ) on nonequilibrium transport via functional bosonization approach.

2. Chung-Hou Chung (NCTU)+ Prof. Miguel Cazalilla,� (Centro� de�F´ısica� de�Materiales�

(CFM) Spain) on interaction effects of topological insulators.

3. Chung-Hou Chung (NCTU)+. Matthias Vojta (TU Dresden) on quantum phase transitions in Kondo systems.

4. Ming-Chiang Chung (NCTS) + Prof. Ingo Peschel (Free university berlin) on quantum information applied in condensed matter.

5. Ming-Chiang Chung (NCTS)+ Prof. Miguel Cazallila� (Centro� de� F´ısica� de�Materiales�( C F M ) S p a i n ) + P r o f . A n i b a l I u c c i (Universidad Nacional de La Plata, Argentina) on quench dynamics of solvable models.

6. Ming-Chiang Chung (NCTS)+ Prof. Pochung Chen(NTHU) + Prof. Sungkit Yip (Academia Sinica) + Prof. Ian McColluch (Unversity of Queenzland, Australia) on spin 2 bosnons in one dimension.

7. Ming-Chiang Chung (NCTS) + Prof. Carlos Trallero-Gino (Departamento de Fisica Teorica, Universidad de La Habana, Cuba) on BEC in one dimension.

8. Hsiu-Hau Lin (NCHU) + Toshiya Hikihara (Hokkaido University) and Jian-Ming Tang (University of New Hamshire) on Graphenes.

IV. Research HighlightsSuperconductivity

Chung-Hou Chung collaborated with Le Hur at Yale university on the designing heterostructures with the high temperature superconductivity [Phys. Rev. B 84, 024526 (2011)]. They propose to increase the superconducting transition temperature Tc of strongly correlated materials by designing heterostructures which exhibit a high pairing energy as a result of magnetic fluctuations. More precisely, applying an effective theory of the doped Mott insulator, they envisage a bilayer Hubbard system where both layers exhibit prominent in t ra layer ( in t raband) d-wave superconducting correlations. Introducing a finite asymmetry between the hole densities of the two layers such that one layer becomes slightly more underdoped and the other more overdoped, they evidence a visible enhancement of Tc compared to the optimally doped isolated layer. Using the


bonding and antibonding band basis, they show that the mechanism behind this enhancement of Tc is the interband pairing correlation mediated by the hole asymmetry which strives to decrease the paramagnetic nodal contribution to the superfluid stiffness. These heterostructures shed new light on f u n d a m e n t a l q u e s t i o n s r e l a t e d t o superconductivity.

Hsiu-Hau Lin and Wen-Min Huang work on Pairing mechanism in multiband superconductors. It has been a long-standing puzzle why electrons form pairs in unconventional superconductors, where the mutual interactions are repulsive in nature. They find an analytic solution for renormalization group analysis in multiband superconductors, which agrees with the numerical results exceedingly well. The analytic solution allows them to construct soluble effective theory and answers the pairing puzzle: electrons form pairs resonating between different bands to compensate the energy penalty for bring them together, just like the resonating chemical bonds in benzene. The analytic solutions allow us to exp la in the pecu l i a r f ea tu res o f c r i t i ca l temperatures, spin fluctuations in unconventional superconductors and can be generalized to cuprates where the notion of multiband is replaced by multipatch in momentum space. Therefore, finding effective attractions between electrons is no longer a necessity and the secret for higher superconducting temperatures lies in boosting pair hopping between different bands.

Quantum Dot

Chung-Hou Chung collaborates with Maco, Simon and Zarand on Non-equilibrium frequency-dependent noise through a quantum dot using a real-time functional renormalization group approach [Phys. Rev. B 83, 201303(R) (2011)]. They construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. They find that the current vertex develops a non-trivial non-local structure in time, governed by a new set of RG equations. Solving these RG equations, they compute the complete frequency and temperature-dependence of the noise spectrum.

Chung-Hou Chung h imsel f worked on Dynamical properties of a nonequilibrium quantum dot close to localized-delocalized quantum phase transitions [Phys. Rev. B 83, 115308 (2011)]. They generalized the non-equilibrium RG approach to account for the dynamics o f the decoherence r a t e . Th i s generalization offers a better and more accurate way to compute various dynamical quantities out o f equ i l i b r i um, wh ich can be measu red experimentally. This was not possible in a more primitive approach by A. Rosch et. al. where the decoherence rate was included in the static limit and in a more ad hoc way. Therefore, this paper can be considered a progress and improvement in the methodology of the nonequilibrium RG approach.

Shun-Jen Cheng and co-workers work on Semiconductor quantum dot as on-demand entangled photon pair emitter. Fabrication of semiconductor quantum dots (QDs) as “on demand” single photon and polarization entangled photon pair sources, as key photonic devices necessary in the applications of optical quantum cryptography and teleportation, has been under development for years, However, generating entangled photon pairs directly from QDs is still very challenging because of inherent fine structure splitting between the intermediate exciton states. Up to date, the true underling physics in the fine structures of QDs remain as a controversial issue. In th i s subjec t , Shun-Jen Cheng and h is co-workers (Hanz Ramirez et al.) present a theoretical model for the electron-hole exchange interaction in three-dimensionally confining semiconductor nanostructures and employ it to successfully explain the observed decreasing tendency of the fine-structure splitting of small InGaAs/GaAs self-assembled quantum dots with increasing the emission energies.[Phys. Rev. B 81, 245324 (2010)] Furthermore, they for the first time present a partial configuration interaction method for coupled quantum dot molecules with the consideration of e-h exchange interaction, and predict that that strongly coupled vertical quantum-dot molecules with high tunneling rate are better sources of entangled photon pairs than single dots.[Phys. Rev. Lett. 104, 206402 (2010) ] Their studies provide a necessary theoretical base


for solving the long existing problem of failure of en t ang led pho ton pa i r gene r t ion f rom a semiconductor QD.

Graphehes

Hsiu-Hau Lin collaborated with Wen-Min Huang and Hikihara on Edge magnetism of Heisenberg model on honeycomb lattice. In their previous study, a single-branch of ferromagnetic magnon with linear dispersion is shown to exist near the (uncompensated) zigzag edge for Heisenberg model on honeycomb lattice. They develop a field-theory description for the edge magnon and find its dynamics is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart, described by the two-dimensional Klein-Gordon equation. Furthermore, they also reveal how the parity symmetry relates evanescent modes on opposite edges in a honeycomb nanoribbon. By employing alternative methods, including Schwinger bosons and density-matrix renormalization group, we also demonstrate that the relativistic edge magnon is robust even when the Neel order in the bulk is destroyed by quantum fluctuations. The edge magnon is a direct consequence of uncompensated edge and may be verified in realistic materials by experimental probes.

Ultracold Atoms applied in condensed matter

Ming-Chiang Chung col laborates wi th Pochung Chen, Sungkit Yip and Ian McColluch on Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice. They study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using non-Abelian density matrix renormalization group (DMRG) method they identify three possible phases: ferromagnetic, dimerized, and trimerized phases. They sketch the phase boundaries based on DMRG. They illustrate two methods for identifying the phases. The first method is based on the spin-spin correlation function while in the second method one observes the excitation gap as a dimerization or a trimerization superlattice is imposed. The advantage of the second method is that i t can also be easi ly implemented in experiments.

Spintronics

Chon-Saar Chu works on spintronics. In two recent papers, they have demonstrated that linear Rashba-type spin-orbit can contribute to spin-Hall effects in a nonuniform driving field case in the d i f f u s i v e r e g i m e . I n t h e f i r s t w o r k , i n collaboration with Prof. A.G. Mal'shukov, we have derived a spin diffusion equation for the case o f a nonuni form dr iv ing f i e ld . The sp in accumulation around a circular void in a 2DEG is solved both numerically and analytically. The work was published in Phys. Rev. B 81, 115312 (2010).

The second work they consider the even more interesting case of a circular void at a system edge. The work is solved semi-analytically. Their approach provides a clear physical picture for the processes leading to the spin accumulation. They find a bulk-like spin flow that arises from the nonuniform driving. The spin flow is expected to be a primary impetus for local spin injection at the sample ede near the edge-void.

The work is accepted for publication in Phys Rev. B (2011).

V. Selected Publications[1] Karyn Le Hur, Chung-Hou Chung, I. Paul,

“Designing Heterostructures with Higher Temperature Superconductivity”, Phys. Rev. B 84, 024526 (2011).

[2] C.P. Moca, P. Simon, C.H. Chung, G. Zarand, “Non-equilibrium frequency-dependent noise through a quantum dot: A real time functional renormalization group approach”, Phys. Rev. B 83, 201303(R) (2011).

[3] Chung-Hou Chung, “Dynamical properties of a nonequilibrium quantum dot close to loca l ized-de loca l ized quantum phase transitions”, Phys. Rev. B 83, 115308 (2011).

[4] D. Bolmatov, C.Y. Mou, “Graphene-based modulation-doped superlattice structures”, Journal of Experimental and Theoretical Physics (JETP) 112, 102 (2011).

[5] M.-C. Chung, Y.-H. Jhu, P. Chen and S.K. Yip, Edge State, “Entanglement Entropy


Spectra and Critical Hopping Coupling of Anisotropic Honeycomb lattice”, Eur. Phys. Lett. 95 27003 (2011).

[6] L.Y. Wang and C.S. Chu, “Rashba-type spin accumulation near a void at a system edge”, Phys, Rev. B 84, 125327 (2011).

[7] A.G. Malshukov and C.S. Chu, “Spin-Hall current and spin polarization in an electrically biased SNS Josephson junction”, Phys. Rev. B, 84, 054520 (2011).

[8] Yu-Huai Liao, Juan I. Climente, and Shun-Jen Cheng*, “Dominant channels of exciton spin relaxation in photoexcited self-assembled (In,Ga)As quantum dots”, Phys. Rev. B 83, 165317 (2011) .

[9] Yan-Ting Chen, Shun-Jen Cheng*, and Chi-S h u n g Ta n g , “ E n g i n e e r e d s p i n - s t a t e transitions of two interacting electrons in semiconductor nanowire quantum dots”, Phys. Rev. B 81, 245311 (2010).

[10] Jun-Ting Kao, Jo-Tzu, Hung, Pochung Chen, and Chung-Yu Mou, “Decoupling of Qubits in Spin Bath under Periodic Quantum Control”, Phys. Rev. A 82, 062120 (2010).

[11] Huang DJ, Okamoto J, Huang SW, and C. Y. Mou, “Transitions of Multiferroic Frustrated Magnets Revealed by Resonant Soft X-ray Magnetic Scattering”, J. of Phys. Soc. Jap. 79, 011009 (2010).

[12] Wen-Ming Huang, Chung-Yu Mou, Cheng-H u n g C h a n g , “ p h a s e c o r r e c t i o n f o r semiclassical quantization rules in multi-d i m e n s i o n a l q u a n t u m s y s t e m s ” , Communications in Theoretical Physics 53, 250 (2010).

[13] S. -J. Tang, Tay- Rong Chang, Chien-Chung Huang, Chang-Yeh Lee, Cheng-Maw Cheng, Ku-Ding Tsuei, H.-T. Jeng, Chung-Yu Mou, “Dispersive resonance bands within the space charge layer of metal- semiconductor junction”, Phys. Rev. B 81, 245406 (2010).

[14] Dima Bolmatov and Chung-Yu Mou, “Josephson effect in graphene SNS junction with a single localized defect”, Physica B 405, 2896 (2010).

[15] Dima Bolmatov and Chung-Yu Mou, “Tunneling Conductance of The Graphene SNS Junction with a Single Localized Defect”, Journal of Experimental and Theoretical Physics 110, 613 (2010).

[16] Bor-Luen Huang, Ming-Che Chang, and Chung-Yu Mou, “Density of s tates of graphene in the presence of strong point defects”, Phys. Rev. B 82, 155462 (2010).

[17] L.Y. Wang, C.S. Chu, A.G. Malshukov, “Spin generation in a Rashba-type diffusive electron system by nonuniform driving field”, Phys. Rev. B 81, 115312 (2010).

[18] H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin and S. J. Cheng*, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots”, Phys. Rev. B 81, 245324 (2010).

[19] Kwai-Kong Ng, “Thermal phase transitions of supersolids in the extended Bose-Hubbard model”, Phys. Rev. B 82, 184505 (2010).


Coordinator: Po-Chung Chen (National Tsing Hua University; email: [email protected])


he “Numerical Methods on Strongly Correlated Physics” is a focus group

under the Quantum Phenomena in the Condensed Matter Physics Working Group. It was formed to provide a platform for condensed matter theorists who are special izing and/or interested in numerical simulations to facilitate interaction and collaboration. In addition, activities and visitor programs are designed to provide opportunities for researchers to es tabl ish internat ional collaborations. In addition, travel funds are available to provide financial support to students and junior researches to attend international conferences. An executive committee of eight members from major institutes is formed to coordinate these activities and oversee the usage of the fund.

In addition to the executive committee, there are twenty-four active faculty members and more than forty junior members (postdocs and graduate students). The focus research topics are (1) numerical methods based on tensor network states, (2) First-principles approach to novel properties of materials, (3) quantum transport in nanodevices, (4) Numerical Methods Based on Monte-Carlo and (5) BEC and superfluidity in cold atom systems.

II. ActivitiesOur focus group organized or sponsored

following activities last year:

Bi-weekly joined group meeting

In t h i s mee t ing se r i e s , wh ich i s he ld

alternatively at NTU/NTHU, members of the FG report recent progress in their own or related research, or external speakers are invited to introduce new developments in the field. The talks focus on numerical method, although the subjects are not limited to these. The goal is to motive junior researchers to identify and discuss research topics, and to forge collaborations via intensive discussion.

Bi-weekly seminar at NTNU

In this seminar series, we invite speakers in the field of condensed matter physics to present their recent works. The topics should cover a wider range of the condensed matter physics. The goal is to broaden the visions of the members and to find p o t e n t i a l p r o b l e m s t h a t c a n b e f u r t h e r investigated.

End-of-semester workshop

We held a one-day workshop on June 29, 2011 in Taipei. The purpose of this workshop is to create a platform for members in the FG, especially postdocs and students, to present their works. This provides an opportunity to practice presentation skills and to familiarize each other’s work.

Summer School for Numerical Methods in Condensed Matter Physics

Joint with the mesoscopic physics FG, we held a “Summer school for numerical methods in condensed matter physics” on September 6-9, 2011 in Hsinchu. The school aims for pedagogical introduction of a variety of numerical approaches t o s t u d e n t s a n d s c i e n t i s t s i n t e r e s t e d i n computational physics. Topics include Monte Carlo methods, exact diagonalization, DMRG, NRG, and functional renormalization group. We invite four world-leading experts, Prof. H. G.

Working Group on Quantum Phenomena in Condensed Matter Physics

B. Focus Group on Numerical Methods on Strongly Correlated Physics


K a t z g r a b e r D r. I a n M c C u l l o c h , D r. A . Weichselbaum, and Dr. M. Pletyukhov and three local speakers, Dr. Derek Larson and Profs. Hong-Yi Chen, and Fu-Jun Jiang to give lectures. In addition, tutorial sessions are organized to help students gain hands-on experience. About 70 students, postdocs and professors registered for the school. In addition, the FG also provided travel support for Ph. D students Ya-Lin Lo (NTU) to attend “Synergies between field theory and exact computational methods”, at Trieste, Itlay.


International Visitors (Dec 10-Sep 11)

•��Prof.�H.�G.�Katzgraber�(Texas�A&M)�•��Prof.�I.�McCulloch�(Univ.�of�Queensland)�•��Dr.�Andreas�Weichselbaum�(LMU)�•��Dr.�Mikhail�Pletyukhov�(RWTH�Aachen)•��Mr.�Michael�Bögli�(University�of�Bern)•��Prof.�Anders�Sandvik�(BU,�USA)

International Collaborations

•��Y.-C�Lin�(NCCU)+A.�W.�Sandvik�(USA)�on�entanglement entropy of spin systems.

•��H.-C�Hsueh� (TKU)�+�G-Y.�Guo� (NTU)�+�Steven G. Louie (Berkeley) on ab initio calculation of excited states of nanotubes.

•��P. � Ch en� (NTHU)� +� I a n� McCu l l o c h�(Australia) on simulation based on MPS.

•��H.-C.�Hsueh� (TKU)�+�W.�Ku� (USA)�on� the�new methodology (TDLDA+U) for strongly correlated system;

•��Y.-J.�Kao�(NTU)�+�A.�W.�Sandvik�(USA),�R.�G. Melko (Canada) on numerical methods based on tensor networks.

•��F.-L.�Lin� (NTNU)�+�T.-C.�Wei� (Canada)�on�entanglement entropy.

•��C.-C.�Kaun� (AS)�+D.�A.�Luzhbin� (Ukraine)�on charge transport in molecular junctions.

IV. Highlights of Research ResultsQuantum transport in nanodevices

C-C. Kaun (AS) and his coworker use first-principles calculations to study electron transport

through nucleotides inside a rectangular nanogap formed by two pairs of gold electrodes. They propose that this setup will greatly enhance the nucleotide selectivity of tunneling signals. Information from three electrical probing processes offers full nucleotide recognition, which survives the noise from neighboring nucleotides fluctuations. [1]

Y.-J. Kao (NTU) and his coworkers study the transport in a molecular junction, in which each unit is coupled to a local phonon bath. Using the nonequilibrium Green's function method, they observe that the conductance oscillates with the molecular chain length and that the period in odd-numbered chains depends strongly on the applied bias For the phonon-free case, they find a crossover from tunneling to thermally activated transport as the length of the molecule increases. In the presence phonon interaction, the transport is thermally driven. A crossover from thermally suppressed conduction to assisted conduction is observed. [2]

First-principles approach to novel properties of materials

H.-C. Hsueh (TKU), G.-Y. Guo (NTU), and their collaborators investigate the quasi-particle band structure and optical properties of zigzag and armchair SiC nanotubes (SiC-NTs) and a single SiC sheet by ab initio many-body calculations using GW and GW plus Bethe-Salpeter equation a p p r o a c h e s . T h e y f i n d s i g n i f i c a n t G W quasiparticle corrections to the Kohn-Sham band gaps and find SiC sheet be a direct band gap material. It is shown that small-radius armchair SiC-NTs could be useful for optical devices working in the UV regime while zigzag SiC-NTs may have potential applications in tunable optoelectric devices ranging from infrared to UV frequencies. [3]

H.-T. Jeng (AS) and collaborators investigate the electronic s t ructure and ferroelectr ic polarization of multiferroic TbMn2O5 using the GGA and the GGA+U methods. They find an insulating charge-orbital ordered ground state driven by octahedral and pyramidal local structures. Associated with the observed charge ordering, the frustrated magnetic structure creates polarizations in the presence of magnetostriction effect. On-site U leads to strong cancellations


between the ionic and e lec t ronic par t of polarizations. It is demonstrated that the main part of the polarizations results from the pyramidal Mn ions. It is found that the dz

2 orbital ordering on the pyramidal Mn3+ sublattice play important roles in the polarization. [4]

Numerical Methods Based on Monte-Carlo

Y.-C. Lin (NCCU) and Prof. A. Sandvik, investigate measures of entanglement entropy based on transition graphs, which characterize state overlaps in the overcomplete valence-bond basis. The transition graphs can be generated using projector Monte Carlo simulations of ground states of specific Hamiltonians or using i m p o r t a n c e s a m p l i n g o f v a l e n c e - b o n d configurations of amplitude-product states. They consider definitions of entanglement entropy based on the bonds or loops shared by two subsystems. The loop based entanglement entropy of the 2D Heisenberg model is shown to satisfy the area law with an addit ive logarithmic correction, unlike single-bond definitions, which exhibit multiplicative logarithmic corrections. [5]

Y.-J. Kao (NTU) and his students study the effects of quantum fluctuations in spin ice by considering an S>1 quantum Heisenberg model with a nearest-neighbor ferromagnetic interaction J and a large non-collinear <111> easy-axis anisotropy D on a pyrochlore lattice. For a finite D >> vertical bar J vertical bar, the low-energy physics is described by a < 111 > Ising model with additional second-and third-neighbor exchange couplings of order O (J2/D), generated by the quantum fluctuations arising from the transverse components of the exchange coupling. The extensive degeneracy of ground states in the D -> infinity limit is lifted, and a q=0 ordered state is selected via the quantum order by disorder mechanism, through a first-order phase transition at low temperatures.[6]

Tensor Network Methods

F.-L. Lin (NTNU) and his student study the connection between topological order and degeneracy of the entanglement spectrum by explici t ly solving 2D dimerized quantum Heisenberg model in the form of tensor product state (TPS) ansatz. A new topological order phase is identified by the topological entanglement entropy. In this phase the entanglement spectrum

is doubly degenerate and the degeneracy is robust against various types of perturbations. The results provide a more viable way to numerically identify the topological order for the generic frustrated systems. [7]

Y.-J. Kao (NTU) and his collaborators present a method for contracting a square-lattice tensor network in 2D based on auxil iary tensors accomplishing successive truncations of eight-index tensors for 2x2 plaquettes into four-index tensors. Since all approximations are done on the wave function the scheme is variational, and thus, the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible produce much better results than the simple product state.[8]

Y.-J. Kao (NTU) and his group use the graphical processing unit (GPU) to accelerate the tensor contractions, which is the most time consuming operations in the variational method based on the plaquette renormalized states. Using a frustrated Heisenberg J1-J2 model on a square lattice as an example, they implement the algorithm based on CUDA. For a single plaquette contraction with the bond dimensions D=3 of each rank of the tensor, results are obtained 25 times faster on GPU than on a current CPU core.[9]

P. Chen (NTHU), M.-C. Chang (NCTS), S.- k Yip (Sinica) and their student show that the Berry phase depends not only on the shape of the system but also on the hopping couplings for b ipa r t i t e honeycomb la t t i ces . Us ing the entanglement entropy spectra obtained by diagonalizing the block Green’s function matrices, the maximally entangled states of the reduced dens i ty matr ix are shown to have 1- to-1 correspondences to the zero-energy states of the lattice with open boundaries. The existence of these states depends on the Berry phase. For systems with finite bearded edges the new maximally entangled states appear pair-by-pair when one increases the hopping coupling h over the critical values hc’s. [10]

Bose-Einstein condensation and superfluidity in cold atom systems

W.-C. Wu (NTNU) and his collaborators study equilibrium vortex formation in rotating binary


Bose gases with a rotating frequency higher than the harmonic trapping frequency. A combined numerical scheme is applied to ensure the binary system being in an equilibrium state when the system is cooled to form condensates. A quartic trapping potential is added to keep the system stable against the large centrifugal force of u l t r a f a s t r o t a t i o n . A c r i t i c a l r o t a t i n g frequency�Ωc� is� derived,�which� characterizes� the�structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency�both�above�and�below�Ωc .[11]

P. Chen (NTHU) and M.–F. Yang (THU) investigate various quantum phase transitions of attractive two-species bosons in a 2D square lattice. Using the algorithm based on the tensor product states, the phase boundaries of the pair-superfluid states with nonzero pair-condensate density and vanishing atomic condensate density are determined. Various quantum phase transitions across the phase boundaries are characterized. The work provides guides to the experimental search of the pair-superfluid phase in lattice boson systems. [12]

V. Selected Publications[1] V. M. K. Bagci and C.-C. Kaun, Phys. Rev. E

84, 011917 (2011).

[2] Ya-Lin Lo, Shih-Jye Sun, and Ying-Jer Kao, Phys. Rev. B 84, 075106 (2011).

[3] H. C. Hsueh, G. Y. Guo, and Steven G. Louie, Phys. Rev. B 84, 085404, (2011).

[4] Tay-Rong Chang, Horng-Tay Jeng, Chung-Yuan Ren, and Chen-Shiung Hsue, Phys. Rev. B 84, 024421 (2011).

[5] Yu-Cheng Lin, and A. Sandvik. Phys. Rev B. 82, 22 (2010).

[6] Yang-Zhi Chou and Ying-Jer Kao, Phys. Rev. B, 82, 132403 (2010).

[7] C h i n g - Yu H u a n g a n d F e n g - L i L i n , arXiv:1104.1139 (2011).

[8] Ling Wang, Ying-Jer Kao, and Anders W. Sandvik, Phys. Rev. E. 83, 056703 (2011).

[9] J. F. Yu, S. C. Hsiao, Y.-J. Kao, Comput. Fluids 45, 55 (2010).

[10] M.-C. Chung, et al, , EPL, 95, 27003 (2011).

[11] C.-H. Hsueh, et al, Phys. Rev. A 84, 023610 (2011).

[12] Pochung Chen and Min-Fong Yang, Phys. Rev. B 82, 180510(R) (2010).


Focus Group on Computational Materials ResearchCoordinator: Ching Cheng (National Cheng Kung University; email: [email protected])


he primary purpose of this program is to enhance the domestic research capacity in

the computational material science based on the first-principles quantum mechanical methods through promoting interactions and collaborations among local members as well as between local members and international noted scholars, and also through attracting outstanding young researchers into this field.

The CMR focus group presently consists of over 20 active faculty members. According to the interests and the existing expertise of the members, we have identified three frontiers, i.e. calculations of the electronic excited states (ES), quantum Monte Carlo methods (QMC), and quantum transport (QT), as advancing priority research areas. Study-group meetings initiated by the members involved in these three topics promote collaborations among members as well as stimulate new ideas and in-depth discussions in these research fields.

In order to t ra in the young generat ion members, the Ph.D. students, postdoctors and the junior faculty members are encouraged to attend international conferences, workshops and schools. The provided fund of this year was found insufficient. As attending international meetings is important for the junior researchers to broaden their research scope, to interact with international peers and noted scholars for generating inspired ideas, etc., we urge for a higher proportion of the grant on this category for young researchers in the coming year.

The focus group is run by a committee whose members consists of three coordinators in charge of the activities related to the three frontiers, i.e. HC Hsueh (TKU) for ES, CM Chang (NDHU) for QMC and CC Kaun (AS) for QT, and another six

senior members as listed under the headline. We are grateful for the generous contributions of four previous EC members, i.e. MH Tsai (NSYSU, retired), GY Guo (NCCU, NTU), MH Lee (TKU) and SF Tsay (NSYSU), and welcome the new EC members of YC Chen (NCTU), M Hayashi (NTU), and CK Yang (NCCU). In the last program-wide meeting (August 2011), the committee has invited CK Yang (NCCU) as the coordinator of CMRFG for the coming year. The missions of the committee are to allocate the budget, to initiate research activities, to invite the long- term and shor t - term vis i tors and to recommend candidates (Ph.D. student or junior scientist) or review applications for attending international school, conference, or workshop using the financial support of CMRFG.

II. Activities The activities supported by CMRFG are listed

according to the following four categories (1) workshops for all members, (2) schools, (3) study-group meetings, (4) peers interactions.

(1) 1/14-1/15: CMRFG Winter Meeting

4/29-4/29: CMRFG mini General Meeting

7/15-7/16: Wo r k s h o p o n E x p l o r i n g t h e Structures and Dynamics of Water at Interfaces

8/07-8/09: T h e 11 t h Wo r k s h o p o n F i r s t -Principles Computational Materials Physics

(2) 4/30-5/01: S c h o o l o n F i r s t - P r i n c i p l e Computational Materials Physics – Ⅰ

5/14-5/15: S c h o o l o n F i r s t - P r i n c i p l e Computational Materials Physics – Ⅱ

7/18-7/22: S c h o o l o n F i r s t - P r i n c i p l e Computational Materials Physics – Advanced Study


(3) 3/18: Minischool on quantum-based modeling of novel energy materials

3/25: Minischool on recent development of f i r s t -pr inc ip les s tudy on s t rongly correlated systems

8/05: Minischool on first-principles many-body theories of excitation in materials

(4) 1/14-1/15: “Poster Presentation Contest” of research works by research students in CMRFG Winter Meeting

The 11th Workshop on First-Principles Computational Materials Physics

This program-wide workshop was held on August 7-9, 2011 in the Sun Moon Lake Youth Acitivity Center, Nantou. The aim of this workshop is to promote in teract ions and collaborations among local members. All participants, particularly PhD students and postdoctors, are encouraged to give a talk in this workshop. In order to bringing in distinct stimulations for the meeting, this year’s program also includes plenary talks delivered by three invited international scholars. Due to the presence of the overseas researchers , some young researchers were encouraged to present their talks in English. The CMRFG Committee also takes this opportunity to learn about the general interests of the community in order to organize beneficial activities for the members in the future.

CMRFG Winter Meeting

In response to some members’ suggestion of holding more than one annual meeting (usually in the summer time) for all the members, we have organized this considerably shorter meeting. It was held in the NCTS(South) with the on-site dinner following the poster-presentation contest so that all the participants have plenty of time for interactions and discussions through the whole evening. The positive feedbacks from the participants are encouraging.

Schools on First-Principles Computational Materials Research

To help the newcomers of this field overcome the hurdle in the beginning, both the introductory-level spring school and the advanced-level

s u m m e r s c h o o l o n t h e f i r s t - p r i n c i p l e s computational materials research are organized. The spring school, lectured by T. C. Leung (CCU), is held in National Center for High-Performance Computing. The summer school, also organized by T. C. Leung (CCU), is held in NCTS (south). Both schools include the practical hands-on sessions. The responses from both students and non-specialist researchers are much positive as there are more than one hundred participants in the spring school and more than fifty participants in the summer school. A small portion of the expenses of the school was provided by the National Center for High Performance Computing.

Workshop on Exploring the Structures and Dynamics of Water at Interfaces

A workshop on exploring the structures and dynamics of water at interfaces was held with scientists mostly from quantum chemistry as well as experimentalists. The purpose of the workshop i s t o p r o v i d e t h e o p p o r t u n i t y f o r t h e experimentalists and theoretical researchers from different disciplines to exchange the latest development in the rich field involving water.

Excited State study group Meeting

The focus of this study group is on the GW methods (VASP and Berkeley GW), the Bethe-Salpeter methods (Berkeley GW) and the time-dependent DFT, for the excited-state properties of the bulk materials and nanomaterials. Two minischools, accompanying with the visits of the international scholars, were held in the past six months.

Quantum Monte Carlo study group Meeting

Two study-group meetings are held in the past s ix months. The discussed topics, as the continuous projects from last year, cover (1) implementation of Wannier functions into the QMC methods, (2) description of van der Waals interactions for insulating and ionic bilayer s y s t e m s u s i n g Q M C m e t h o d s a n d t h e i r comparisons to those using DFT methods with different density functional schemes, (3) magnetic moments of small metallic clusters using QMC methods.



Examples of collaborations between CMRFG members are listed as follows:

1. CM Chang (NDHU), C Cheng (NCKU) and CM Wei (AS) on the applications of the Quantum Monte Carlo methods.

2. GY Guo (NTU), TC Leung (CCU) and HC Hsueh (TKU) on the ab initio study for the excited state of nanomaterials.

3. CC Kaun (AS) and TC Leung (CCU) on the quantum transport in graphene nanoribbons and in nanomachines.

4. CM Wei (AS) and JL Kuo (AS) on the high-pressure phases of ice.

International collaborations are listed as follows:

1. TC Leung (CCU) and CT Chan (HongKong) on the optical properties of nanomaterials.

2. CM Wei (AS) and N Drummond (UK) on the applications of the Quantum Monte Carlo methods.

3. HC Hsueh (TKU) and SG Louie (USA) on E x c i t o n i c p r o p e r t i e s c a l c u l a t i o n i n nanomaterials and defects.

4. HC Hsueh (TKU) and Wei Ku (USA) on Dynamic behaviour of strongly bounded excitons.

IV. Highlights of Research Results The communi ty of the f i rs t -pr inciples

electronic calculations for materials of this country has flourished in the last few years. The number of faculty members in the community started by less than ten now reaches over twenty. The members benefits extremely from the interactions through the activities supported by the NCTS. That the members share their individual exper t i se wi th in the communi ty wi thout reservation also advances the community’s strength as a whole. How these could lead directly to the actual research results, e.g. journal p u b l i c a t i o n s o r i n v i t e d t a l k s , i s n o t a s straightforward to identify as might have been implied in the performance evaluations required by the funding agency. Not to mention that those

substantial research outcome also benefit largely from the personal NSC projects of the members as well as, for some, the joint projects.

However, the majority of the members have benefited enormously from the mutual visits and the study-group meetings of the focused topics supported by the CMRFG which could not be acquired from other resources otherwise. Continuous supports of these visits and meetings with extensions through invitations and potential collaborations with the international leading experts are expected to lead to concrete and eminent research results as the pursuit all the time of the NCTS.

(1) Excited State study group meetings

The group explores the applicability of the established codes for the electronic excitation using the GW, the Bethe-Salpeter and the time-dependent DFT methods. Investigations are applied to the covalent and ionic insulators as well as the nanosystems. Extensions of these studies to optical spectrum and absorption spectrum are also developed. After many-year continuous works and collaborations between the members and overseas experts, the first paper working on excited states of extended systems is published this year (Excitonic effects in the optical properties of a SiC sheet and nanotubes by H. C. Hsueh, G. Y. Guo, Steven G. Louie, Phys. Rev. B84, 085404). We expect many more fruitful results in this field to come henceforth.

(2) Quantum Monte Carlo study-group meetings

To successfully apply the QMC methods to the extended bulk systems, the generation of good initial many-body wavefunctions is essential. Theoretical discussions lead to the suggestion of using the maximally localized Wannier functions g e n e r a t e d f r o m t h e D F T c a l c u l a t i o n s . Implementation of this scheme into the presently available QMC methods was completed and, to our disappointment, no gain in the process was found. A different approach involving including results from different many-electron wavefunction is proceeded for further tests.

(3) Quantum Transport

The quantum transport has become one of the main fields of the members in this focus group. The important results include calculations of the


Seebeck coefficient, study on the effect of thermoelectric cooling as well as study of single-molecule refrigerators.

(4) NanoMaterials and Graphene-related systems

Many research works involve studies of nanomaterials as well as the graphene-related sys tems . The re su l t s inc lude tunne l ing conductance, effect of defects, and optical proteries of graphene, bilayer graphene and graphene nanoribbons.

V. Selected Publications[1] “Single-molecule refrigerators: Substitution

and gate effects”, Yu-Shen Liu and Yu-Chang Chen, Applied Physics Letters 98, 213103.

[2] “Exploring the interaction between the boron nitride nanotube and biological molecules”, C h i h - K a i Ya n g ” , C o m p u t e r P h y s i c s Communications 182 39–42.

[3] “Low-energy e lec t ronic s t ruc tures of nanotube-nanoribbon hybrid systems”, C. H. Lee, S. C. Chen, C. K. Yang, W. S. Su*, and M . F . L i n * , C o m p u t e r P h y s i c s Communications 182 68–70.

[4] “ A f i r s t - p r i n c i p l e s s t u d y o n t h e e lec t romechanica l e ffec t of graphene nanoribbon”, W.S. Su, B. R. Wu, and T. C. Leung, Computer Physics Communications 182 99–102.

[5] “Electronic structure and transport properties of SrAl2Si2: Effect of Yttrium substitution”, C.S. Lue, C.P. Fang, A.C. Abhyankar, J.W. Lin, H.W. Lee, C.M. Chang*, Y.K. Kuo*, Intermetallics 19 1448-1454.

[6] “Structural and electronic properties of bismuth and lead nanowires inside carbon nanotubes”, Chi-Hsuan Lee and Chih-Kai Yang*. J. Phys. Chem. C 115, 10524–10530.

[7] “Atomic-Scale Field-Effect Transistor as a Thermoelectric Power Generator and Self-Powered Device”, Yu-Shen Liu, Hsuan-Te Yao, and Yu-Chang Chen*, J. Phys. Chem. C115, 14988–14996.

[8] “Effect of Thermoelect r ic Cool ing in Nanoscale Junctions”, Yu-Shen Liu, Bailey C. Hsu, and Yu-Chang Chen, J. Phys. Chem. C115, 6111–6125.

[9] “The dielectric properties of La(Mg(0.5)Ti(0.5))O(3) ceramics studied by Raman-scattering, infrared reflectivity spectroscopy, and first-principles calculations”, Hsiang-Lin Liu, Hung-Chung Hsueh, I-Nan Lin, Ming-Ti Yang, Wei-Chung Lee, Yi-Chun Chen, Chia-Ta Chia and Hsiu-Fung Cheng, J. Phys.: Cond. Matt. 23, 225901.

[10] “Size effect of Pd clusters on hydrogen adsorption”, H. W. Lee, and C. M. Chang, J. Phys-Cond. Matt. 23, 045503.

[11] “Structural and electronic properties of hydrogen adsorptions on BC(3) sheet and graphene: a comparative study”, Feng-Chuan Chuang, Zhi-Quan Huang, Wen-Huan Lin, M a r v i n A . A l b a o , Wa n - S h e n g S u , Nanotechnology 22 135703.

[12] “Electronic s tructures of an epitaxial graphene monolayer on SiC(0001) after gold intercalation: a first-principles study”, Feng-Chuan Chuang, Wen-HuanLin, Zhi-Quan Huang, Chia-Hsiu Hsu, Chien-Cheng Kuo, Vidvuds Ozolins and V Yeh, Nanotechnology 22, 275704.

[13] “Structural and electronic properties of graphene nanotube-nanoribbon hybrids”, Chi-Hsuan Lee, Chih-Kai Yang, Ming-Fa Lin*, Cheng-Pong Chang*, and Wang-Sheng Su, Phys. Chem. Chem. Phys. 13, 3925–3931.

[14] “Counting statistics in nanoscale junctions”, Yu-Shen Liu and Yu-Chang Chen*, Phys. Rev. B83, 035401.

[15] “Seebeck coefficients in nanoscale junctions: Effects of electron-vibration scattering and local heating”, Bailey C. Hsu, Yu-Shen Liu, Sheng Hsien Lin, and Yu-Chang Chen*, Phys. Rev. B83, 041404 (R).

[16] “Excitonic effects in the optical properties of a SiC sheet and nanotubes”, H. C. Hsueh, G. Y. Guo, Steven G. Louie, Phys. Rev. B84, 085404.


Highlights of ProgramsParticles and Fields Focus Group on Cosmology and Particle AstrophysicsCoordinator: Chao-Qiang Geng (NCTS/National Tsing Hua University; email: [email protected])

he Focus Group on Cosmology and Particle Astrophysics (FGCPA) was

established in 2009 and this is the third year of its operation. For the weekly activities, it has been divided into three Local Chapters, in Taipei, Hsinchu and Tainan, respectively, for seminars and working group meetings. We further held Joint Retreats with other LeCosPA at NTHU as well as other NCTS Focus Groups. We are proud to report that in this 3rd year the numbers of our NTCS affiliated and acknowledged papers are 21 and 16, respectively (as of 9/20/2011). There is a dramatic increase for the NTCS affiliated papers from the first two years.

I. Brief DescriptionThe goals of FGCPA are as follows.

•��Organization�of�summer�or�winter�school�to�offer�short - term CPA courses to s tudents and researchers.

•��Invitation� of� short-term� foreign� visitors� to�seminars or school lectures.

•��Encouraging� and�promoting� cooperation� and/or�joint research projects among domestic research groups.

•��Training� of� graduate� students� and� post-docs�through their attendance of international schools or visits to foreign research institutes on the longer-term basis.

•��Invitation� of� distinguished� cosmologists� and�particle astrophysicists for 3-month or longer-term visits.

•��Establishing� exchange�programs�with� foreign�research organizations and conducting exchange activities.

Coordinator:

耿朝強/清大(Geng, Chao-Qiang/National Tsing Hua Univeristy and NCTS)

Core Members:

陳丕燊/臺大(P i s in Chen/Nat iona l Ta iwan University)

林貴林/交大(Guey-Lin Lin/National Chiao Tung University)

李沃龍/師大(Wolung Lee/National Taiwan Normal University)

劉國欽/淡江(Guo-Chin Liu/Tamkang Univeristy)

黃偉彥 /臺大(W-Y. Pauchy Hwang/National Taiwan University)

吳建宏/中研院(Kin-Wang Ng/Academia Sinica)

陳泉宏/成大(Chuan-Hung Chen/National Cheng Kung University)

In addition to the Core Members, there are many professors, researchers, postdocs, PhD and Master students participate in this FG.


II. ActivitiesSeminars

Taipei Chapter: This seminar series is located a t N T U a n d o r g a n i z e d b y P a u c h y Hwang. It has been holding seminars every week except during the Summer.

Hsinchu Chapter: This bi-weekly seminar s e r i e s i s l o c a t e d a t N T H U / N C T S . I t i s organized jointly by Chao-Qiang Geng (NTHU) and Guey-Lin Lin (NCTU).

Tainan Chapter: This series is located at NCKU and organized by Chuan-Hung Chen. Since there are relatively fewer FG members in southern Taiwan, it was decided that this series is held non-regularly and jointly with the existing seminar series in the Physics Department of NCKU.

Working Groups

Between 2009-2010, FGCPA was pursuing the following 5 research topics organized jointly with LeCosPA: Cosmic Rays and Neutrinos: Guey-Lin Lin (orgainzer); Baryon Asymmetry of the Universe (BAU): Chao-Qiang Geng (organizer); Dark Energy Phenomenology: Je -An Gu (organizer); String Cosmology: Debaprasad Maity (organizer); Gravity and Structure Formation: Antonio Enea Romano (organizer). In 2011, the five groups are still in active, in particular the groups based on LeCosPA, NTU. However, the emphasis of the working groups at NTHU and NCTU is extended to much more broader topics in cosmology and particle astrophysics, such as dark matter, dark energy and neutrino physics.

Joint Meetings and Retreats

Our FG has organized a Joint Meeting on Dark Energy with LeCosPA in June 18, 2011 at NTU. The next Joint Meeting with LeCosPA will be in November 2011 in Hsinchu. The Joint Retreat w i t h t h e F G o n L H C t h i s y e a r w i l l b e co-organized by CW Chiang (NCU/NCTS) and will be held in early December 2011 in Hsinchu.

Workshops

•��2011�Cross-strait�Meeting�on�Particle�Physics�and Cosmology, April 1-5, 2011, NTHU/NCTS, Hsinchu, Taiwan

•��24th Spring School on Particle & Fields, April 6-9, 2011, NTHU/NCTS, Hsinchu, Taiwan

•��International�Workshop�on�Neutrino�Physics,�Dark Matter and Gamma Rays, Nov. 4-6, 2011, NCTU/NCTS, Hsinchu, Taiwan

Attendance of International Activities

•��Three�PhD� students:�Chung-Chi�Lee,�Ling-Wei�Luo and Yi-Peng Wu had a week visit to C h o n g q i n g U n i v e r s i t y o f P o s t a n d Telecommunication during Feb. 2011 after the C h i n e s e n e w y e a r t o e s t a b l i s h s o m e collaborations on Dark Energy.

•��Chao-Qiang�Geng� attended� the�workshop�on�“Gravity, Particle and Cosmology”, May 4-8, 2011, Chongqing, China, where he presented a plenary talk.

•��Three�PhD� students:�Chung-Chi�Lee,�Ling-Wei�Luo and Yi-Peng Wu a t tended the 11 th RESCEU/DENET Summer School: Dark Energy in the Universe, July 25-29, Kumamoto, Japan, where two of them (Lee and Luo) made oral presentations.

•��One�postdoc,�Fei-Fan�Lee�(NCTU),�attended�the�EPS-2011 in Grenoble, France, July 21-27, 2011, where he made an oral presentation.

•��Chao-Qiang�Geng� attended� two�workshops�on�“Dark Matter and New Physics” and “Dark Energy”, July 24-Aug. 4 , 2011, Weihai , Shandong, organized by ITP, Beijing, where he presented two talks.

•��Chao-Qiang�Geng� and� four� PhD� students:�Chung-Chi Lee, Ling-Wei Luo, Huan-Hsin Tseng and Yi-Peng Wu will attend “Dark matter and new physics”, “String Phenomenology and Cosmology” and the seventh international workshop “Dark Side of the Universe (DSU 2011)” at KITPC, Beijing, between September 21-October 19, 2011.


With the very high degree of overlap between FGCPA and LeCosPA in terms of research topics and members, many international visitors and collaborations are shared, with benefits to both.


Visitors

•��Professor� Shinji� Tsujikawa� of� Tokyo�U� of�Science, Japan visited NTHU/NCTS under the support of NCTS FG CPA between April 5-10, 2011. He is an expert on dark energy. He was a key speaker at 2011 spring school on “Particles and Fields”.

•��Dr.�Zhao-Feng�Kang�of� Institute� of�Theoretical�Physics, Beijing visited NCTS under the support of NCTS FG CPA between Feb. 28-May 16, 2011.

•��Dr.�E.N.�Saridakis�of�UA,�Greece�visited�NCTS�under the support of NCTS FG CPA between April 10-June 20, 2011. Dr. Saridakis has finished three research papers with NCTS as Affiliation.

•��Dr.�T.�Araki�of�Institute�of�High�Energy�Physics,�Beijing, will visit NCTS under the support of NCTS FG CPA between Oct. 30-Nov. 6, 2011.


•��Collaboration� between�Shinji�Tsujikawa� (Tokyo�U of Science, Japan) and Chao-Qiang Geng (NTHU/NCTS) on the thermodynamics in modified gravity theories. See #3 in the publication list.

•��Collaboration� between�Dr.�Kazuharu�Bamba�(KMI, Japan) and Chao-Qiang Geng (NTHU/NCTS) on modified gravity theories and large-scale magnetic fields. See #2, #3, #16 and #18 in the publication list.

•��Collaboration� between�Dr.�E.N.�Saridakis� (UA,�Greece) and Chao-Qiang Geng (NTHU/NCTS) on new dark energy models. See #19 and # 21 in the publication list.

•��Collaboration� between�Dr.�T.�Araki� (IHEP,�Beijing) on dark matter and neutrino physics. See #1, #6 and #16 in the publication list.

•��Collaboration�between�Dr.�S.H.�Ho�(MIT,�USA)�and Chao-Qiang Geng (NTHU/NCTS) on Localizing fields on brane and Kalb-Ramond fields. See #10 and #15 in the publication list.

•��Collaborations�of�Pisin�Chen� (NTU)�with�many�others on Cosmology and Astro-particle physics. See the pub l i ca t ion l i s t w i th NCTS as Acknowledgement.

VI. Highlights of Research ResultsIt is significant that members have been invited

for Talks at international workshops, conferences, and schools in cosmology. In particular, several Ph.D students presented talks in the international meetings. Here we would like to highlight some of the research results.

•��Equation�of�State�in�Modified�Gravity�Theories�

The Coordinator of FGCPA, Chao-Qiang Geng, is a Plenary Speaker at the seventh international workshop “Dark Side of the Universe (DSU 2011)”, Sept. 26-30, KITPC, Beijing. This result was also reported by Chung-Chi Lee (Ph.D student at NTHU) at the 11th RESCEU/DENET Summer School: “Dark Energy in the Universe”, July 25-29, Kumamoto, Japan. The work shows that the crossing of the phantom divide line of Equation of State=-1 is a generic feature in the past and future in viable modified gravity theories.

•��Gravitational�Waves�in�Viable�Modified�Gravity�Theories

Chao-Qiang Geng was invited to attend the Weihai Meeting on “Dark Energy”, July 24-Aug. 4, 2011,Weihai, Shandong, organized by ITP, Beijing. During the meeting, CQ Geng presented the keynote talk at the meeting. He summarized gravitational waves in viable f(R) theories under a non-zero background curvature. In particular, the work shows that the gravitational waves in viable f(R) may be detected by the current and future gravitational wave probes, such as LISA and ASTROD-GW. This study has been published at JCAP.

V. PublicationsNCTS as Affiliation

[1] “Dark Matter in Inert Triplet Models”, Takeshi Araki, C.Q. Geng, Keiko I. Nagao, Phys. Rev. D83 (2011) 075014.

[2] “Phantom crossing in viable f(R) theories”, Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee, Int. J. Mod. Phys. D20 (2011) 1339-1345.


[3] “Thermodynamics in Modified Gravity Theories”, Kazuharu Bamba, Chao-Qiang Geng, Shinji Tsujikawa, Int. J. Mod. Phys. D20 (2011) 1363-1371.

[4] “Top window for dark matter”, K. Cheung, K. Mawatari, E. Senaha, P.Y. Tseng, T.C. Yuan. Int. J. Mod. Phys. D20 (2011) 1413-1421.

[5] “Scalar dark matter and standard model with four generations”, Xiao-Gang He, Shu-Yu Ho, Jusak Tandean, Ho-Chin Tsai, Int. J. Mod. Phys. D20 (2011) 1423-1431.

[6] “Signatures of Dark Matter in Inert Triplet Models”, Takeshi Araki, C.Q. Geng, Keiko I. Nagao, Int. J. Mod. Phys. D20 (2011) 1433-1440.

[7] “Gravitational Waves in Viable f(R) Models”, Louis Yang, Chung-Chi Lee, Chao-Qiang Geng, JCAP 1108 (2011) 029.

[8] “Type II Seesaw Higgs Triplet as the inflaton for Chaotic Inflation and Leptogenesis”, Chian-Shu Chen, Chia-Min Lin, Phys. Lett. B695 (2011) 9-12.

[9] “An A5 Model of Four Lepton Generations”, Chian-Shu Chen, Thomas W. Kephart, Tzu-Chiang Yuan, JHEP 1104 (2011) 015.

[10] “Bimodal/Schizophrenic Neutrino as a Bridge between Inflation and Dark Energy”, Chian-Shu Chen, Chia-Min Lin, Eur. Phys. J. C71 (2011) 1643.

[11] “Localizing fields on brane in magnetized background”, C.Q. Geng, Shih-Hao Ho. arXiv: 1101.4710 [hep-th], Eur. Phys. J. C (2011) 71, 1738.

[12] “Cosmon as the Modulon: Non-Gaussianity from Dark Energy”, Chian-Shu Chen, Chia-Min Lin. arXiv: 1104.0982 [hep-ph] . [Preprint]

[13] “Matter Bounce Cosmology with the f(T) Gravity”, Yi-Fu Cai, Shih-Hung Chen, James B. Dent, Sourish Dutta, Emmanuel N. Saridakis, arXiv:1104.4349 [astro-ph.CO].

[14] “Kinematically Blocked Curvaton”, Lu-Yun Lee, Chia-Min Lin, Chian-Shu Chen. arXiv: 1105.3801 [astro-ph.CO]. [Preprint]

[15] “Entropic Force Scenarios and Eternal

Inflat ion,’’ Taotao Qiu, Emmanuel N. Sar idakis . arXiv:1107.1013 [hep- th] . [Preprint]

[16] “Semileptonic decay”, C.Q. Geng, Y.K. Hsiao. arXiv:1107.0801 [hep-ph]. Phys. Lett. B (2011) (in press).

[17] “Large-scale magnetic fields from inflation due to a CPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields”, Kazuharu Bamba, C.Q. Geng, S.H. Ho, W.F. Kao. arXiv:1108.0151 [astro-ph.CO]. [Preprint]

[18] “Large θ13 from finite quantum corrections in quasi-degenerate neutrino mass spectrum”, Ta k e s h i A r a k i , C h a o - Q i a n g G e n g . arXiv:1108.3175 [hep-ph], JHEP (2011) (in press). [Preprint]

[19] “'Teleparallel’ Dark Energy”, C.Q. Geng, C.C. Lee, E.N. Saridakis and Y.P. Wu, arXiv: 1109.1092 [hep-th]. [Preprint]

[20] “Thermodynamics of cosmological horizons in f(T) gravity,” K. Bamba and C.Q. Geng, arXiv:1109.1694 [gr-qc]. [Preprint]

[21] “Observation Constraints on Teleparallel Dark Energy”, C.Q. Geng, C.C. Lee and E.N. Saridakis, arXiv: 1110.0913 [astro-ph]. [Preprint]

NCTS as Acknowledgement

[1] “RMDM and Lepton Flavor Violation”, Yi Cai, Xiao-Gang He, Michael Ramsey-Musolf, Lu-Hsing Tsai, arXiv: 1108.0969 [hep-ph]. [Preprint]

[2] “Lifshitz theories with extra dimensions and 3+1-d Lorentz invariance”, Xiao-Gang He, Sandy S.C. Law, Raymond R. Volkas. arXiv:1107.3345 [hep-ph]. [Preprint]

[3] “Probing annihilations and decays of low-mass galact ic dark mat ter in IceCube DeepCore array- Part I : track events”, Fei-Fan Lee, Guey-Lin Lin. arXiv:1105.5719 [hep-ph]. [Preprint]

[4] “Cosmological Behavior of a Parity and Charge-Parity Violating Varying Alpha Theory”, Debaprasad Maity, Pisin Chen, Phys.Rev. D83 (2011) 083516.


[5] “Landau Damping of Baryon Structure Formation in the Post Reionization Epoch”, Feng-Yin Chang , P i s in Chen , a rXiv : 1006.5777 [astro-ph.CO]. [Preprint]

[6] “Solving the Cusp-Core Problem with a Novel Scalar Field Dark Matter”, Kung-Yi Su, Pisin Chen, JCAP 1108 (2011) 016.

[7] “Correlation between Global Parameters of Galaxies,’’ Yu-Yen Chang, Rikon Chao, Wei-Hao Wang, Pisin Chen, arXiv: 1009.0030 [astro-ph.GA]. [Preprint]

[8] “ B l a c k H o l e R e m n a n t s i n t h e E a r l y Universe”, Fabio Scardigli, Christine Gruber, Pisin Chen, Phys. Rev. D83 (2011) 063507.

[9] “Comments on 'Remarks on the spherical scalar field halo in galaxies”, Kung-Yi Su, Pisin Chen, arXiv:1009.0869 [astro-ph.GA]. [Preprint]

[10] “Cosmological and Solar-System Tests of f(R) Modified Gravity”, Wei-Ting Lin, Je-An Gu, Pisin Chen, Int. J. Mod. Phys. D20 (2011) 1357-1362.

[11] “Near-Field Effects of Cherenkov Radiation Induced by Ultra High Energy Cosmic Neutrinos”, Chia-Yu Hu, Chih-Ching Chen, Pisin Chen. arXiv: 1012.5155 [astro-ph.HE]. [Preprint]

[12] “Cosmological Imprints of a Generalized Ch ap ly g in G as M o de l f o r t h e Ea r ly Universe”, Mariam Bouhmadi-Lopez, Pisin Chen, Yen-Wei Liu. Phys. Rev. D84 (2011) 023505.

[13] “Constraining PCP Violating Varying Alpha Theory Through Laboratory Experiments”, Debaprasad Maity, Pisin Chen, Phys. Rev. D84 (2011) 026008.

[14] “Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT”, Yen Chin Ong, Pisin Chen, arXiv: 1106.3555 [hep-th]. [Preprint]

[15] “Confronting Tracker Field Quintessence with Data”, Pao-Yu Wang, Chien-Wen Chen, Pisin Chen, arXiv: 1108.1424 [astro-ph.CO]. [Preprint]

[16] “ T h e E a r l y - Ti m e E v o l u t i o n o f t h e Cosmological Perturbations in f(R) Gravity”, Je-An Gu, Tse-Chun Wang, Yen-Ting Wu, Pisin Chen, W-Y.Pauchy Hwang. arXiv: 1108.3038 [astro-ph.CO]. [Preprint]


Focus Group on Gravitation

Coordinator: Da-Shin Lee (National Dong Hwa University; email: [email protected])


he purposes of this FG are:

1. To generate a long-term collective force in Grav i t a t i on r e sea r ch among t he l oca l communities and the Asia-Pacific area;

2. To generate interdisciplinary and cutting-edge research activities on Gravitation

3. To create both academic-wise and career-wise chances for talented graduate students and postdocs.

To achieve the goal we have identified scope of activities mostly on quantum fields in curved spacetime with applications in Cosmology, black holes physics, quasi-local energy expressions, fundamental problems of General Relativity, numerical General Relativity, canonical quantum gravity, and other areas such as stochastic gravity.

Another special effort of our FG is to create opportunities for postdocs and graduate students to visit prestige research institutes overseas such as the University of Maryland, Perimeter Institute, APCTP, Yukawa Institute, Institute of Applied Mathematics, Academia Sinica, Beijing. This visiting program can not only sharpen the academic ability of individual junior researchers, but also can broaden the spectrum of their academic careers.

The coordinator of the FG is Lee, Da-Shin (Professor, NDHU) on mom-equilibrium quantum field theory and cosmology.

Major members of our FG are

•��Chen,�Chiang-Mei� (Associate�Professor,�NCU)�on gravitation and string theories

•��Cho,�Hing-Tong�(Professor,�TKU)�on�gravitation�and black holes

•��Lin,�Shih-Yuin� (Assistant�Professor,�NCHU)�on�quantum and statistical field theory in curved spacetime and relativistic quantum information

•��Nes te r,� James� M.� (Professor,� NCU)� on�gravitation and quasi-local energy

•��Soo,�Chopin� (Professor,�NCKU)�on�quantizing�gravity and cosmology

•��Yo,�Hwei-Jang�(Associate�Professor,�NCKU)�on�numerical general relativity

•��Yang,� I�Ching� (Associate�Professor,�NTTU)�on�general relativity

•��Wu,�Chun-Hsien.� (Assistant�Professor,SCU)�on�quantum field theory in curved spacetime

•��Yu,�Hoi-Lai� (Professor,�Academia�Sinica)� on�quantizing gravity and cosmology

Frequent visitors are Bei-Lok Hu (University of Maryland), Roh-Suan Tung (NYU, Singapore), Yun-Kau Lau (Applied Mathematics Institute, Academia Sinica, Beijing), Larry H. Ford (Tufts University), Misao Sasaki (Kyoto University), Ray Rivers (University of London).

II. Activities The main activities organized and to be

organized in the year of 2011 are summarized as follows:

(1) Participation in the school/workshop at Shanghai, 10-14 February, 2011 (the support of the travel expense for 2 postdocs and 6 graduate students is about 200K from the previous year’s budget).

(2) 2011 Mini-workshop on Gravitation, 18 February 2011 (25 participants +the expense 77K from the previous year’s budget).

(3) Gravi ta t ion Focus Group Meet ing and M i n i w o r k s h o p , 8 A u g u s t , 2 0 11 ( 2 5 participants + the expense 66K using this year’s budget).

(4) Student seminars starting from September (5-7 seminars + allocated budget 35K).

(5) Annua l workshop/school a t NCKU in December, 2011 (allocated budget 100K).

(6) Participation in the school/workshop at Kyoto


in 2012 (the budget for postdocs/students to cover traveling is about 150K).

The visitors we invited mostly come to attend our activities. Of course, we always try to arrange for a longer visit to other institutes to enhance the scientific interactions with local colleagues. The benefit of our FG activities is long term. The highlighted effort is the student training program. In addition to encouraging and supporting students’ participation in international conferences abroad we will continue the exchange program with the Chinese Academy of Sciences at Beijing. This year we started to hold graduate student seminars in which the graduate students are encouraged to present their work at other universities of our FG members. This activity can not only help train the students to be good presenters but also provides an opportunity to enhance interaction between the research groups.


Visitors

The main part of our budget was planned for organizing conferences and the support for students to attend an international conference. So we do not have much money for other purposes, including inviting visitors.

In addition to our frequent visitors listed above, the visitors of our FG this year include:

(1) Professor Jack Y. Ng (UNC at Chapel Hill), 7 -10 Augus t , 2011 ( a key speake r i n Gravi ta t ion Focus Group Meet ing and Miniworkshop with the covered local expense about 18K).

(2) Professor Wade Naylor (the University of Osaka), who plans to pay a visit to Professor Hing-Tong Cho in November (the allocated budget to cover the air ticket+ local expense is about 60K).

(3) Dr. Jose-Luis Jaramillo (Max-Planck-Institut fur Gravitat ionphysik (Albert Einstein Institut), 15 - 20 February, 2011.

(4) Professor Laszlo B. Szabados (Research Institute for Particle and Nuclear Physics, Budapest), who will visit Professor Hoi-Lai Yu during 10-15 October, 2011.


Our members have worked wi th the i r collaborators from overseas for a long time. One of our frequent visitors, Professor Bei-Lok Hu (University of Maryland), has a long-term collaboration with Professor Shin-Yuin Lin on the fundamental issues of quantum and statistical field theory in curved spacetime and relativistic quantum information, and Professor Hing-Tong Cho on stochastic gravity. Professor Hing-Tong Cho has also established the strong collaborations with Prof. Wade Naylor of the University of Osaka and Prof. Alan Cornell of the University of Witwatersrand in South Africa on the topic of higher dimensional black holes. In addition, the international collaborators of Professor James M Nester involve Professors P. Baekler, L. Bates, J. Frauendiener, F. W. Hehl, and L.B. Szabados on various topics of gravity.

IV. Highlights of Research Results Here we highlight the research results of our

FG members:

(1) Prof. Prof. Hwei-Jang Yo’s group at NCKU have produced a successful numerical code in numerical general relativity. Successful works include the coalescence of binary black holes, which is one of the most promising sources for the gravitational wave detection, and on simulating rapid-rotating black holes with the adaptive mesh refinement techniques. This achievement had already put Taiwan in the frontier in numerical general relativity world-wide.

(2) Prof. Shih-Yuin Lin’s series of papers at NCHU on the Unruh-DeWitt detector theory from 2006 to 2010 has brought a deeper level o f u n d e r s t a n d i n g o f l o c a l q u a n t u m measurement.

(3) Prof. Hing-Tong Cho’s work at TKU on the correlators of the stress-energy tensor in maximally symmetric spacetimes that reveals its relation to the noise kernel has been a major achievement in the theory of stochastic gravity.

(4) Prof. James M. Nester and Chiang-Mei Chen’s group at NCU continue to produce cutting edge results on quasi-local energy expressions and torsion physics in General Relativity that have attracted much attention internationally.


(5) Chopin Soo (NCKU) and Hoi-Lai Yu’s (AS) work on the new formulation of Horava-Lifshi tz Quantum Gravi ty as a Master Constraint Theory that had brought in not only a new formulation of renormalizable quantum gravity theories but also fundamental insight into the dynamical structure of General Relativity.

(6) Prof. Da-Shin Lee’s work (NDHU) on field theoretic approach to quantum noise that may have potential application to improve the performance of laser interferometers.

V. PublicationsPapers with NCTS as the affiliation

[1] “Surface plasmons in a metal nanowire coupled to colloidal quantum dots: Scattering properties and quantum entanglement”, Guang-Yin Chen, Neill Lambert, Chung-Hsien Chou, Yueh-Nan Chen, and Franco Nori, Phys. Rev. B 84, 045310, 2011.

[2] “Quantum entanglement and entropy in particle creation”, Shih-Yuin Lin, Chung-H s i e n C h o u , B . L . H u , P h y s . R e v. D81:084018, 2010.

[3] “Digital origin of cosmic inflation” Chung-Hsien Chou & Hoi-Lai Yu, Mod. Phys. Lett. A25:1483-1489, 2010.

[4] “Entanglement creation between two causally disconnected objects” Shih-Yuin Lin & B.L. Hu. Phys. Rev. D81:045019, 2010.

Papers with acknowledged NCTS

[1] “Stress-energy tensor correlators of a quantum field in Euclidean RN and AdSN spaces via the generalized zeta-function method”, H. T. Cho and B. L. Hu, Phys. Rev. D 84, 044032, 2011.

[2] “Scalar field fluctuations in Schwarzschild-de Sitter space-time”, Hing-Tong Cho, Kin-Wang Ng, and I-Chin Wang, Class. Quantum Grav. 28, 055004, 2011.

[3] “ D o m a i n w a l l s p a c e - t i m e s w i t h a cosmological constant”, Chih-Hung Wang, Hing-Tong Cho, and Yu-Huei Wu, Phys. Rev. D83, 084014, 2011.

[4] “Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole”, B. Chen, C.-M. Chen and B. Ning, Nucl. Phys. B853 196-209, 2011.

[5] “An Analytic Analysis of Phase Transitions in Holographic Superconductors”, C.-M. Chen and M.-F. Wu, Prog. Theor. Phys. 126, 387-395, 2011.

[6] “Optimal Choices of Reference for a Quasi-loca l Energy: Spher ica l ly Symmetr ic Spacetimes”, Ming-Fan Wu, Chiang-Mei Chen, Jian-Liang Liu, James M. Nester, accepted by Phys. Rev. D, 2011 ; arXiv: 1109.4738 [gr-qc].

[7] “Quasi-local energy and the choice of reference”, Jian-Liang Liu, Chiang-Mei Chen, James M Nester, Class. Quant. Grav. 28, 195019, 2011.

[8] “Poincare gauge theory with coupled even and odd parity dynamic spin-0 modes: dynamical equations for isotropic Bianchi cosmologies”, F.-H. Ho and J.M. Nester accepted for publication in Int. J. Mod. Phys. D [arXiv: 1106.0711].

[9] “Witten spinors on maximal, conformally flat hypersurfaces”, J. Frauendiener, J.M. Nester and L.B. Szabados, Class. Quantum Grav. 28 185004, 2011.

[10] “Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part”, P. Baekler, F.W. Hehl, and J.M. Nester, Phys. Rev. D 83, 024001, 2011 [arXiv:1009.5112].

[12] “Poincare gauge theory with coupled even and odd parity spin-0 modes: cosmological normal modes”, F.-H. Ho and J.M. Nester, accepted for publication in Ann. Phys. (Berlin) DOI 10.1002/andp.201100100.

[13] “Quantum modifications to gravity waves in de Sitter spacetime”, Jen-Tsung Hsiang, L. H. Ford, Da-Shin Lee, and Hoi-Lai Yu, Phys. Rev. D 83, 084027, 2011 .

[14] “Pontaneous vortex production in driven c o n d e n s a t e s w i t h n a r r o w F e s h b a c h resonances”, Chi-Yong Lin, Da-Shin Lee, and Ray J. Rivers, Phys. Rev. A 84, 013623, 2011.


Focus Group on Lattice QCD and Hadron PhysicsCoordinator: Chung-Wen Kao (Chung Yuan Christian University; email: [email protected])

Committee members: Juinn-Wei Chen (National Taiwan University), Ting-Wai Chiu (National Taiwan University), Tung-Han Hsieh (Academia Sinica), Fu-Juin Jiang (National Taiwan Normal University), David Chi-Jen Lin (National Chiao-Tung University), Cheng-Pang Liu (National Dong-Hwa University)


n LQCD, the scientific goals are (a) pu r su ing l a rge - sca l e unquenched

calculations with optimal domain-wall quarks and building up the capacity for large scale computing with the new GPU technology (b) using lattice gauge field theories to explore physics beyond standard model, and (c) studying the properties of the heavy baryons on lattice. In hadronic physics, the goals are (a) understanding QCD viscosities and their relations to phase transitions (b) investigating the hadron properties and the QCD phase structure via models and effective field theories, (c) systematic time reversal violation studies of nuclear and atomic systems. Also, we would l ike to collaborate with str ing and c o n d e n s e d m a t t e r t h e o r i s t s t o s t u d y superconductivity and antiferromagnets using nonperturbative method such as AdS/CFT and/or Monte Carlo simulation.

II. ActivitiesLots of activities have been organized to

induce new ideas and collaborations:

(1) Weekly/biweekly meetings: (a) Lattice QCD and Hadron physics biweekly seminar at NTU, video conferencing with NDHU and Academia Sinica. (b) Seminars Series at NCTU(weekly), co-funded by LQCDHP and Cosmology focus g roups (c ) Seminars Ser ies a t NDHU (biweekly), co-funded by LQCDHP and Cosmology focus groups (d) TWQCD collaboration at NTU (weekly) (e) Joined LHC journal club with the LHC initiative.

(2) Schools and Workshops: (a) Mini-workshop o n B e y o n d S t a n d a r d M o d e l L a t t i c e Simulations (Nov 12, 2010.) (b) The 14th Taiwan Nuclear Physics Winter School (Jan.17-22, 2011, NDHU) (c) Lecture series given by Piai Maurizio (May 3,4, 2011)( (d) The 15th Taiwan Nuclear Physics Summer School (June 27-30, 2011, Academia Sinica IoP).


The list of visitors can be found from our focus group website (http://phys.cts.ntu.edu.tw/en/) and the international collaborations can be found from o u r p u b l i c a t i o n l i s t s h o w n b e l o w. T h e collaboration between TWQCD and JLQCD was formed since 2006. This collaboration has worked out many important results. C.J. David Lin has also formed collaboration with an Oska U. group on walking Technicolor, a Taiwan-UK-US collaboration on b-baryon simulations, as well as a Taiwan-Germany collaboration on Higgs-Yukawa system simulations. C.J. David Lin also formed collaboration with W. Detmold (W&M) and Matthew Wingate (Cambridge) to work on the property of the b-baryons. Juinn-Wei Chen has worked with groups in China. F-J Jiang continues his collaboration with Bern group.

IV. Highlights of Research ResultsA. Lattice QCD

A-1. LHCb physics from lattice QCD: Chi-Jen David Lin has collaboration with William Detmold (College of William and Mary) and Matthew Wingate (Cambridge University), on the physics related to the LHC-b program. The LHC will produce a significant amount of polarized b-baryon samples which allow the measurements of the spectrum and the decays of these baryons. This year they finished a series of papers on the extraction of all the axial couplings between heavy hadrons and pion, starting from chiral perturbation theory to the numerical calculation. It is the first lattice QCD calculation for the baryon axial couplings, and one of the papers has been submitted to Phys. Rev. Lett.

A-2. Walking technicolour on the lattice: Chi-Jen David Lin and his research associate Kenji Ogawa have been collaborating with colleagues in Japan on a project in walking technicolour on the lattice. This year, they finished the calculation for a candidate theory and established firm (renormalization scheme independent) evidence that the theory is conformal


in the IR. Their result will be submitted to Phys. Rev. Lett. soon.

A-3. Strong-Yukawa coupling on the lattice: As part of the academic summit project in physics of extra generation of fermions, George Hou, Chi-Jen David Lin Bastian Knippschild, Kenji Ogawa , Brian Smigielski, together with colleagues in Germany are making progress in simulating strong-Yukawa systems on the lattice. From their preliminary result in the study of finite-size scaling, they discovered the existence of a new phase in the strong-Yukawa regime. Right now they are collecting more data for the analysis of the spectrum in this regime.

A-4. Large-scale simulations of unquenched lattice QCD with optimal domain-wall quarks: The TWQCD collaboration led by Ting-Wai Chiu has made a breakthrough in applying the new GPU technology in large scale computing. It is the first group to use a GPU cluster with sustained 36 Te ra f lops to pe r fo rm l a rge - sca l e LQCD simulations, and is one of the three groups (together with RBC/UKQCD, JLQCD) that can perform large scale unquenched simulations of lattice QCD with exact chiral symmetry. Their results have been published in PRD.

B. Hadronic Physics

B-1. The ratio between Shear viscosity and entry density: The ratio eta/s, shear viscosity (eta) to entropy density (s), reaches its local minimum at the (second order) phase transition temperature in a wide class of systems. It was suspected that this behavior might be universal. However, a counterexample is found by Juinn-Wei Chen in a system of two weakly self-interacting real scalar fields with one of them condensing at low temperatures while the other remains in the symmetric phase. There is no interaction between the two fields. The resulting eta/s is monotonically decreasing in temperature despite the phase transition. This is an important discovery in this field.

B-2. Two-flavor chiral perturbation theory for hyperons: Motivated by poor convergence of the three-flavor chiral perturbation theory in describing the properties of hyperons, Fu-Juib Jiang, Tiburz, and Walker-loud has investigated the two-flavor chiral expansions for the study hyperon properties. They find that, despite higher-order corrections, there is a useful perturbative expansion for the masses and isovector axial

charges of both spin-half and spin three-half hyperons.

C. Strongly Coupling Systems in Condensed matter

C-1. d+id Holographic Superconductors: A holographic model of d+id superconductors based on the action proposed by Benini, Herzog, and Yarom is studied. This model has a charged spin two field in an AdS black hole spacetime. Working in the probe limit, the normalizable solution of the spin two field in the bulk gives rise to a d+id superconducting order parameter at the boundary of the AdS. Juinn-Wei Chen and his collaborators calculate the fermion spectral function in this superconducting background and confirm the existence of fermi arcs for non-vanishing Majorana couplings. By changing the re la t ive s t reng th gamma of the d and id condensations, the position and the size of the fermi arcs are changed. When gamma=1, the spectrum becomes isotropic and the spectral function is s-wave like. By changing the fermion mass, the fermi momentum is changed. They also calculate the conductivity for these holographic d+id superconductors where time reversal symmetry has been broken spontaneously. A non-vanishing Hall conductivity is obtained even without an external magnetic field.

C-2. High precision determination of the low-energy constants for antiferromagnets with an O(N) symmetry: Motivated by the cubical regime in magnon chiral perturbation theory, Jiang proposes a new method of calculating the low-e n e rg y c o n s t a n t s p i n w a v e v e l o c i t y f o r antiferromagnets with an O(N) symmetry in a Monte Carlo simulations. Using his idea, Jiang and Wiese has calculated the low-energy constants, namely the staggered magnetization density, spin stiffness, and spinwave velocity of the 2-dimentional quantum antiferromagnets to an unprecedented accuracy.

C-3. Investigation of unconventional quantum phase transitions: Motivated by the unconventional quantum phase transition for the staggered dimerized quantum Heisenberg model as suggested in Physical Review Letter 100, 127202 (2008), Jiang has reinvestigated the quantum phase transition induced by dimerization of this model. In particular, Jiang employed the idea of fixing the aspect ratio of spatial winding number s squa red in h i s s tudy. Wi th t he


unconventional finite-size scaling Jiang proposes, he showed that the quantum phase transition is indeed well understood by the theoretical O(3) universality class.

C-4. Effective field theory for quantum antiferromagnets on the honeycomb lattice: Jiang and his collaborators has constructed a low-e n e r g y e f f e c t i v e f i e l d t h e o r y f o r a n antiferromagnet on the honeycomb lattice. One novel result of their theory is the appearance of f-wave symmetry when performing a 90 degrees rotation of the ground state wave function. Although still controversial experimentally, their theoretical result of f-wave symmetry seems to agree with known experimental data.

V. Selected Publications[1] “Kaon Thresholds and Two-Flavor Chiral

Expansions for Hyperons”, F.-J. Jiang, B. C. Tiburzi, and A. Walker-loud, Phys. Lett. B695, 329-336 (2011).

[2] “Minimum Shear Viscosity over Entropy D e n s i t y a t P h a s e T r a n s i t i o n ? – A Counterexample”, J.W. Chen, C.T. Hsieh, H.H. Lin, Phys. Lett. B701, 327-331 (2011).

[3] “Topological Susceptibility in Two Flavors Lattice QCD with the Optimal Domain-Wall Fermion”, T.W. Chiu, T.H. Hsieh, Y. Y. Mao, Phys. Lett. B 702, 131-134 (2011).

[4] “Nonet meson properties in Nambu--Jona-Lasinio model with dimensional versus cutoff regularization,” T. Inagaki, D. Kimura, H. Kohyama, A. Kvinikhidze, Phys. Rev. D83, 034005 (2011).

[5] “How Perfect a Gluon Plasma Can Be in Perturbative QCD?”, J.W. Chen, J. Deng, H. Dong, Q. Wang, Phys. Rev. D 83, 034031 (2011).

[6] “Model analysis of thermal UV-cutoff effects on the ch i ra l c r i t ica l sur face a t f in i te temperature and chemical potential,” J.W. Chen, H. Kohyama, U. Raha, Phys.Rev.D83 094014 (2011).

[7] “Chiral restoration at finite T under the m a g n e t i c f i e l d w i t h t h e m e s o n - l o o p correction,” Seung-il Nam, Chung Wen Kao, Phys. Rev. D 83 (2011) 096009.

[8] “ S h e a r Vi s c o s i t y i n We a k l y C o u p l e d N-Component Scalar Field Theories” J.W.

Chen, M. Huang, C.T. Hsieh, H.H. Lin, Phys. Rev. D83 (2011) 115006.

[9] “d+id Holographic Superconductors”, J.W. Chen, Y.S. Liu, D. Maity, JHEP 05:032, 2011.

[10] “Method of calculating the spin-wave velocity of spin-1/2 antiferromagnets with O(N) symmetry in a Monte Carlo simulation”, F.-J. Jiang, Phys. Rev. B 83, 024419 (2011).

[11] “High-precision determination of low-energy effective parameters for a two-dimensional Heisenberg quantum antiferromagnet”, F.-J. Jiang and U.-J. Wiese, Phys. Rev. B 83, 155120 (2011).

[12] “Constraint Effect ive Potent ia l of the Magnetization in the Quantum XY Model”, U. Gerber, C. P. Hofmann, F.-J. Jiang, G. Palma, P. Stebler, and U.-J. Wiese, J. Stat. Mech. 1106:P06002 (2011).

[13] “New One-Flavor Hybrid Monte Carlo Simulation Method for Lattice Fermions with γ 5 H e r m i t i c i t y ” , K . O g a w a , a r X i v : 1104.2255, accepted for publication in Phys. Lett. B.

[14] “Equally Conformal but More Perfect than Previous ly Thought - Shear and Bulk Viscosities of a Gluon Plasma in Perturbative QCD”, J.W. Chen, J. Deng, H. Dong, Q. Wang, 2011, e-Print: arXiv: 1107.0522 [hep-ph], submitted to Phys. Rev. D.

[15] “Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model” , F. J . J iang , a rXiv : 1108.0715 [cond-mat.str-el], submitted to Phys. Rev. B.

[16] “Axial couplings in heavy hadron chiral perturbation theory at the next-to-leading order”, W. Detmold, C.-J.D. Lin and S. Meinel, arXiv: 1108.5594, submitted to Phys. Rev. D.

[17] “Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet on the Honeycomb Lattice”, F.Kampfer, B.Bessire, M.W.C.Hofmann, F.J.Jiang and U.J.C.Wiese, arXiv: 1109.1419 [cond-mat.str-el], submitted to Phys. Lett. B.

[18] “Axial couplings and strong decay widths of heavy hadrons”, W. Detmold, C.-J.D. Lin and S. Meinel, arXiv: 1109.2480, submitted to Phys. Rev. Lett.


Focus Group on LHC PhysicsCoordinator: Cheng-Wei Chiang (National Central University; email: [email protected])


he LHC Focus Group has an executive committee consisting of Prof. Chuan-

Hung Chen of NCKU, Prof. Kingman Cheung of NTHU, Prof. Cheng-Wei Chiang of NCU (Chief Coordinator of the year), Prof. Xiao-Gang He of NTU, and Prof. Kwei-Chou Yang of CYCU, and Prof. Tzu-Chiang Yuan of AS. There are about 20 other faculty members from various institutes in this FG. We also have a good size of postdocs and graduate students actively participating our activities.

The goals of this FG are to bring out all the existing theoretical efforts, to establish close working relations with our experimental groups, and also to train young researchers and students to play an important role in this field.

Our focus, as stated in our very original p roposa l , i s LHC-re la t ed phys ic s , more specifically in the following directions:

•��Invest igat ion� of� physics� of� e lectroweak�symmetry breaking and Higgs mechanism

•��Physics�beyond�the�standard�model.

•��Probing�the�nature�of�dark�matter

•��Flavor�physics�and�CP�violation

II. ActivitiesTo bring all interested parties in Taiwan to be

more coherently involved in research, the FG act ively promotes the fol lowing types of activities:

(1) Support regular journal-club meetings or seminars at various universities where there is sufficient interest. This year, we supported seminars held at CYCU and NCU, and journal club meetings at NTU and NTHU, including the accommodation support for the speakers if they stay additional time for collaborations. This provided a platform for scholars to present their research results and exchange

ideas, to discuss about latest experimental data and implications, and to educate young theorists such as postdocs and graduate students. Some new research projects were often stimulated in such events.

(2) Hold workshops of different sizes/purposes. We h e l d t h e 9 t h P a r t i c l e P h y s i c s Phenomenology Workshop (PPP9), organized by Chiang in early June on the beautiful NCU campus. During this 4-day workshop, over 30 foreign scholars (among totally about 120 participants) were invited to participate and give lectures or research talks on topics related to the LHC physics. Many of the foreign participants stayed after the workshop to visit other institutes (such as AS and NCTS) and give more ta lks or in teract wi th local physicists. To encourage postdocs and graduate students to participate, we also supported their accommodation and/or transportation fares to the workshop if they requested. We will have an end-year LHC FG workshop, organized jointly by Cheung and Yuan. With about 6 months apart from PPP9, we expect that this workshop will offer a good opportunity for local people to share their findings.

(3) Support School activities. We supported a couple of graduate students to go to the Yukawa Summer Institute, held in Japan this year. This Summer Institute has been a regular event for years, and just started to rotate among three countries in Asia recently. Traditionally, we also support the Spring School or Particles and Fields each year. Yet this year’s Spring School did not indicate such a need.


Though not limited in the previous section, it is also an important goal of our FG to invite researchers, young and well-established alike, from abroad to Taiwan. Up to now, we had invited and supported the visits of Prof. M. Chabab, Prof. D. Choudhury, Prof. W.Y. Keung,


and Prof. B. Wang. The support level goes from merely local expenses to full-trip support. Each of the first three visitors had stayed for about 2 weeks. During the period, they were encouraged to visit different institutes and interact with people t he re . The hope was t o e s t ab l i sh some collaborations between members in our FG and the visitors and to promote research in Taiwan. Thanks to such opportunities, Cheung and Yuan had formed another collaboration with Prof. Keung on a couple of collider physics topics. Chiang and Prof. Choudhury joined force to study a new physics model explanation for anomaly events found in Tevatron experiments, and collaborated with Prof. Keung on an issue related to anomalous muon interactions.

IV. Highlights of Research ResultsIn the following, we divide our research results

into several topics and only highlight a few selected works.

Collider Physics

CDF and D0 Collaborations at Fermilab Tevatron have observed several anomalous results in recent years. Earlier this year, CDF reported unexpected Wjj event excess at the invariant mass o f a r o u n d 1 4 0 G e V, l e a d i n g t o a l o t o f speculations about new physics possibility. Several members of the FG form respective teams to study this issue and put out a few papers [1,2,3].

The large top-antitop quark forward-backward asymmetry reported by CDF had generated a lot of interest to many people, especially to those who have been working on physics beyond the standard model. In [4], Cheung and Yuan updated their previous analysis, where a phenomenological model of W’ was proposed to account for the large asymmetry. They calculated the invariant mass distribution as well as the rapidity dependence for the asymmetry, and determined the parameter space of the W’ model to explain the recent CDF results while keeping the total top-antitop pair production cross section agree with standard model. In [5], Chen and his collaborators proposed an unparticle explanation to account for the observed anomaly as well.

In [6], Chiang and his collaborators studied the Drell-Yan processes at the LHC in the context of most general interactions allowed by symmetries.

They considered the neutral and charged interactions separately, and proposed how we could learn from data the information of mass, spin, and interaction properties of the new boson.

Higgs Physics

According to the latest LHC ATLAS and CMS data, the standard model (SM) Higgs particle has not been found yet. A large mass space had been ruled out by direct searches. In [7], He and his collaborators discussed why the discovery could be difficult and the implications of the result.

Flavor Physics and CP Violation

Chen and his collaborators extended the SM by adding an SU(2)-singlet heavy quark, resulting in Z-mediated flavor-changing neutral currents (FCNC’s) to enhance LSCA. Combining with other constraints, they found that the enhancement is only a factor of two and insufficient to explain the D0 data [8]. With his collaborators, Chua studied the model with a lepton triplet carrying nonzero hypercharge [9,10]. They found that such new particle might have Yukawa interactions with SM leptons, yet the effects were too small to observed in usual detectors . He and his collaborators recently studied how to use the unparticle idea to explain recently observed Bs mixing [11]. Their result was even reported by the popular magazine New Scientist (volume 2813). Yang and Cheng applied light-cone sum rules and light-cone distribution amplitudes to tensor mesons. They computed the form factors for B decays to JPC=2++ tensor meson [12]. Since the polarization study of B TV, TA, TT decay might reveal the helicity structure thereof, they explained the importance of nonfactorizable effects in view of the observat ion of the B–→K2

*0π– decay [13].

Dark Matter

In the dark matter research [14,15], Cheung and Yuan employed an effective interaction approach to analyze various operators for a fermionic or scalar dark matter interacts with standard model fermions or gluon, thereby capturing a large class of dark matter models in the market and performing model-independent analysis. They used the anti-proton spectrum measured by PAMELA and the diffuse gamma-ray spectrum observed by Fermi-LAT to deduce lower limits for the effective scales of the effective operators.


H e a n d h i s c o l l a b o r a t o r s s t u d i e d t h e phenomenology of the so-called darkon model. In one work, they discuss the possibility of a low-mass dark matter particle and the accompanying invisible Higgs boson decay [16]. In another work, they successfully built models of dark matter and neutrino mass whose symmetry does not go beyond that of the SM [17].

Interdisciplinary Physics

In summer 2010, one shocking experimental finding was about the proton size. The result showed that the proton size determined from the Lamb shift of muonic hydrogen was about 4% smaller than the corresponding result in the regular hydrogen, at the 5 sigma level. This anomaly led Chiang and his collaborators to consider new physics possibilities. They found that the anomaly posed a challenging problem in front of us because it could not be explained by a large class of new interactions while satisfying other low-energy experimental constraints [18].

V. Selected Publications[1] Chuan-Hung Chen, Cheng-Wei Chiang,

Takaaki Nomura, Fusheng Yu, “A Light charged Higgs boson in two-Higgs doublet mode l fo r CDF Wj j anomaly” , a rXiv : 1105.2870 [hep-ph].

[2] T. Enkhbat, Xiao-gang He, Yukihiro Mimura, Hiroshi Yokoda, “Colored Scalars And The CDF W+dijet Excess”, 1105.2699 [hep-ph].

[3] Xiao-Gang Ge, Bo-Qiang Ma, “The CDF dijet excess f rom in t r ins ic quarks” , a rXiv : 1104.1894 [hep-ph].

[4] Kingman Cheung and Tzu-Chiang Yuan, “Top Quark Forward-Backward Asymmetry in the Large Invariant Mass Region”, Phys. Rev. D 83 (2011) 074006 [arXiv: 1101.1445 [hep-ph]].

[5] C.H. Chen, G. Cvetic and C.S. Kim, “Forward-backward asymmetry of top quark in unparticle physics”, Phys. Lett. B 694, 393 (2011) [arXiv: 1009.4165 [hep-ph]].

[6] Cheng-Wei Chiang, Neil D. Christensen, Gui-Jun Ding, Tao Han, “Discovery in Drell-Yan Processes at the LHC”, arXiv: 1107.5830 [hep-ph].

[7] Xiao-Gang He, German Valencia , “An extended scalar sector to address the tension

between a fourth generation and Higgs searches at the LHC”, arXiv: 1108.0222 [hep-ph].

[8] C .H . Chen , C .Q . Geng and W. Wang , “Z-mediated charge and CP asymmetries and FCNCs in Bd,s processes”, JHEP 1011, 089 (2010) [arXiv: 1006.5216 [hep-ph]].

[9] C . K . C h u a a n d S . S . C . L a w , “Phenomenological constraints on minimally coupled exotic lepton triplets”, Phys. Rev. D 83, 055010 (2011) [arXiv: 1011.4730 [hep-ph]].

[10] Sandy S.C. Law, “Constraints on exotic lepton doublets with minimal coupling to the standard model”, [arXiv:1106.0375 [hep-ph]].

[11] “Chun-Fu Chang, Kingman Cheung and Tzu-Chiang Yuan, “Global Study of Electron-Quark Unparticle Interactions”, Eur. Phys. J. C71 (2011) 1611 [arXiv: 0912.1849 [hep-ph]].

[12] Kwei-Chou Yang, “B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules”, Phys. Lett. B695:444-448 (2011) [arXiv: 1010.2944 [hep-ph]].

[13] Hai-Yang Cheng and Kwei-Chou Yang, “Charmless Hadronic B Decays into a Tensor Meson”, Phys. Rev. D 83, 034001 (2011) [arXiv:1010.3309 [hep-ph]].

[14] Kingman Cheung, Po-Yan Tseng and Tzu-Chiang Yuan, Gamma-ray Constraints on Effective Interactions of Dark Matter, JCAP 1106 (2011) 023 [arXiv:1104.5329 [hep-ph]]

[15] Kingman Cheung, Po-Yan Tseng and Tzu-Chiang Yuan, “Cosmic Antiproton Constraints on Effective Interactions of the Dark Matter”, JCAP 1101 (2011) 004 [arXiv:1011.2310 [hep-ph]].

[16] Yi Cai, Xiao-Gang He, Bo Ren, “Low Mass Dark Matter and Invisible Higgs Width In Darkon Models”, Phys. Rev. D 83, 083524 (2011) [arXiv: 1102.1522 [hep-ph]].

[17] Yi Cai, Xiao-Gang He, “Michael Ramsey-Musolf, Lu-Hsing Tsai, RνMDM and Lepton Flavor Violation”, arXiv: 1108.0969 [hep-ph].

[18] Vernon Barger, Cheng-Wei Chiang, Wai-Yee Keung, and Danny Marfatia, “Proton size anomaly”, Phys. Rev. Lett. 106, 153001 (2011) [arXiv: 1011.3519 [hep-ph]].


Focus Group on String Theory

Coordinator: Chuan-Tsung Chan (Tunghai University; email: [email protected])


he string theory focus group is one of the earliest founding units of the NCTS

Physics Division. Our research goal is to make theoretical study of the string theory as a unified framework of quantum gravity. Our group committee consists of 12 faculty members from 8 U n i v e r s i t i e s ( 5 n a t i o n a l p l u s 3 p r i v a t e Universities), and the current coordinator is Chuan-Tsung Chan (Department of Physics, Tung-hai University). In addition to faculty members, the active group members now include 10 post-docs researchers, and 12 students. We have various research teams which select their individual research topics based on their interests and expertise (the details are given in below). The coordinator in 2012 will be Yi Yang at NCTU (Department of Electro-physics).

II. Activities The major activities of our group consist of

four major categories:

(1) The regular seminar series at NTU (organized by Hirotaka Irie), a bi-weekly HEP seminar series at NTNU (organized by Shou-Huang Dai), and string seminars at NCTS (organized by Furuuchi Kazuyuki), and joint COSHEP seminar series at NCTU (organized by George Moutsopoulos). We invite many visitors to report on the recent progress of String theory, and learn from each other during discussions. In the year of 2010-2011, we have held more than 70 seminars and invited 16 visitors to our seminar series.

(2) The 4th annual Taiwan String Theory Workshop will be held at NCTU (main organizer: Yi Yang) in December this year. This workshop has become one of our regular events in summarizing the latest development and reviewing our own progress in the past year. In the near future, we also wish to include some of the bas ic s t r ing theory courses for

promoting our field and making educational service to the theoretical physics community, maybe a role model is like summer school on general relativity (held by NCTS, north) in August 2011. Besides, we tried to renew the contact with mathematicians (those who specialized in geometry and analysis). For instance, a leading expert on matrix model, Alexander R. Its, visited us and gave an overview talk about Painlevé transcendents and random matrices.

(3) Special study groups like the minimal string study group in 2008, and the ADS/CMT study group (hosted by both NTU and NTNU) are useful venues for interested participants to gather and form research teams. Many of our recent papers are products of these programs, in addition, these works also involve experts in other fields, e.g., hardon physicist Jiunn-Wei Chen, condensed matter physicist Ying-Jer K a o , a n d p a r t i c l e p h e n o m e n o l o g i s t Debaprasad Marity are both collaborators and frequent seminar attendants of our group.

(4) We support post-docs and students to attend major conferences and/or schools in order to get more solid trainings. For instance, we supported one NTU graduate student (Chi-Hsien Yeh) and NCTS post-doc (Hirotaka Irie) to the Strings 2011 conference, also one master student (Pei-Hua Liu) and one post-doc (Shou Huang Dai) from NTNU will attend the Asian Winter School of Strings, Particles and Cosmology in Japan.

Regard ing to the p romot ion of young researchers in this year: three postdocs, Wu-Yen Chuang (Dept. of Math, NTU) and Wen-Yu Wen (Dept. of Physics, CYCU), Jia-Rui Sun (Shanghai, China), became faculty members. One postdoc, Dr. Tomohisa Takimi moved to India (TIFR). Three Ph.D. students (Chien-Ho Chen, Xue-Yan Lin, Shang-Yu Wu) got their degrees from NTU and Shang-Yu Wu continues his career in physics and became a postdoc in NCTU. Two students (Ying-Ming Huang and Ming-Fan Wu) earned their master degrees from NCU. One research


assistant at NTU, Sheng-Lan Ko, moved to UK (Durham University) for Ph.D program and one NTNU master, Chien-Hsun Wang, entered NTU as a Ph.D student.


Many members in our group have established long-term collaborations with frequent/long-term visitors, e.g., Chiang-Mei Chen + Bin Chen, Pei-Ming Ho, Kazuyuki Furuuchi + Takeo Inami, Pei-Ming Ho + Yutaka Matsuo, Choon-Lin Ho + Ryu Sasaki. These partnerships not only result in many interesting papers, they also help us to connect with the international community. It is an encouraging sign that our research efforts have attained reasonable international visibility.

IV. Highlights of Research Results Here we summarize highlights of research

results made by our members in the period of 2010-2011:

(1) Choon-Lin Ho has joint work with Ryu Sasaki on the discovery of exceptional orthogonal polynomials , which can be real ized as solutions of the exactly solvable quantum mechanical problems.

(2) Jen-Chi Lee, Yi Yang and Yoshihiro Mitzuka have continued the study on the str ing scattering amplitudes (especially in the Regge l imi t and a l so wi th so l i ton ic t a rge t – D-particle). The NCTU team, together with many collaborators, has uncovered many interesting pattern of the string scattering amplitudes in the past few years.

(3) The NTU team, as led by Pei-Ming Ho, with Tomohisa Takimi and students, together with the NCTS scientists Kazuyuki Furuuchi, Dan Tomino, focus on the M-brane dynamics. In particular, their collective efforts (including: Lie three algebra, self-dual gauge theories, generalized non-commutative geometry) have attracted lots of citations in the international community.

(4) The main research focus of NCU team, as led by Chiang-Mei Chen and Jia-Rui Sun, is on the holographic descriptions of various non-supersymmetric black-hole backgrounds. Their

earnest effort has made useful impacts to this vastly developed field.

(5) Feng-Li Lin, Shou-Huang Dai, Shoichi Kawamoto, and Wen-Yu Wen, together with other collaborators, have studied the dynamics of strongly-correlated system (from QCD to superconductors) using the techniques of ADS/CFT correspondence. Hsien-Chung Kao has a joint work with condensed-matter theorists on the connections of chiral anomaly and the transport property of grapheme.

(6) The minimal-string/matrix-model team, consists of Chuan-Tsung Chan, Hirotaka Irie, and Chi-Hsien Yeh (CIY), has suggested to use multi-cut matrix model as a constructive definition of non-critical M theory. Their study on the Stokes phenomena has led to interesting discovery of integrable structures of the non-critical String/M theory.

(7) Wu-yang Chuang and collaborators have a series of work on the study of wall-crossing phenomena and its relation with ADHM theory.

It is worth mentioning that the work of Pei-Ming Ho was recognized by both NSC of Taiwan and OCPA, and he received two grand prizes from these organizations. The work of CIY (as presented by Hirotaka Irie) was selected by the Strings 2011 conference as one of the Gong Show talks.

V. Selected Publications[1] “Massive Superstring Scatterings in the Regge

Regime”, Song He (Beijing, Inst. High Energy Phys.), Jen-Chi Lee (NCTU. & NCTS, Hsinchu), Keijiro Takahashi (NCTU.), Yi Yang (NCTU. & NCTS, Hsinchu). Jan 2010. 35 pp. Published in Phys.Rev. D83 (2011) 066016, e-Print: arXiv: 1001.5392 [hep-th].

[2] “Regge Closed String Scattering and its Implication on Fixed angle Closed String Scattering”, Jen-Chi Lee, Yi Yang (NCTU). Jan 2010. 10 pp. Published in Phys.Lett. B687 (2010) 84-88, e-Print: arXiv: 1001.4843 [hep-th].

[3] “A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions”, Pei-Ming Ho, Kuo-Wei Huang (NTU), Yutaka Matsuo (Tokyo U.).


UT-11-11. Apr. 2011. 23 pp. Published in JHEP 1107 (2011) 021, e-Print: arXiv: 1104.4040 [hep-th].

[4] “D-brane in R-R Field Background”, Pei-Ming Ho, Chi-Hsien Yeh (NTU). Jan 2011. 26 pp. Published in JHEP 1103 (2011) 143, e-Print: arXiv: 1101.4054 [hep-th].

[5] “D1-brane in Constant R-R 3-form Flux and Nambu Dynamics in String Theory”, Chong-Sun Chu (Durham U., Dept. of Math.), Pei-Ming Ho (NTU. & NCTS, Taipei). Nov 2010. 30pp. Published in JHEP 1102 (2011) 020, e-Print: arXiv: 1011.3765 [hep-th].

[6] “More on the Nambu-Poisson M5-brane T h e o r y : S c a l i n g l i m i t , b a c k g r o u n d independence and an all order solution to the Seiberg-Witten map”, Chien-Ho Chen (NTU), Kazuyuki Furuuchi (NCTS, Hsinchu), Pei-Ming Ho, Tomohisa Takimi (NTU). Jun 2010. 39 pp. Published in JHEP 1010 (2010) 100, e-Print: arXiv: 1006.5291 [hep-th].

[7] “Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models”, Chuan-Tsung Chan (Tunghai U.), Hirotaka Irie (NTU. & NCTS, Taipei & NCTS, Hsinchu), Chi-Hsien Yeh (NTU. & NCTS, Taipei). Nov 2010. 80 pp. Published in Nucl.Phys. B854 (2012) 67-132 e-Print: arXiv: 1011.5745 [hep-th].

[8] “D-branes Wrapped on Fuzzy del Pezzo Surfaces”, Kazuyuki Furuuchi (NCTS, Hsinchu), Kazumi Okuyama (Shinshu U.). Aug 2010. 43 pp. Published in JHEP 1101 (2011) 043, e-Print: arXiv: 1008.5012 [hep-th].

[9] “Non-Linearly Extended Self-Dual Relations From The Nambu-Bracket Description Of M 5 - B r a n e I n A C o n s t a n t C - F i e l d Background”, Kazuyuki Furuuchi (NCTS, Hsinchu). Jan 2010. 17 pp. Published in JHEP 1003 (2010) 127, e-Print: arXiv:1001.2300 [hep-th].

[10] “Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra”, Shoichi Kawamoto (NTNU), Tomohisa Takimi (NTU), Dan Tomino (NCTS). Mar 2011. 41 pp. Published in J.Phys.A A44 (2011) 325402, e-Print: arXiv: 1103.1223 [hep-th].

[11] “Unruh effect and Holography”, Takayuki Hirayama (NCTS, Hsinchu & NTNU), Pei-Wen Kao (NTNU& Keio U.) , Shoichi Kawamoto, Feng-Li Lin (NTNU). Jan 2010. 27 pp. Published in Nucl. Phys. B844 (2011) 1-25 e-Print: arXiv: 1001.1289 [hep-th].

[12] “Quantum corrections of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra”, Dan Tomino (NCTS, Hsinchu). Jul 2010. 21 pp. Published in Nucl. Phys. B844 (2011) 164-181, e-Print: arXiv: 1007.3090 [hep-th].

[13] “M. Lewkowicz, Hsien-chung Kao, and B. R o s e n s t e i n , 2 0 11 “ S i g n a t u r e o f t h e Schwinger pair creation rate via radiation generated in graphene by a strong electric current”, Phys. Rev. B 84, 035414.

[14] “Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole”, Bin Chen (Peking U. & Peking U., CHEP), Chiang-Mei Chen (NCU), Bo Ning (Peking U.). Oct 2010. 18 pp. Published in Nucl.Phys. B853 (2011) 196, e-Print: arXiv: 1010.1379 [hep-th].

[15] “Double Field Theory for Double D-branes”, Cecilia Albertsson (Tokyo U.), Shou-Huang Dai (NTNU), Pei-Wen Kao (Keio U.), Feng-Li Lin (NTNU). Jul 2011. 34 pp. Published in JHEP 1109 (2011) 025, e-Print: arXiv: 1107.0876 [hep-th].

[16] “Holographic Multi-Band Superconductor”, Ching-Yu Huang, Feng-Li Lin (NTNU), Debaprasad Maity (NTU& NCTS, Taipei). Feb 2011. 13 pp. Published in Phys. Lett. B 7 0 3 ( 2 0 1 1 ) 6 3 3 - 6 4 0 , e - P r i n t : arXiv:1102.0977 [hep-th].

[17] “Dynamical Instability of Holographic QCD at Finite Density”, Wu-yen Chuang (Rutgers U., Piscataway), Shou-Huang Dai, Shoichi Kawamoto, Feng-Li Lin (NTNU), Chen-Pin Yeh (NTU). RUNHETC-2010-12. Apr 2010. 13 pp. Published in Phys. Rev. D83 (2011) 106003 e-Print: arXiv: 1004.0162 [hep-th].

[18] “String theory of the Omega deformation”, Simeon Hellerman, Domenico Orlando, Susanne Reffert (Tokyo U., IPMU). Jun 2011. 38 pp. e-Print: arXiv: 1106.0279 [hep-th].


Focus Group on Atomic, Molecular and Optical PhysicsCoordinator: Daw-Wei Wang (NCTS/National Tsing Hua University; email: [email protected])

Highlights of ProgramsInterdisciplinary Fields


M O f o c u s g r o u p i s a f o r u m f o r researchers in AMO community in

Taiwan to work and grow together in the frontier research.

Coordinator: Daw-Wei Wang (National Tsing Hua University)

Committee members: Wen-Chin Wu (NTNU), Shih-Chuan Gou (NCUE), Ming-Chiang Chung (NCTS), Jiang-Nan Liu (FCU), Yi-Wei Liu (NTHU), Ying-Cheng Chen (IAMS), Te-Kuei Fang (FCU), Wei-Chi Liu (NTNU), Ray-Kuang Lee (NTHU)

Group size: Active faculty members are about 40, including experimentalists.

Goal: (1) To encourage more cooperation between researchers in this community, especially cooperation between different institutes and between theorists and experimentalists, (2) To attract more researchers and students to join related research and to form a stable research environment, (3) To enhance the research quality by actively cooperating with international frontier researchers.

Research direction: (1) Strongly correlated effects in cold atoms/molecules, (2) Dynamical properties of Weakly interacting Bose gases, (3) Atomic structure theory and spectroscopy. Besides these three major subjects, we also partially support researches in high intensity laser, cold atom experiments, and quantum optics etc.

II. Activities International Workshop: In the May 2011, we held an International Workshop on Ultracold Atoms and Molecules in National Tsing-Hua University, organized by Daw-Wei Wang, Shih-Chuan Guo, and our visitor, Miguel Cazalilla. We invited several world-leading-edge theorists and experimental groups to introduce their work on ultracold atoms and molecules. This includes Leticia Tarruell (T. Esslinger’s group in ETH,), Guido Pupillo (Innsbruck), Anatoli Polkonikov (Boston U.), Cheng-Hsun Wu (M. Zwierlein’s group in MIT), Blair Blakie (U. Otago), and Joachim Brand (Massey U.).

Some of our invited speakers have built close collaboration with researchers in Taiwan. For example, Prof. Blakie and Prof. Brand visited prof. Shih-Chuan Guo’s department a few days before and after the workshop. They wil l exchange student and develop numerical studies on the spinor condensate dynamics at finite temperature. Prof. Guido Pupillo and Prof. Anatoli Polkonikov has had collaboration with Prof. D.-W. Wang before and will continue to work on related subjects.

AMO Summer School: In Aug. 2011, we held the 8th AMO summer school in National Cheng-Kong University, organized by Prof. Chin-Chung Tsai. This year, besides of active researchers in the AMO field, we also invited several international speakers, including Chih-Sung Chuu in Stanford, and new postdoc, Richard Jen, to broaden the knowledge horizon of students. We also continue the student session for Ph.D student to present their research results to junior students so that


they could learn more details about the research work in Taiwan community.


Visitors

(1) Long term visitor

We have two long term visitors in this year. One is Prof. Miguel Cazalilla, to stay in NCTS during Feb. 15 and May 15. His visit brought a great impact to the AMO community in various ways : Fo r example , P ro f . Caza l i l l a ha s collaboration with (i) Prof. D.-W. Wang in NTHU on the analytic renormalization group theory of anisotropic superfluidity at zero and finite temperature, compared to the numerical quantum Monte Carlo results; (ii) with Dr. M.-C. Chung in NTCS on thermalization of an exactly solvable model; (iii) with Prof. C.-H. Chung in NCTU on the interaction effect in topological insulator. Research results either have been submitted or have been in prepared. Furthermore, Prof. Cazalilla acknowledge NCTS’s hospitality for his papers finished during these three months, including an review paper published in Review of Modern Physics [1].

The second long-term visitor is Dr. Bo Xiong from IoP of Chinese Academy of Science. Prof. Xiong has a fruitful experience in the calculation of condensate dynamics as well as the spinor dynsmics. His visit is to collaborate with Prof. Daw-Wei Wang on exotic Rydeberg atom states in fermionic cold atoms. Dr. Bo now becomes a postdoc of Prof. Daw-Wei Wang n related subject.

(2) Short term visitor

(i) Professor Tu-nan Chang (USC) is a regular short term visi tor of our focus group and continually leads the joint experimental and theoretical team (including T. S. Yih, C. C. Chu, and J. I. Lo at the National Central University, H. S. Fung and Y. Y. Lee at the NSRRC, and T. K. Fang and C. H. Chen at Fujen University) on atomic structure study. Recently they have important results on the application to plasma physics (see below). (ii) We also invite Prof. T.-L. Ho (Ohio State U.) to visit NCTS and gave four l ec tu res in a workshop abou t the recen t

development of ultracold atom systems. Finally, (iii) we also have short-term visitors Prof. Cheng Chin (Chicago U.), (iv) Chia-Ming Li (CAS), (v) Ping-Nan Ma (ETH, Zurich), (vi) Guin-Dar Lin (U. of Michigan) to give lectures and to have fruitful discussion with local experimentalists and theorists, (vii) Barbara Capogrosso-Sansone (ITAMP, Harvard) to give lectures and have variable discussion with Prof. P.-C. Chen for numerical s tudy of quantum Monte Carlo application in long-ranged interaction of cold atoms.

International cooperation

( i ) D.-W. Wang (NTHU) recent ly has collaboration with Prof. E. Demler (Harvard, USA) , G. Shyalpnikov (LPTMS, France), Cheng Chin (Chicago U., USA), and Nikolaj Zinner (Aarhus U., Demark). (ii) Prof. R.-K. Lee (NTHU) has collaboration with Prof. Yuri S. Kivshar and Prof. Wieslaw Krolikowski in Australian Nat’l U., Prof. Wen-Xing Yang, (Southeast U. , China) , Prof. Ming Shen, (Shanghai U., China), Prof. Emmanuel Paspalakis (U. Patras, Greece), Prof. Boris A. Malomed, (Tel Aviv University, Israel), Prof. Gaetano Assanto, (U. Studi Roma Tre, Italy), and Prof. Alexander P. Alodjants (Vladimir State U., Russia). (iii) Prof. Chung-Hou Chung (NCTU) has a collaboration with Prof. M. Cazalilla. (iv) Prof. T.-K, Fang (FJU) collaborates with Prof. T.-N. Chang (USC). (v) Prof. Shih-Chuan Gou collaborates with Prof. Makoto Tsubota (Osaka City U., Japan) and Blair Blakie (U. Otago, New Zealand). (vi) Prof. Ming-Chiang Chung collaborates with Prof. Ingo Peschel (Free U. Berlin), Prof. Miguel Cazallila (Centro�de�F´ısica�de�Materiales� (CFM),�Spain)� ,�Prof. Anibal Iucci (U. Nacional de La Plata, Argentina), Prof. Ian McColluch (U. Queenzland, Australia), and Prof. Carlos Trallero-Gino (U. La Habana, Cuba).

IV. Highlights of Research Results Strongly interacting cold atoms and polar molecules: (1) Prof. D.-W. Wang and P.-C. Chen develop worm algorithm QMC, and demonstrate the f i rs t verif icat ion of universal scal ing hypothesis in superfluid to Mott insulator transition [2]. (2) Prof. D.-W. Wang collaborate


with Prof. E. Demler (Harvard) to study the many-body physics of polar molecules in multi-layer and multi-tube systems. Results are published in Phys. Rev. Lett. [3,4]. (3) Prof. D.-W. Wang and his group develop a new method for liquid-to-solid transition in 2D harmonic trap, giving a new mechanism for polarization cooling [5]. (4) Prof. W.-C. Wu (NTNU) develop theory for the center of mass motion of dipolar atoms in bilayer systems [6]. (5) Prof. S.-C. Guo (NCUE) and his group study the non-equilibrium dynamics and the formation of topological defects in a rapid rotating spinor BEC in the limit of fast quench [7]. (6) Prof. P.-C. Chen (NTHU) developed tensor product states method to study the quantum phase transition of two species hard core bosons [8]. The i r work t hus p rov ides gu ides t o t he experimental search of the pair-superfluid phase in lattice boson systems.

Q u a n t u m d y n a m i c s o f B o s e - E i n s t e i n Condensate: (1) W.-C. Wu (NTNU) and his group have recently investigated the dynamics of a gap soliton in 1D optical lattice [9], taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap solitons and nonlinear Bloch waves exists for the whole span of the interaction strength. (2) Prof. W.-C. Wu and Prof. S.-C. Guo (NCUE) consider the system being evaporatively cooled to form condensates and a combined numerical scheme is applied to ensure the binary system being in an authentic equilibrium state [10]. Vortex structures are studied in detail with rotation� frequency�both�above�and�below�Ωc�and�with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts. (3) Prof. Ray-Kuang Lee has several important works on the dynamics and entanglement of soliton and nonlinear optics, but unfortunately he forgot to acknowledge NCTS in his paper.

Slow light in cold atoms: (1) Prof. S.-C. Guo (NCUE) and Prof. Ite Yu (NTHU) We model the effects of the atomic thermal motion on the p r o p a g a t i o n o f a l i g h t p u l s e i n a n electromagnetically induced transparency (EIT) medium by introducing a set of effectively temperature-dependent parameters, including the Rabi� frequency� of� the� coupling� field,� optical�

density and relaxation rate of the ground state coherence, into the governing equations [11]. (2) They also present a numerical scheme to study the dynamics of slow light and light storage in an EIT medium at finite temperatures [12]. Allowing for the motional coupling, they derive a set of coupled Schrödinger�equations�describing�a�boosted�closed�three-level EIT system according to the principle of Galilean relativity. This warrants that the current scheme can be applied to determine the decaying profile of the ground-state coherence as well as the temperature of the EIT medium.

Atomic structure and spectroscopy: (1) Prof. Te-Kuei Fang (FJU), NCTS visitor Prof. Tu-Nan Chang, and collaborators have a joint theoretical and experimental investigation for electric-field effects on the ground-state photoionization of Ca [13]. Using a B-spline-based complex-rotation method with spin-dependent interaction, our theoretically calculated spectrum is found to be in good agreement with the observed spectrum from a cross-beam photoionization experiment for field strengths up to 25 kV/cm. The result of this work was also presented in an invited talk at the OCPA7. (2) They also study the atomic processes under varying plasma environment. Their result was presented at the APS/DAMOP meeting and has been submitted to Phys. Rev. Lett.

V. Selected Publications[1] M. A. Cazalilla, R. Citro, T. Giamarchi, E.

Orignac, and M. Rigol, arXiv:1101.5337 (accepted to be appear in Rev. Mod. Phys.).

[2] Shiang Fang, Chia-Ming Chung, Ping Nang Ma, Pochung Chen, and Daw-Wei Wang, Phys. Rev. A 83, 031605(R) (2011).

[3] Andrew C. Potter, Erez Berg, Daw-Wei Wang, Bertrand I. Halperin, Eugene Demler, Phys. Rev. Lett. 105, 220406 (2010).

[4] B. Wunsch, N. T. Zinner, I. B. Mekhov, S.-J. Huang, D.-W. Wang, and E. Demler, Phys. Rev. Lett. 107, 073201 (2011).

[5] Yi-Ya Tian and Daw-Wei Wang, Europhys. Lett. 91, 66006 (2010).

[6] C.-C. Huang and W. C. Wu, Phys. Rev. A 82, 053612 (2010).


[7] S.-W. Su, C.-H. Hsueh, I.-K. Liu, T.-L. Horng,Y. - C. Tsai, S.-C. Gou, and W. M. Liu, Phys. Rev. A 84, 023601 (2011).

[8] Pochung Chen, and Min-Fong Yang, Phys. Rev. B 82, 180510(R) (2010).

[9] T. F. Xu, X. M. Guo, X. L. Jing, W. C. Wu, and C. S. Liu, G, Phys. Rev. A 83, 043610 (2011).

[10] C.-H. Hsueh, T.-L. Horng, S.-C. Gou, and W. C. Wu, Phys. Rev. A 84, 023610 (2011).

[11] Shih-Wei Su, Yi-Hsin Chen, S.-C. Gou and Ite A Yu, J. Phys. B: At. Mol. Opt. Phys. 44, 165504 (2011).

[12] Shih-Wei Su, Yi-Hsin Chen, Shih-Chuan Gou,Tzyy-Leng Horng, and Ite A. Yu, Phys Rev. A 83, 013827 (2011).

[13] T. K. Fang, J. I. Lo, T. S. Yih, and T. N. Chang, Phys. Rev. A 82, 063402 (2010).


Focus Group on Plasma ScienceCoordinator: Lin-Ni Hau (National Central University; email: [email protected])

Committee members: Tsun-Hsu Chang (National Tsing Hua University), Kuan-Ren Chen (National Cheng Kung University),

Hong-Yu Chu (National Chung Cheng University)


t is widely believed that most of the observable matter in the universe is in the

ionized state, referred to as the fourth state of matter – plasma. In the laboratory plasmas are produced to conduct controlled thermonuclear fus ion research and var ious fundamental laboratory studies such as non-neutral plasma, dusty plasma and laser plasma researches etc. Plasma science also has important applications in the industry such as plasma processing in the fabrication of semiconductors and the growth of new materials etc. The density and temperature of plasmas of interest range over tens of orders of magnitude that one of the challenges in the study of plasma physics is to develop various suitable physical principles for understanding the extremely complex and rich behaviors of plasmas. Plasma physics has been regarded as the frontier field of physics of complex systems and have been continuously evolving and growing for the l a s t f i f t y y e a r s b o t h t h e o r e t i c a l l y a n d experimentally. The members of academic plasma community in Taiwan have diverse expertise in plasma science including space/astrophysical plasma, dusty plasma, laser plasma, fusion plasma, non-neutral plasma etc. but have relatively weak interaction and collaboration on research. In the past few years the NCTS has served to play a role in promoting the interaction and plasma education among the community members and institutions. For example, under the support of NCTS the first national plasma science workshop was held in 2003 organized by Prof. Lin-Ni Hau of NCU (中央) and Prof. K. R. Chen of NCKU. The first international plasma science meeting held in Taiwan and organized by Prof. Lin-Ni Hau in 2004 was also sponsored by NCTS which brought many wor ld-c lass p lasma

physicists to Taiwan interacting with local members. In early 2011 Prof. Lin-Ni Hau was appointed by director Li of NCTS as the primary coordinator of plasma focus group. Considering the geographic distribution of various plasma groups, she has invited Prof. K. R. Chen of NCKU (成大), Prof. Hong Yu Chu of NCCU (中正) and T.-H. Chang of NTHU (清大) to serve as the committee members of NCTS plasma focus group. (Invitation was also sent to the faculty members of NTU though the commitment of serving in the committee is not enforced.) In early July the four committee members had a meeting at NCTS discussing the related issues of running the plasma focus program. The discussion meeting lasted for nearly four hours which has helped bui lding up a good consensus among the commit tee members wi th diverse plasma expertise. It is agreed that each committee member will help organize some activities on plasma research and educat ion in his /her university and institution though no major funding is actually needed from the NCTS. We have also discussed about organizing a short plasma course for students who are interested in plasma research in the coming winter break. More importantly, we will help promote the collaboration among plasma physicists on various topics such as laser plasma, dusty plasma, space and astrophysical plasmas etc. It is also agreed that the committee members will communicate frequently via emails and try to m e e t r e g u l a r l y a t N C T S t o d i s c u s s t h e perspectives of plasma research.

II. Activities A cross-strait meeting on fusion research and

plasma science was held on July 28-31, 2011 with more than forty participants from China, Taiwan and USA. This meeting is organized by Prof. Lin I of NCU and partially sponsored by NCTS – plasma focus program. The format of this


meeting is very different from other meetings, in particular, each speaker is given only for 5-min oral presentation supplemented by the poster presentation. Each talk though short gave very concise and comprehensive introduction and highlight of the studied topic. Between two sessions there is at least 90 min break for the participants to discuss in detail and interact closely with each other in the area of poster papers. This format turns out to be very effective on initiating the close interaction and exchange of ideas among meeting participants. The students of Prof. Lin I are the main body on organizing the meeting and arranging the whole details from which they not only served but also learned. They also presented several poster papers and have benefited from intense discussion with plasma scientists from China and USA. The papers presented at the meeting cover a wide range of topics on plasma research including fusion plasma, laser plasma, dusty plasma, space plasma and low temperature plasma etc. All participants not only have chance presenting their works but also have learned from listening to the interesting works by others. Scientists from China have high regard on the quality of plasma researches (theoretical and experimental) conducted by local scientists. The three-day meeting has also created an opportunity for domestic plasma scientist to gather which has not happened for a long while. The success of this meeting is evaluated highly by all participants. At the meeting it was proposed by local scientists that a workshop may be planned and sponsored by NCTS for graduate students. In the coming months activities in various formats will be planned and initiated to enhance the interaction among local plasma scientists and students. A short course on plasma physics will also be organized during the coming winter break.


Prof. Liu Chen of UC-Irvine with expertise on fusion and space plasma has had a long term association with the plasma scientists of Taiwan. In recent years he has collaborated closely with Prof. S. H. Chen of NCU (who was in charge of plasma focus group – laser plasma project) on

laser plasma interaction and on gyrotron emission. They have coauthored a paper presented at the Cross-Strait Plasma Meeting held in July and partially sponsored by NCTS. Their collaboration will be continued and encouraged as well as supported by the plasma focus program. Under the invitation and recommendation by Prof. Lin-Ni Hau, the world-wide known plasma physicist, Prof. Padma Shukla of Ruhr-University Bochum (RUB) in Germany has agreed to serve as the foreign editor of Chinese Journal of Physics (CJP). Prof. Shukla is well known for his theoretical contribution on dusty plasma physics. Under the invitation of Prof. Lin I he made a visit to NCU in July, 2010 which has lead to a joint paper published in Physics Letters. Prof. Shukla was invited to be the coauthor of a theoretical p a p e r p u b l i s h e d i n C J P, 2 0 1 0 o n t h e h y d r o m a g n e t i c w a v e s p r o p a g a t i n g i n a magnetized dusty plasma. The collaboration between Prof. Shukla and Prof. Hau and/or Prof. I will be continuously encouraged and supported by the plasma focus program. Note that Prof. Shukla’s first visit to Taiwan in 2004 was sponsored by the NCTS while his second visit invited by Prof. Lin I was supported by NSC. In the future we plan to invite several renowned plasma physicists to visit Taiwan and establish collaboration on certain topics.

IV. Highlights of Research Results The plasma focus group was just formed in

early July. Thus there is yet no major research result which is produced under the NCTS funding. Nevertheless the group members have been very active in plasma research and invited to various international meetings to give invited talks. For example, Prof. Lin-Ni Hau was invited to a prestigious workshop entitled “International Astrophysical Forum Alpbach 2011” held in Austria to give an invited talk on “Nonlinear theory of proton firehose instability”.

V. Publication The plasma focus group was just formed in

early July. Thus there is yet no published paper carrying the NCTS as the affiliation.


Focus Group on Quantum Information ScienceCoordinators: Chung-Hsien Chou (National Cheng Kung University; email: [email protected])

His-Sheng Goan (National Taiwan University; email: [email protected])

1. Brief Description

he ma in miss ion o f the Quan tum Information Science (QIS) focus group is

to build a platform of communication and discussion for researchers in this area in Taiwan. In the last few years, we have brought QIS researchers in Taiwan to work and discuss research together and to hold activities, such as scientific seminars, workshops and short-term schools. We have also been seeking to establish l inks and exchanges as well as to init iate collaborations with other QIS researchers worldwide.

Coordinators: Hsi-Sheng Goan (NTU) and Chung-Hsien Chou (NCKU)

Committee members: Yia-Chung Chang (AS), Wei-Min Zhang (NCKU), Chi-Yee Chueng (AS), Zheng-Yao Su (NCHC), Alec Maassen van den Brink (AS), Pochung Chen (NTHU), Yueh-Nan Chen (NCKU), Li-Yi Hsu (CYCU), Shih-Yuin Lin (NCUE)

Focused topics: Quantum Decoherence, Measurement, Entanglement, and Communication.

II. Activities and BeneficiariesActivities

1. Taiwan-France joint school on Quantum I n f o r m a t i o n S c i e n c e & Wo r k s h o p o n Quantum Measurement , May 13~16 (2011).

2. Miniworkshop on Theoretical Developments in Quantum Information and Optomechanics, July 26 (2011).

3. Mini-workshop on Quantum Information Science and Related Topics, Aug 6 (2011).

4. The 6th Winter School on Quantum Information Science to be held in Feb. (2012)

5. QIS seminars at NCKU, NTU, and CYCU.

Beneficiaries

The beneficiaries Taiwan-France joint school on Quantum Information Science & Workshop on Quantum Measurement is three-fold: 1. To continue the success of the schools on 'Quantum Information Science' held annually in Taiwan , supported by NCTS. 2. To promote and enhance the interaction between France and Taiwan sides. 3. To exchange the most recent development in theories and in experimental techniques and observations in the field of quantum information science and quantum measurements in both sides.

Training of young-generation physicists

F i n a n c i a l s u p p o r t s f o r i n t e r n a t i o n a l collaborations: we have supported Dr. Che-Min Li to visit Prof. Nori’s group at RIKEN and initiate new research projects.


Visitors

1. Prof. A. Buchleitner, Universität Freiburg (April 5 ~ 8, 2011)

2. Prof. Julien Laurat, Laboratoire Kastler Brossel, France (May 9 ~ 16, 2011)

3. Prof. Daniel Braun, Universite Paul Sabatier, France (May 12 ~ 19, 2011)

4. Prof. Olivier Buisson, Institut NEEL, France (May 13 ~ 16, 2011)

5. Prof. B. L. Hu, Univ. of Maryland, USA (May 13 ~ 24, June 1 ~ 9, July 25 ~ Aug. 3 2011)

6. Prof. Philippe Grangier, CNRS, France (May 17 ~ 20, 2011)


7. Prof. Yu Yang, The University of Utah, USA (Aug. 6 ~ 8, 2011)

8. Prof. Ting Yu, Stevens Institute of Technology, USA (July 26, Aug. 6 ~ 8, 2011)

9. Prof. Zidan Wang, The University of Hong Kong (Aug. 6 ~ 8, 2011)

10. Prof. Choo Hiap Oh, National University of Singapore, Singapore (Aug. 6 ~ 8, 2011)

11. Prof. Jiangfeng Du, University of Science and Technology of China, China (Aug. 6 ~ 8, 2011)

12. Prof. Jinshuang Jin, Hangzhou Normal University, China (Sept. 6 ~ 19, 2011)

13. Prof. Chang-Pu Sun, Chinese Academy of Sciences, China (Sept. 26 ~ Oct. 15, 2011)


1. QIS member: Prof. W. M. Zhang Collaborators: Prof. H. T. Tan (Huazhong) and Prof. Jin (Hangzhou)

Projects or Activities: Non-Markovian dynamics of open quantum systems, Intrinsic coherence dynamics.

2. QIS members: Dr. G. Y. Chen and Prof. Y. N. ChenCollaborator: Prof. Buchleitner (Freiburg)

Projects or Activities: (1) Research Visit, (2) Joint Proposal for Clusters of excellence in Germany, (3) Project on photosynthesis.

3. QIS members: Dr. C. M. Li, Dr. G. Y. Chen and Prof. Y. N. ChenCollaborator: Prof. Nori (Riken, Japan)

Projects or Activities: (1) Research visiting, (2) Project on Quantum Measurement.

4. QIS members: Dr. C. M. Li and Prof. Y. N. Chen

Collaborator: Prof. J. W. Pan

Projects or Activities: (1) Research visiting of Dr. C. M. Li, (2) Project on Quantum Entanglement.

5. QIS member: Prof. H.-S. Goan Collaborators: Prof. Todd. A Brun (USC) and Prof. X.Z. Yuan (Shanghai Jiao Tong U.)

Projects or Activities: Single spin measurement using magnetic resonance force microscopy (MRFM), Spin qubit coupled to antiferomagnetic environment.

6. QIS members: Prof. C. H. Chou and Prof. S. Y. Lin Collaborator: Prof. B. L. Hu (U. Maryland, USA)

Projects or Activities: Project on relativistic entanglement dynamics.

IV. Highlights of Research ResultsResearch results

A. Decoherence

1. Intrinsic coherence dynamics and phase localization in nanoscale Aharonov-Bohm interferometers

The nonequilibrium real-time dynamics of electron decoherence is explored in the quantum transport through the nanoscale double-dot Aharonov-Bohm interferometers [1]. We solve the exact master equation to find the exact quantum state of the device, from which the changes of the electron coherence through the magnetic flux in the nonequilibrium transport processes is obtained explicitly.

2. Dynamics of a driven spin coupled to an antiferromagnetic spin bathWe study the behavior of the Rabi oscillations

of a driven central spin (qubit) coupled to an antiferromagnetic spin bath (environment) [2]. It is found that the decoherence behavior of the central spin depends on the detuning, driving strength, qubit–bath coupling and an important factor�Ω,� associated�with� the�number�of� coupled�atoms, the detailed lattice structure and the temperature of the environment. If detuning exists, Rabi oscillations may show the behavior of collapses and revivals; however, if detuning is absent, such a behavior will not appear. We investigate the weighted frequency distribution of the time evolution of the central spin inversion and find that the eigenstates of the qubit self-Hamiltonian emerge as pointer states in the weak system–environment coupling limit.


B. Quantum entanglement and measurement

1. Entangling two distant nanocavities via a waveguide

We p r e s e n t a s c h e m e f o r g e n e r a t i n g continuous-variable entanglement between two spatially separated nanocavities in photonic crystals, which are mediated by a coupled-r e s o n a t o r o p t i c a l w a v e g u i d e [ 3 ] . T h e entanglement degree and purity of the generated states are investigated. It is shown that a steady and pure entanglement between separated nanocavities can be generated only with a weak cavity-waveguide coupling when the cavities are resonant with the band center of the waveguide.

2. Surface plasmons in a metal nanowire c o u p l e d t o c o l l o i d a l q u a n t u m d o t s : S c a t t e r i n g p ro p e r t i e s a n d q u a n t u m entanglementWe investigate coherent single surface-

plasmon transport in a metal nanowire strongly coupled to two colloidal quantum dots [4]. Remote entanglement of the wave functions of the two quantum dots can be created if the interdot distance is equal to a multiple half-wavelength of the surface plasmon. Furthermore, by applying classical laser pulses to the quantum dots, the entangled states can be stored in metastable states that are decoupled from the surface plasmons.

3. Retardation effects in quantum dot systems coupled via one-dimensional waveguidesWe investigate the retardation effect on the

radiative decay and entanglement of two quantum dots [5]. The retardation effect is found to be very weak if the dots are coupled to free-space vacuum reservoir. To enhance the effect, we propose to embed the dots inside a one-dimensional waveguide. It is found that populations and entanglement can saturate to non-vanishing values with appropriate conditions. Furthermore, entanglement sudden-rise and sudden-fall are also observed due to this non-Markovian retardation.

4. Instantaneous projective measurement in a relativistic quantum field

As a foundation of the study on quantum teleportation in relativistic systems, I showed the consistency of the quantum state of the Unruh-DeWitt detectors moving in a relativistic quantum field with the projective measurements on the

detectors, which are local in space [6].

C. Non-Markovian dynamics

1. Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations

The exact non-Markovian dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir [7] . The exact t ime-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics of the cavity but they are washed out in the steady-state limit in the Markovian regime.

2. Non-Markovian finite-temperature two-time correlation functions of system operators An extremely useful evolution equation that

allows systematically calculating the two-time correlation functions (CF's) of system operators for non-Markovian open (dissipative) quantum systems is derived [8]. Non-Markovian open quantum system models that are not exactly solvable can use our derived evolution equation to easily obtain their two-time CF's of system operators, valid to second order in the system–environment interaction. Our evolution equation is app l icab le fo r bosonic and /or fe rmionic environments and can be applied to a wide range of sys tem–environment models wi th any factorized (separable) system–environment initial states (pure or mixed).

Invited presentations

1. Profs. Wei-Min Zhang and Hsi-Sheng Goan, Invited Speakers, the 5th Asia-Pacific Workshop on Quantum Information Science, Singapore, Singapore, May 2011.

2. Profs. Wei-Min Zhang and Hsi-Sheng Goan, Invited Speakers, the 4th International Workshop on Solid-State Quantum Computing, Shanghai, China, Dec. 2010.

3. Prof. Hsi-Sheng Goan, Invited Speaker, the 6th Cross-Strait and International Conference on Quantum Manipulation, Beijing, China, Dec. 2010.


Cooperation with experimental group

Dr. Che-Ming Li is collaborating with Prof. J. W. Pan’s group at Heidelberg. Their work, “Verifying genuine high-order entanglement”, was recently published in high-impact journal [13].

V. Publications[1] M. W. Y. Tu, W. M. Zhang and J. S. Jin, Phys.

Rev. B 83, 115318 (2011).

[2] X. Z. Yuan, H.-S. Goan and K. D. Zhu, New J. of Phys. 13, 023018 (2011).

[3] H. T. Tan, W. M. Zhang and G. X. Li, Phys. Rev. A 83, 062310 (2011).

[4] G. Y. Chen, N. Lambert, C. H. Chou, Y. N. Chen and F. Nori, Phys. Rev. B 84, 045310 (2011).

[5] H. B. Chen, G. Y. Chen and Y. N. Chen, Opt. Commun. 284, 4529 (2011).

[6] S.-Y. Lin, arXiv:1104.0772 (Submitted to PRD).

[7] H. T. Tan and W. M. Zhang, Phys. Rev. A 83, 032102 (2011).

[8] H.-S. Goan, P. W. Chen and C. C. Jian, J. Chem. Phys. 134, 124112 (2011).

[9] P. W. Chen and C. C. Jian19nd H.-S. Goan, Phys. Rev. B 83, 115439 (2011).

[10] J. Y. Lien, Y. N. Chen, and C. H. Chou, New J. Phys. 13, 083036 (2011).

[11] C. H. Chou, B. L. Hu and Y. Subasi, J. Phys.: Conf. Ser. 306, 012002 (2011).

[12] S.-Y. Lin, J. Phys.: Conf. Ser. 306, 012060 (2011).

[13] C. M. Li, K. Chen, A. Reingruber, Y. N. Chen and J. W. Pan, Phys. Rev. Lett. 105, 210504 (2010).

[14] P. C. Chen, C. Y. Lai and M. F. Yang, Phys. Rev. B 81, 020409 (2010).

[15] C. H. Chou and H. L. Yu, Phys. Lett. A 18, 1483 (2010).

[16] S. Raghunathan, T. A. Brun and H. S. Goan, Phys. Rev. A 82, 052319 (2010).

[17] L. Y. Hsu and K. S. Wu, Phys. Rev. A 82, 052102 (2010).

[18] P. C. Chen and M. F. Yang, Phys. Rev. B 82, 180510 (2010).

[19] N. Lambert, Y. N. Chen, and F. Nori, Phys. Rev. A 82, 063840 (2010).

[20] W. Chen, G. Y. Chen, and Y. N. Chen, Opt. Lett. 36, 3602 (2011).



oal: The aim of this “TH-LHC Initiative” is to bring in strong theory support for

enhanced mutual contact with cutting-edge experiment. It complements the theory part of the 5-year (2011-2016) NTU 拔尖計畫 “Scaling the Particle Frontier”, and the 5-year (2010-2015) NSC 攻頂計畫 “Beyond Kobayashi-Maskawa — Search for 4th generation quarks”, targeting physics at the LHC. The Coordinator is the CI/PI of both projects, hence providing synergy and confluence of resources, with this Initiative playing crucial “extra piece of coal” role, to kindle the flame into a stronger fire — the goal.

Coordinator: George W.S. Hou

Key Members:

Xiao-Gang He, Yukihiro Mimura (NTU 拔尖), Hiroshi Yokoya (TH-LHC Initiative), David C.J.Lin (NCTU); Kai-Feng Chen, Paoti Chang, Minzu Wang, Bob Hsiung (NTUHEP), Rong-Shyang Lu, Yuan Chao (both NSC 助研究學者), Paolo Bartalini (NTU 拔尖), Yuan-Hann Chang, Shin-Shan Yu, Chia-Ming Kuo (NCUHEP), Cheng-Wei Chiang (NCU), and Song-Ming Wang (ASHEP/ATLAS) [underlined are the “EC” members; experimentalists are viewed as members].

Group Size:

above, plus postdocs (T. Enkhbat, K. Tsumura,

S. Majee, M. Kohda, F. Xu; H. Kohyama; and B. Smigielski and K. Ogawa from lattice), students and visitors, altogether well over a dozen theorists.

Research Focus (from Phase-III 6-year proposal of NCTS filed in Fall 2008):

Before 2012 Help find t' and b' quarks at LHC, and elucidate associated Flavor and CP Violation physics (other topics of course pursued)

Before 2015 Help elucidate the impact on CPV for BAU, EWSB and New Resonances, and prepare for Super B factory and ILC

II. Activities A forum established in the past is the “Particle

Physics Journal Club” (PP-JC, or just JC) held each Monday lunchtime at NTU, and sponsored by LHC FG. This JC is unusual in Taiwan, as both theorists and experimentalists are present in good numbers, ranging from mature researchers to beginning students. It is a legacy of the Belle era, exempla ry fo r t he good TH-EXP c ros s -fertilization. In anticipation of the LHC era, the JC was broadened to Particle Physics a few years ago. The NTUHEP group is well funded by NSC and NTU, and has significant manpower base. The purpose of this TH-LHC Initiative is to try to replicate the success of the Belle era, catalyzing passage into the LHC era, to put Taiwan on the map of LHC physics.

Initiative (sub-project I): Build-up of Theory Support for LHC PhysicsCoordinator: Wei-Shu Hou (National Taiwan University; email: [email protected])

Highlights of Programs

Highlights of Focus Group -›› III-54

The newly organized “LHC Journal Club” (LHC-JC) since 9/2010 held biweekly on Friday’s, focuses on theoretical and experimental paper reading (the original meaning of JC), starting with aspects of fourth generation studies, and went on to become a forum to discuss latest results from Fermilab, and now the LHC itself. This group-building effort brings the many new members up to date with theoretical and experimental developments. With rapid data accumulation at the LHC, this “continuous workshop” has forged many new collaborative efforts.

A very successful LHC Symposium was held in January 2011 at NTNU, as a special Symposium within the PSROC 2011 Annual Meeting. The Coordinator was invited by PSROC to organize this Symposium, as one of the three highlight Symposia within the 2011 Annual Meeting. We invited one Deputy Spokesperson each from ATLAS and CMS (D. Charlton and A. De Roeck), as well as the former Spokesperson of LHCb (T. Nakada, also the current ECFA Chair). On theory s i d e , w e i n v i t e d r e n o w n e d c o l l i d e r phenomenologist, Tao Han of Wisconsin, as well as MadGraph5 author, Johan Alwall (previous LHC Initiative Assistant Fellow) of Fermilab. Thus, we brought forefront knowledge of the LHC Era to the Taiwan community. First results from experiment were presented, including the b' search with 2010 CMS data by NTUCMS group.

Indeed, through such interplay with theory, by summer 2011 NTUCMS delivered the world best limits on mb' > 495 GeV, while mt' > 450 GeV. These numbers are approaching the Unitarity Bound of 500-550 GeV. NTUCMS has also pursued vector like quarks, in the signature of T → tZ (noted by M. Peskin in LP2011 Summary talk), where theory support came from the LHC-JC miniworkshops under this Initiative. This biweekly continuous Workshop functioned as very important meeting ground of theorists and experimentalists, and was linked to CERN.

On collider phenomenology, we have the experienced LHC Initiative Assistant Fellow H. Yokoya and NTU 拔尖計畫 Associate Fellow Y. Mimura to interface and collaborate with NTU and NCTS members , a s we l l a s conduc t independent research. Further, as a response to the forced reduction of LHC-Initiative 2010 funding

by NSC, the Coordinator worked closely with Prof. Xiao-Gang He during 2010 for recruiting theory manpower, utilizing the resources with regular NSC funding (including NTUHEP) and NTU funding (拔尖計畫). A total of 8 theorists (not counting the Coordinator and Prof. He) were gathered, plus two more along the “Higgs-Yukawa on Lattice” line, as listed in I. The approval of the competitively reviewed 攻頂計畫 “Beyond Kobayashi-Maskawa — Search for 4th Generation Quarks” in 2010, one of the only two such projects in Physics so far, endorses our Academic goal strongly, and the Project synergizes well with this Initiative.

With this added manpower (not all publications acknowledge NCTS), on flavor/CPV studies, we continued elucidating the situation for heavier t’ and b’, studying issues like current LHCb/CMS measurements on CPV and rare decays, nEDM, as well as explored strong Yukawa-bound heavy QQ(bar) mesons. Another new development is the formation of the “Higgs-Yukawa on Lattice” study program, where a talk was delivered by D.C-J. Lin at Lattice 2011 of progress made. A broad spectrum of phenomenology studies continue to be spearheaded by Prof. Xiao-Gang He, from collider physics, to Dark Matter, to neutrinos.

In good part through our efforts, there is a visible worldwide interest in the 4th generation, with people such as Soni, Buras, Chanowitz, Langacker, Dawson and Wise publishing papers, with many small workshops organized around the world (e.g. one in Germany and one in UK in 9/2011 alone, and one coming up in 10/2011 at Istanbul, where the Coordinator is a major Scientific Organizer), or special talks on the 4th generation within traditional meetings. The Coordinator himself was invited to give plenary talks on 4G at both the Cross Straits meeting at NCTS in 4/2011, and PPP9 at NCU in 6/2011, as well as serving as Chairs for both occasions. He was invited by the University of Paris for a talk in 10/2010 last year (after 9/2010 report).

Although the summer 2011 progress on nonobservation of 4th generation quarks, and in particular the LHC statement (shared by CMS and ATLAS) that “Higgs boson in SM with 4 th generations is ruled out in the mass range of 120 to 600 GeV”, has made most people view the 4th

III-55 ‹‹- Highlights of Focus Group

generation once again disfavorably, the game is far from over: the SM Higgs itself may be ruled out in similar range by end of 2011! We are quite on track towards the case of 4th generation and the Higgs boson both being heavy, hence more relevant to the set dual goals of BAU and EWSB. We are well recognized as a world leader on this pursuit.

As for conferences and schools, we are in contact with SI2011 (with SI2012 to be held in Taiwan), and have sent postdocs to EPSHEP2011 and LP2011. We also partially sponsored the NumS-HEP 2011, a simulation school held just before Annual Meeting and organize by C.L. Shan under sponsorship of LHC FG. Lattice postdocs have visited DESY Zeuthen for collaborative work.


Since 9/2010 up till 3/2011 (and within 2010 budget ) , we had the v i s i to rs Chung Kao (Oklahoma), Philip Gerhold, Karl Jansen (DESY Zeuthen), Tao Han (Wisconsin), Johan Alwall (Fermilab), Yukinari Sumino (Tohoku). The visits of Tao Han and Johan Alwall were for the LHC Symposium, but they gave additional talks or lectures.

For 2011, we supported the month-long visit of C.-P. Yuan of Michigan State, which overlapped with the OCPA7 held at NSYSU in 8/2011, where he was Chair. He gave good advice for LHC phenomenology work, and promised to come on short notice during his sabbatical at Peking University. In 12/2011, we will support the visit by H.C. Cheng of UC Davis, for a focused workshop on broadening NTUCMS scope for new heavy quark search; a second workshop on the same line would be held in January 2012, and would involve C.-P. Yuan and K. Hagiwara, plus other theorists.

A new 3-year international Exchange project was filed by the Coordinator to NSC, and Karl Jansen to DAAD, to facilitate young researcher exchange for Lattice work.

IV. Highlights of Research Results Paper [1] and [2] reflect two complementary

strategies to measure CKM elements involving the 4th generation, for small or large mixing, with the latter more interesting; Paper [2] is being revised since LHCb (and CMS) has made major progress on BS → J/ΨΦ and μμ. Paper [3] investigates hadronic� contributions� to� ΔΓS and found no indication of OPE breakdown, hence if the D0 “ASL anomaly” persists with LHCb, then the New Physics�would�have� to� contribute� to�ΔΓS, and would be rather exotic.

Paper [4] ventures into considering strong, relativistic Yukawa bound states of Q and , and is a pioneering work towards 2012 (and future) LHC running. The leading effect would be the production and decay of a color octet, isosinglet (near degenerate t', b') vector meson “ω8”, produced via q annihilation; a corollary is that the gg fusion channel is not quite affected, and search program for the bulk of 4G quark p r o d u c t i o n c o u l d c o n t i n u e . T h i s phenomenological approach complements the Lattice Higgs-Yukawa study that is ongoing (and described in II), and is according to the outline of 攻頂計畫 for the support of direct 4G search. For this purpose, papers [5] and [7] are useful precursor studies for in case new heavy quarks are found.

Paper [6] illustrates the prowess of Prof. Xiao-Gang He in face of anomalies appearing at the collider frontier, and arose from the LHC-JC miniworkshop discussions on Fermilab Wjj anomaly. We have not listed many papers from Prof. He, only because he is also associated with LHC-FG. Note also that many papers from Theory group at NTU did not acknowledge NCTS, hence not discussed here.

V. Publications[1] “Threshold Effects in the Decay of Heavy b'

and t' Quarks”, Y. Chao, K.-F. Chen, S.-K. Chen, W.-S. Hou, B.-Y. Huang, Y.-J. Lei, Phys.Rev.D84:014029,2011.

[2] “ Measuring the Fourth Generation b --> s Quadrangle at the LHC”, W.-S. Hou, M. Kohda, F. Xu, arXiv:1107.2343 [hep-ph].


[3]��“Long-Distance�Contribution� to�ΔΓS of the Bs- s (bar) System”, C.-K. Chua, W.-S. Hou, C.-H. Shen, arXiv:1107.4325 [hep-ph], to appear in PRD.

[4] “Early LHC Phenomenology of Yukawa-bound Heavy Q Mesons”, T. Enkhbat, W.-S. Hou, H. Yokoya, arXiv:1109.3382 [hep-ph].

[5] “Measuring the top Yukawa coupling at the ILC at sqrt(s) = 500 GeV”, R. Yonamine , K. Ikematsu, T. Tanabe, K. Fujii, Y. Kiyo, Y. S u m i n o , H . Y o k o y a , P h y s . R e v .D84:014033,2011.

[6] “Colored Scalars and The CDF W+dijet Excess”, T. Enkhbat, X.-G. He, Y. Mimura, H. Yokoya, arXiv:1105.2699 [hep-ph].

[7] “Boost-invariant Leptonic Observables and Reconstruction of Parent Particle Mass”, S. Kawabata, Y. Shimizu, Y. Sumino, H. Yokoya, arXiv:1107.4460 [hep-ph].


Initiative (sub-project I): Theory and Simulation of Plasmonic MetamaterialsCoordinator: Guang-Yu Guo (National Taiwan University/ National Chengchi University, email: [email protected])

Committee members: Ming-Wen Chu and Michitoshi Hayashi (National Taiwan University),

Wei-Chih Liu (National Taiwan Normal University)


urface plasmon polaritons (SPPs) are electromagnetic waves confined to a

metal-dielectric interface and coupled to the quantized collective oscillation of free charge carriers. The low-dimension nature of SPPs and the strong electromagnetic field at the interface are responsible for a number of fascinating phenomena in fundamental science and exciting opportunities for technological applications such as enhancing Raman scattering by astronomical orders, enabling extraordinary transmission of light through nanoholes, guiding electromagnetic waves with SPPs beyond the diffraction limit. Therefore, plasmonic nanostructures have been attracting an enormous amount of experimental and theoretical interest worldwide in recent years. Indeed, a large number of experimental groups in Taiwan, in particular, the prominent groups of Ding-Ping Tsai and Yang-Fang Chen (NTU-Physics), Cheng-Hsuan Chen, Ming-Wen Chu, Chih-Wei Chang (NTU-CCMS), Ta-Jen Yen (NTHU-Materials) and Shangjr Gwo (NTHU-Phys), have already begun to conduct research in p l a s m o n i c s - r e l a t e d n a n o - s c i e n c e s a n d nanotechnologies in recent years. For example, Din-Ping Tsai’s group recently reported that the classical phenomenon of optical activity, which is traditionally associated with chirality of organic molecules, proteins, and inorganic structures, can be observed in artificial planar media which exhibit neither 3D nor 2D chirality. They observed the effect in the microwave and optical parts of the spectrum at oblique incidence to regular arrays of nonchiral subwavelength metamolecules in the f o r m o f s t r o n g c i r c u l a r d i c h r o i s m a n d birefringence indistinguishable from those of

chiral three-dimensional media [PRL 102 (2009) 113902]. The group of Cheng-Hsuan Chen and Ming-Wen Chu has established the combined technique of scanning transmission electron microscopy (STEM) in conjunction with electron energy-loss spectroscopy (EELS) and i ts applications for mapping and probing plasmonics modes in individual Ag and Au nanoparticles (NPs). The plasmonics critically relies on the detailed knowledge of electric near fields associated with various surface-plasmon (SP) modes on metall ic NPs. The STEM-EELS rout inely provides the nanometer spat ia l resolution by focusing a subnanometer electron beam (~2 Å) on NPs and analyzing the energy losses of the electrons to the NPs.

While experiments plunge ahead, they need strong theory support. Having identified this direction as promising, and with Taipei taking the lead, we wish to enhance Theory Support, to hopefully make a difference over next years.

II. ActivitiesTo provide a platform for local professors,

postdocs and students to have discussions, to exchange ideas and to learn related theoretical methods and experimental techniques, we have organized about 10 monthly meetings (see http://phys.cts.ntu.edu.tw/listworkshop.aspx for details). In each meeting, two people who can be faculty members, postdocs or graduate students, are invited to give one talk each, and the number of participants varies from ~20 to ~60. The content of the meetings include sharing the latest research results and news from attending international conferences, introducing computation and simulation methods as well as new experimental techniques. For example, in the March meeting,


Prof. Jer-Shing Huang (NTHU-Chem) gave a talk o n “ O p t i c a l n a n o a n t e n a a n d p l a s m o n i c nanocircuitry” and Dr. Ming-Yaw Ng (Academia Sinica-RCAS) gave a talk on “Laser-induced breathing modes in metallic nanospheres”. In the May meeting, Prof. Chia-Chien Huang (NCHU-Phys) gave a talk on “Numerical calculation of mode characteristics for plasmonic waveguides using an efficient pseudospectral frequency domain scheme” and Prof. Wei-Chih Liu (NTNU-Phys) gave a talk on “Observations from the 5th International conference on surface Plasmon photonics”. In the June meeting, the postdoc of NCTSn, Dr. Shulin Sun gave a talk on “Probing optical resonances modes in microcavity based on FDTD and FEM simulation”and Mr. Jason Wu (a master student of NTU-CCMS) presented his thesis work on “Beyond standing wave model: A novel metamaterial with unusual torerance on geometry”.

One of highlights of the Initiative’s activities this year is the “Tutorials of Computational Plasmonics and Metamaterials” held last Summer (2011) in NTU-Physics (see http://phys.cts.ntu.edu.tw/workshop/2011/1000817/PM.aspx for details). The tutorials attracted 99 participants from both theoretical and experimental groups in the field all over Taiwan. Most of them are young researchers including graduate students and postdocs as well as young faculty members. The carefully designed program includes (1) three lectures on the history and physics of plasmonics and metamaterials given by Wei-Chih Liu (NTNU-Physics), Pi-Gang Luan (NCU-Electro-optics), and Chih-Wei Chang (NTU-CCMS), (2) two hand-on sessions on electromagnetic simulations using the FDTD method by Yung Chiang Lan and Shih-Hui Chang (NCKU-Electro-optics), (3) two lectures plus demos on Mie s c a t t e r i n g t h e o r y a n d d i s c r e t e d i p o l e approximation (DDA) method by Ruey-Lin Chern (NTU-Applied Mechanics) and Guang-Yu Guo (NCCU-GIAP/NTU-Physics), respectively, and (4) two lectures on applications of electromagnetic simulations to plasmonic metamaterials by Chia-Chien Huang (NCHU-Physics) and Shulin Sun (NCTS-North), respectively. This tutorials is the first of this kind in Taiwan, and in the last feedback session, many young participants expressed their gratitude and requested that the

tutorials of this kind should be organized annually.

Like past years, we have been actively trained our young researchers wi th wide ly used theoretical methods and also ourselves with new theoretical techniques. In this context, Shulin Sun (the postdoc of the NCTS-North) has played an important role. Dr. Sun has been brought with him the expertise of two major electromagnetic simulation methods, namely, the FDTD and FEM methods, and thus he taught six master students how to use the FDTD and FEM methods in plasmonic metamaterials. Indeed, three of these graduate students just graduated last summer (2011). In addition, Michitoshi Hayashi has been teaching one research assistant how to perform e x c i t e d s t a t e c a l c u l a t i o n s f o r m e t a l l i c nanoparticle-molecular systems in order to reveal the microscopic mechanism of SERS. Guang-Yu Guo has been teaching two students how to use the DDA and KKR methods to ca lcu la te electromagnetic responses of metallic nanoparticle clusters. Ding-Ping Tsai also has one postdoc and one PhD student learning how to simulate nanoplasmonics using the FDTD method. Encouragingly, our team members have mastered several complementary basic theories and computational methods, and are working with our e x p e r i m e n t a l c o l l e a g u e s a s w e l l a s o u r distinguished foreign visitors to tackle some fascinating issues in the field of plasmonics and metamaterials, as indicated by our publication list below.

Therefore, the main purpose this year is to build up internationally competative Theory Support for Plasmonic Metamaterials. To this end, we have proceeded in three directions: (1) to build up domestic expertise of theory and simulations of plasmonic metamaterials, and (2) to provide a platform where local experimentalists and theoreticians can get together to interact and collaborate, (3) to invite prominent overseas scientists to visit the NCTSn as either long term or short term visiting scientists.


We have been extremely lucky that upon Din-Ping Tsai’s invitation, Profs. Peter Nordlander (a


world renowned scientist in theoretical and computational modeling of plasmonics and photonics) and Naomi Halas of Rice Univ. visited Ta iwan f rom Feb . 20 to 27 , 2011 . The i r c o l l o q u i u m l e c t u r e s t i t l e d “ P l a s m o n i c nanostructures: Artif icial Molecules” and “Plasmonics: nanoscale manipulation of light” in NTU attracted a huge audience of several hundred people, and the International Conference Hall of NTU-Physics was packed with attendees. During their short stay in Taipei, they had extensive interactions with local scientists. The couple also visited several other universities including NTHU, NTOU, NTNU etc. Their visit has been extremely useful to graduate students, postdocs as well as faculty members in the field.

We have been able to invite the prominent scientist Prof. Pui-Tak Leung (D. of Physics, Portland State U.) (July 18 – Aug. 15, 2011). Prof. Leung gave a lecture titled “Optical properties of inhomogeneous metallic particles on Aug. 12. Prof. Leung has been in fruitful collaboration with several groups in Taiwan including Din-Ping Tsai, Hai-Pang Chiang and Guang-Yu Guo, and hence he visited Taiwan almost every summer. He also helped supervising quite a few PhD and master graduate students. Indeed, he has many joint publications with the groups mentioned above. His visit this year again has been profitable to both the host and himself in terms of sharing research exper ience as wel l as in fu ture collaborations in this exciting emerging area in nanotechnology.

IV. Highlights of Research Results 1. Op t i c a l m a g n e t i c re s p o n s e i n t h re e -

d imens iona l metamater i a l o f upr ight plasmonic meta-molecules [Opt. Exp. 19 (2011) 12837]

Th i s i s a succes s fu l s t o ry on f ru i t f u l collaborations between experimentalists and theoreticians fostered by the academic activities of our Initiative. Metamaterials composited with sub-wavelength split ring resonators (SRRs) have attracted a wide attention because of a number of extraordinary properties, such as artificial magnetism, optical chirality, negative refraction index and optical spectrum manipulation.

Electromagnetic (EM) properties of SRR were first studied in microwave region in 2000. Since 2004, interest in the EM properties of SRRs expanded to the optical frequency region. In particular, U-shape SRRs were shown to exhibit a series of resonant modes as predicted by the LC circuit model, in which the capacitance was contributed by the charges accumulating near the ends while the inductance was contributed by the current flowing inside the U-shape SRR which can be viewed as a magnetic coil. U-shape SRRs can be excited by an incident light with electric field perpendicular to two prongs of U-shape SRR, or an incident light with magnetic field oscillating through the gap of U-shape SRR. By increasing the dimension of the U-shape SRR, higher order resonance modes can also be excited. However, due to the challenges in fabrications, so far most U-shape SRRs were fabricated as planar or multi-layered structures, some of those are three dimensional structures but in micrometer scale. To excite the magnetic resonances of such planar SRRs, one must apply an off-normal incident light which possesses the required H field component. Such a restriction significantly lowers the coupling efficiency between the magnetic field of incident light and the resonant SRR. We recently fabricated photonic metamaterial, an array of vertical (off-plane) U-shape SRRs in nanometer scale, and studied their optical properties by both experiments and numerical simulations. A unique characteristic of our structure is that its magnetic resonance can be excited by normally incident light, overcoming the above-mentioned coupling issues faced by planar SRRs. We found such erected SRRs to exhibit rich plasmonic resonances, showing unique magnetism responses related to the magnetic field of incident light.

2. Plasmonic Bloch oscillations in cylindrical metal-dielectric waveguide arrays

Optical Bloch oscillations (OBOs), an analog of electron Bloch oscillations in crystal, are periodic oscillations of optical beams that propagate in dielectric waveguide arrays, caused by the alternating total internal reflection and Bragg reflection between the two boundaries of the waveguide arrays. Recently, plasmonic Bloch oscillations (PBOs) have also been observed in chirped metal–dielectric waveguide arrays


(MDWAs) and in uniform MDWAs with a linearly increasing dielectric constant. OBOs are also found in an array of curved dielectric waveguides, in which the curvature of the arrays effectively results in both a chirped structure and a gradient in the refraction index. Cylindrical MDWAs have been proposed for use as cloaking devices and hyperlenses. However, the possibility of PBOs existing in cylindrical MDWAs has never been discussed. Therefore, the group of Yung-Chiang Lan of Institute of Electro-optical Sci. and Eng., NCKU (an active member of our Initiative) recently explored PBOs in cylindrical MDWAs by performing numerical FDTD simulations and theoretical analyses [Optics Letters 35, 4012-4014]. Optical conformal mapping is used to transform cylindrical MDWAs into equivalent ch i rped s t ruc tures wi th permi t t iv i ty and permeability gradients across the waveguide arrays, which is caused by the curvature of the cylindrical waveguide. The PBOs are attributed to the transformed structure. The ray trajectories predicted using the Hamiltonian optics formalism correlate well with the simulation results. This study implies that, when a spatial Gaussian wave is excited in the equally spaced cylindrical MDWAs, it is very likely that the PBO is an inevitable result of surface plasmon propagation in the MDWAs.

3. Toroidal dipolar response in a metamaterial

The toroidal dipole, an elusive counterpart of the charge and magnetic dipoles, is produced by currents flowing on the surface of a torus along its meridians. Toroidal multipoles are fundamental electromagnetic excitations different from those associated with the familiar charge and magnetic multipoles. They have been held responsible for parity violation in nuclear and particle physics. First-principles calculations have revealed the existence of toroidal dipoles for certain molecular structures and ferroelectric systems, but direct ev idence o f t he i r ex i s t ence in c l a s s i ca l electrodynamics has remained elusive.

Din-Ping Tsai (a key member of our Initiative) and his UK collaborators recently demonstrated a classical system in which the electromagnetic response is directly related to the resonant excitation of the toroidal dipole [Science 330 (2010) 1510]. The resonant toroidal response has

been observed in a “metamaterial slab,” a two-dimensional array of artificially engineered electromagnetic scatterers of toroidal symmetry. Metamaterials enable us to access novel and exotic electromagnetic phenomena not found in nature (such as negative refraction and cloaking) by controlling the symmetry and character of the response through artificial structuring on a subwavelength scale. To emphasize the toroidal d i p o l a r r e s p o n s e , w e h a v e d e s i g n e d a metamolecule, the elementary building block of our metamaterial, where both the electric and magnetic dipole moments induced by an incident e lec t romagnet ic wave (as wel l as h igher multipoles) are substantially suppressed while the toroidal response is spectrally isolated and resonantly enhanced to a detectable level. The qualitative arguments produced above are fully supported by our calculations performed using a full three-dimensional Maxwell equations solver based on the finite element method. We modeled the interaction of the metamaterial array with a linearly polarized wave in the spectral range from 14.5 to 17.0 GHz. Calculated densities of the induced electrical currents were used to compute scattered powers of the resulting conventional magnetic and charge multipoles, as well as the toroidal dipole of the metamolecule.

V. Publications[1] K.-Y. Yang, Y.-F. Chau, Y.-W. Huang, H.-Y.

Yeh, and D. P. Tsa i , “Des ign of h igh birefringence and low confinement loss photonic crystal f ibers with five rings hexagonal and octagonal symmetry air-holes in fiber cladding”, J. Appl. Phys. 109, 093103 (2011).

[2] T. Yasuike, K. Nobusada, M. Hayashi, “Collectivity of plasmonic excitations in small sod ium c lus te r s wi th r ing and l inea r structures”, Phy. Rev. A 83, 013201, (2011).

[3] H. C. Hsueh, G. Y. Guo and S. G. Louie, “Excitonic effects in the optical properties of a SiC sheet and nanotubes”, Phys. Rev. B 84, 085404 (2011).

[4] W. T. Chen, C. J. Chen, P. C. Wu, S. Sun, L. Zhou, G. Y. Guo, C. T. Hsiao, K. Y. Yang, N. I. Zheludev, D. P. Tsai, "Optical magnetic


response in three-dimensional metamaterial of upright plasmonic meta-molecules", Optics Express 19, 12837-12842 (2011).

[5] J.-H. Li, J.-D. Chai, G.-Y. Guo, and M. Hayashi, “The quantified NTO analysis for the electronic excitations of molecular many-body systems”, Chem. Phys. Lett. 514, 362 (2011).

[6] H. Y. Xie, P. T. Leung, D. P. Tsai, “Reciprocity theorem for nonlocal optics: Completion of proof and application to spectroscopic analysis”, J. Optics 12, 035006 (2010).

[7] D. Cai and G. Y. Guo, “Spatial localization of quantized states responsible for sharp optical transition in AlGaN/GaN superlattice”, J. Appl. Phys. 107, 103533 (2010).

[8] H. Y. Chung, G. Y. Guo, H.-P. Chiang, D. P. Tsai, and P. T. Leung, “Accurate description of the optical response of a multilayered spherical system in the long wavelength approximation”, Phys. Rev. B 82, 16544 (2010).

[9] W. T. Chen, P. C. Wu, C. J. Chen, H.-Y. Chung, Y.-F. Chau, C.-H. Kuan, and D. P. Tsai , “Elect romagnet ic energy vor tex associated with sub-wavelength plasmonic Taiji marks”, Optics Express 18, 19665 (2010).

[10] V. Klimov and G.-Y. Guo, “Bright and dark P l a s m o n m o d e s i n t h r e e c y l i n d e r nanocylinder cluster”, J. Phys. Chem. C 114, 22398 (2010).


Research Activities of Individuals

Chian-Shu Chen (email: [email protected])

Postdoctoral researcher, 2010/8/1~2012/7/31

Research Activities on Neutrino Physics and Cosmology

n 2011 my research activity in NCTS has been focused on neutrino physics and

cosmology, and mostly the connection between these two fields. The topics cover the mass generation of tiny neutrino masses, flavor symmetry, dark matter, nucleosynthesis, matter-antimatter asymmetry, inflation, and dark energy. For neutrino mass we consider a model [1] in which neutrino masses are generated through radiative quantum corrections at one-loop level. Extra scalars and vector- l ike leptons are introduced in the model . By imposing Z 2 symmetry, the neutrino masses as well as anomalous muon magnetic moment can be generated via one-loop effects at TeV-scale. An explanation for connecting dark matter with leptogenesis is presented in this paper. Especially we consider the so-called catalyzed nucleosythesis via a relative long-lived charged particle to solve the Lithium problem observed in astrophysics recently. The problem indicates that for the amount of lithium6 and lithium7 there is a discrepancy between standard theoret ical prediction and experimental measurement. In this model the small neutrino masses imply the long lifetime of the charged particle hence it will play a role as catalysis in the processes of producing light elements in the early Universe and solve the lithium abundance problem. Furthermore, this scenario can be tested at LHC and/or future experiments.

For flavor symmetry problem, we investigate the implication for the possible existence of forth generation [2]. As it is well known that the large

mixing angles reveal in neutrino oscillation experiments may be the hints for flavor symmetry of fermions. We study a model of four generations in the lepton sector based on the discrete group A5 (the even permutation of five objects). The best features of the three family A4 model survive, including the tribimaximal pattern of three generation neutrino mixings. In this model the electron mass is zero at tree level but calculable through quantum corrections. The hierarchy of the neutrino masses can be obtained as a result of the breaking of A5 down to A4.

Recently, I extend my research to some interesting topics in cosmology especially the inflation, dark energy, density perturbations. Inflation not only solves many puzzles in cosmology and high energy physics but also provides a nice framework for generating primordial density perturbations which are the seeds of the structure formation for the Universe. Dark energy makes up 73% of the total energy density and accelerates the expansion of current Universe. In [3] we first show that the complex SU(2) triplet scalar in type-II seesaw mechanism can be treated as an inflaton. The feature in seesaw mechanism of high energy scale to suppress the neutrino masses can be nicely fit into chaotic inflation scenario. We further investigate the necessary condition for reheating induced by inflaton decays and generating matter-antimatter asymmetry via leptogenesis. After this work we developed the idea that the seesaw mechanism not only explains the neutrino mass but also connects two periods of the Universe, inflation and dark

III-63 ‹‹- Research Activities of Individuals

energy (accelerated expansion Universe). Two methods are proposed by us: one uses the supersymmetry wi th so-ca l led b imordal /schizophrenic neutrino [4] and the other employs the idea that neutrino mass is growing with the evolution of the Universe. And we also found the p o s s i b i l i t y t h a t t h e p r i m o r d i a l d e n s i t y perturbations can be generated through the quantum fluctuations of dark energy during inflation [5]. Usually the dark energy is treated to play an important role only in current Universe not in the early Universe. More investigations about these topics and the primordial density perturbations will be pursued in my future works, especially those are related to neutrinos. I believe this mysterious particle not only provides the evidence beyond the Standard Model but also is the key to understand the underlying physics of dark matter and dark energy.

Currently, there are several new experimental discoveries in neutrino physics, such as the mixing angle θ 13 and the neutrino velocity anomaly. Neutrino mixing matrix contains three mixing angles and one Dirac CP phase and two Majorana phases if neutrinos are Majorana fermions. Two large mixing angles are confirmed in solar and atmospheric neutrino oscillation experiments. Very recently (June 2011) new results have been announced by two long-baseline accelerator experiments probing the νμ to νe appearance channel. In particular, the Tokai-to-Kamioka (T2K) experiment has observed sin2 θ13 ~ few %, which is near the upper bound of previous experimental constraints. In other words the last mixing angle θ13 is “large” in many theoretical expectations. I now work with new postdoctor Ryo Takahashi of National Tsing Hua University to study the large θ13 problem. We further extend my previous model of four generation leptons in A5 symmetry to include four generation of quarks. And the flavor symmetry is replaced by Binary Icosahedral symmetry. We discover there is interesting relation between quark mixing matrix (CKM matrix) and lepton mixing matrix (PMNS matrix) in this model. And we may have the relation of θC ~ θ13 which agrees with the experimental results. Furthermore we also try to consider a serious model of so-called radiative seesaw mechanism. These models include discrete Z2 symmetry and connect dark matter to neutrinos nicely. As a result the

neutrino masses can be generated at one-loop level through dark matter mediation. We are going to study a series of this type of models and investigate their implications in leptonic flavor channels and leptogenesis. An idea of sterile neutrino as dark matter which is hinted in MINOS experiment is ongoing. We try to make a model that is included the idea of radiative seesaw mechanism and keV sterile neutrinos. I will continue my investigation along the line in neutrino physics and it applications in cosmology.

References[1] Chian-Shu Chen and Chung-Hisen Chou,

“Neutrino masses, muon g-2,dark matter, lithium problem, and leptogenesis at TeV-scale”, Phys. Lett. B699:68-73(2011).

[2] Chian-Shu Chen, Tomas W. Kephart, and Tzu-Chiang Yuan, “An A5 Model of Four Lepton Generations”, Journal of High Energy Phys.1104:015(2011).

[3] [2011] Chian-Shu Chen and Chia-Min Lin, “Type II Seesaw Higgs Triplet as the inflaton for Chaotic Inflation and Leptogenesis”, Phys. Lett. B695:9-12(2011).

[4] C h i a n - S h u C h e n a n d C h i a - M i n L i n , “Bimodal/Schizophrenic Neutrino as a Bridge between Inflation and Dark Energy”, Eur. Phys. J. C71:1643(2011).

[5] Chian-Shu Chen and Chia-Min Lin, “Cosmon as the Modulon: Non-Gaussianity from Dark Energy”, Phys. Lett. B705:161-164(2011).

Research Activities of Individuals -›› III-64

Chun-Chung Chen (email: [email protected])

Assistant research scholar, 2009/10/1~2012/9/30

Research Activities on Biophysics

ver the past year, I have continued my study on the emergent structures of plastic neural

networks as well as on the evolutionary dynamics in Eigen's model and cyclic competition.

Plastic Neural NetworksIn a plastic network of spiking neurons, we found

that, while driven by noise, interesting structures emerge in the transition region between the stable phases of the system. Specifically, we see path or ring structures near the low activity end, while hub structures can form near the high activity end of the transition region. [1] These distinct groups of s t ructures represent the s implest nontr ivial conformations one can find in a connected network (Figure 1). Simulation results suggest the system

does not morph directly from one group of structures into the other but instead returns to a unstructured network before structuring in a different group. We gained insight on such observation by drawing from analogy to the vector analysis in Euclidean space and

defined a vector field based on the synaptic weights of the network, which was shown to be curl-ful for the path or ring conformations and curl-free for the hubs (See Figure 2).

Evolutionary DynamicsThe quasi-species model proposed by Eigen [2]

describes molecular evolution through point mutations. We mapped the dynamics to that described by an effective Hamiltonian and applied

Figure 2: Weight product along small loops as an analogy to the curl operator in vector analysis. The path and ring conformations are curl-ful while the hub conformations are curl-free

Figure 1: The emergent structures of the plastic neural network account for the broaden distribution of the synaptic weights.


variational ansatz to obtained good estimates on the error threshold of the quasi-species transition. [5] To demonstrate the advantages of such a mapping, we applied the variational method, which remains effective for large sequence length, to more complex fitness landscapes with, for example, peak-mesa-like competition, and o b t a i n e d g o o d a g r e e m e n t w i t h e x a c t diagonalization in small sequence lengths. Our results allowed us to obtain a criterion for a stable mesa population phase within the quasi-species.

Ext inc t ion in an ecologica l sys tem of competing species is the dynamics of transition to an absorbing state, where once species disappears, it will never reappear again. An expectation of phase transitions in these kinds of systems is that, without additional symmetry or conservation, they generally belong to the directed percolation (DP) universality class. [3] The cyclic competition we have been studying is a three-species system following a rock-paper-scissors-like competition. A s w e h a v e l e a r n e d , i n t w o a n d h i g h e r dimensions, the extinction time of the system generally increases exponentially with the size of the system. That is, the system is well protected from extinction in the thermodynamic limit. My recent study on the variations of the dynamic rules in the competition has revealed that the scaling of extinction time in 2D systems can be changed to follow a powerlaw instead of being exponential when certain parameters of the competition are varied. For example, when we break the symmetry of the system with spontaneous birth (Figure 3c) of one species, the system makes a DP-like transition when the birth rate is increased. On the other hand, when the cyclicity is eliminated (Figure 3d) while the three-fold symmetry is preserved, the scaling of the system can be described by a so-called voter model [4] which is known to have random-walk-like scaling in 2D. The study of these crossover behaviors is a common strategy in non-equilibrium statistical p h y s i c s t h a t s h o u l d h e l p t o b e t t e r o u r understanding of the cyclic competition.

Figure 3: Variations of three-species cyclic competition in 2D. a) With green species being more immune to predation. b) With mobility of individual. c) With spontaneous birth of green species. d) Without cyclicity.

References[1] Chen, Chun-Chung and Jasnow, David,

“Event-driven simulations of a plastic, spiking neural network”, Physical Review E (2011), 031908.

[2] Eigen, M., “Molekulare selbstorganisation und evolution”, Naturwissenschaften (1971), 465-523.

[3] Hinrichsen, Haye, “Non-equilibrium critical phenomena and phase t ransi t ions into absorbing states”, Advances in Physics (2000), 815.

[4] L igge t t , Thomas Mi l ton , “S tochas t i c interacting systems: contact, voter, and exclusion processes”, Springer (1999).

[5] Tu, Min-Feng and Huang, Ching-I and Lin, H s i u - H a u a n d C h e n , C h u n - C h u n g , “Variational ansatz for quasispecies in the E i g e n m o d e l ” u n p u b l i s h e d , a r X i v.org:1011.5098.


Hong-Da Chen (Institute of Systems Biology and Bioinformatics, National Central University; email:[email protected] )


Research Activities on Alternative Splicing and Cancer Stem Cell

n 2010, my research focused on two parts: Alternative Splicing and Cancer

Stem Cell.

The sequencing of the human genome has raised important questions about the nature of genomic complexity. It was widely anticipated that the human genome would contain a much larger number of genes (estimates based on expressed-sequence clustering ran as high as 150,000 genes). The report of only 32,000 human genes thus came as a surprise. This basic disparity indicated that the number of human expressed sequence (mRNA) forms was much higher than the number of genes, suggesting a major role for a l te rnat ive sp l ic ing in the product ion of complexity. Recent genome-wide analyses of alternative splicing indicate that 40–60% of human genes have alternative splice forms, suggesting that alternative splicing is one of the most significant components of the functional complexity of the human genome [1]. moreover, some data indicate the presence of alternative splice forms in up to 80% of human genes [2].

My research is used Exon array data to predict transcription in the alternative splicing event. Current approaches of bioinformatics studies, due to the probe-level algorithm, in alternative splicing there are substantial limitations. for example, when the simple exon lose(insert), often have high identification rate. But, if splicing is complex or multi-option, difficult to predict the correct. Our approach is based on the “Method of Merging Gaussians [3], using a combination of known transcription, to predict alternative splicing event in mRNA-level. We hope that will become a useful tool.

Another preliminary work is cancer stem cell research. Some research indicate, the similar signalling pathways may regulate self-renewal in stem cells and cancer cells [4,5]. Such cancer cell have abi l i ty to self-renewal and avoid to

apoptotic, termed “Cancer stem cell” (CSCs) [6]. CSCs are defined operationally through their ability to efficiently seed new tumors upon inoculation into recipient host mice [7,8]. This functional definition is often complemented by including the expression in CSCs of markers that are also expressed by the normal stem cells in the tissue-of origin [9].

T h r o u g h l i t e r a t u r e s e a r c h , w e h o p e comprehensive understanding the CSCs. Using high-throughput chip to analysis gene expression pathway and network, our strategy is combine the Gene Ontology, Gene set enrichment analysis and Gene in te rac t ion ne twork , to f ind nove l biomarkers and effective drugs.

References[1] Modrek, B. & Lee, C., “A genomic view of

alternative splicing”, Nature genetics 30, 13–19 (2002).

[2] Lee, C. & Wang, Q., “Bioinformatics analysis of a l te rna t ive sp l ic ing” , Br ie f ings in bioinformatics 6, 23 (2005).

[3] Chen, C.-H. et al., “An all-statistics, high-speed algorithm for the analysis of copy number variation in genomes”, Nucleic Acids Research (2011).doi:10.1093/nar/gkr137.

[4] Villanueva, T., “Cancer stem cells: Wnt — looking outside in”, Nat Rev Cancer 10, 386-387 (2010).

[5] Reya, T., Morrison, S.J., Clarke, M.F. & Weissman, I.L., “Stem cells, cancer, and cancer stem cells”, Nature 414, 105–111 (2001).

[6] Hanahan, D. & Weinberg, R.A., “Hallmarks of Cancer: The Next Generation”, Cell 144, 646-674 (2011).


[7] Lalonde, R.J. & Cho, R.M., “The impact of i n c a r c e r a t i o n i n s t a t e p r i s o n o n t h e employment prospects of women”, Journal of Quantitative Criminology 24, 243–265 (2008).

[8] Lobo, N.A., Shimono, Y., Qian, D. & Clarke, M.F., “The Biology of Cancer Stem Cells”, Annu. Rev. Cell Dev. Biol. 23, 675-699 (2011).

[9] Al-Hajj, M., Wicha, M.S., Benito-Hernandez, A . , M o r r i s o n , S . J . & C l a r k e , M . F. , “Prospective identification of tumorigenic breast cancer cells”, Proceedings of the National Academy of Sciences 100, 3983 -3988 (2003).


Hsuan-Yi Chen ( Department of Physics, National Central University and Institute of Physics, Academia Sinica;

email: [email protected])

Center scientist, 2010/08/01~2012/07/31

Research Activities on Soft Matters and Biophysics

y research activities in the past year are in the field of soft matters and biophysics.

The research topics include cell adhesion, actin-based motility, contact angle hysteresis. Non-equilibrium statistical physics is the common theme in these topics.

In the study of cell adhesion, the mechanical response of a ligand-receptor cluster was studied by my student HH Liang and I [1]. We considered a cluster of N ligand-receptor pairs between two parallel surfaces under an applied force that increases linear with time. The force is assumed to be shared equally between the closed bonds in the clusters. Although the open bonds are allowed to rebind because the surfaces are close to each other, the force experienced by the closed bonds increases as the cluster gradually lose the closed bonds due the external force, therefore eventually the cluster dissociates under external force. This is the simplest model for a mechanical pulling experiment on such systems. Before we studied this system, all previous theoretical investigation on such experiments had to assume some specific form for the ligand-receptor interaction, and their results more or less depend on the choice of this interaction. Different from such approach, we constructed the free energy landscape of the cluster under any given force, and derived a scaling form for the dissociation force of the cluster. More specifically, we found that for a cluster there is a critical force Fc and a critical loading rate c such that apart from the trivial regimes of extremely high and low loading rates, the dissociation force of the cluster scales like F-Fc ~ N1/3 [ln(Gc/G)]2/3. This scaling form is confirmed by our numerical simulations for two distinct choices of ligand-receptor interactions. This study calls for future experimental studies on l igand-receptor clusters and has potential application in the mechanical response of focal adhesions, adhesion sites in cell adhesions with

high density of bonds.

Actin-based motility is an important class of self-propelled motion in which the chemical energy of actin polymerization is utilized to power the motion in a highly viscous environment. Recent experiments on actin-based motility of functionalized beads and bacteria found that the trajectories of the propelled objects are in general not s t ra ight . To understand the physical mechanism that generates such curved trajectories, my student Fu-Lai Wen, my collaborator Kt Leung (Academia Sinica) and I proposed a phenomenological model to investigate the stability and geometry of the trajectory of a circular bead in two dimensions [2]. In our model, the force and actin density on the surface of the bead are influenced by the translation and rotation of the bead, which in turn is induced by the asymmetric distributions of those densities. We found that this feedback can destabilize a straight trajectory, leading to circular, S-shape and other geometrical trajectories through bifurcations in the distributions of the force and actin density. Furthermore, we find that there is a deep relation between our model and models of self-propelled deformable domains. In a simplified description, the motion of a self-propelled deformable domain is induced by its shape change, and the dynamics of the domain velocity (a vector) is coupled to a second-rank tensor that describes domain shape. In our model for actin-based motility, the motion of the particle is dictated by the actin density distribution (described by a vector and a second rank tensor) and force density distribution (described by a vector). Therefore it is fair to say that they belong to two different universality classes of self-propelled motion. This discovery is an important advance in sell-propelled motion, a fast growing branch of non-equilibrium statistical physics.


Contact angle hysteresis is a long-standing problem in soft matter physics. Recently P. Tong at Hong Kong Univers i ty of Science and Technology has developed an AFM probe to study the motion of a micro-size rod perpendicular to a liquid surface [3]. From his experimental results we are able to propose a model in which strongly correlated defects produce a complex energy landscape for the contact line such that the advancing and retreating path of the contact line are different. The resulting hysteresis is different from the classical model proposed by de Gennes and Joanny in which the contact line is pinned by dilute, mutual-independent defects, where the hysteresis is produced by single defects.

References[1] Strength of adhesion clusters under shared

linear loading, Hsin-Hui Liang and Hsuan-Yi Chen, Phys. Rev. E, 83, 061914 (2011).

[2] Symmetry-breaking mot i l i t i es in two dimensions, Fu-Lai Wen, Kwan-tai Leung and Hsuan-Yi Chen, submitted to Phys. Rev. Lett. (2011).

[3] Understanding of the contact angle hysteresis beyond de Gennes, Y. Wang, S. Guo, H-Y Chen, E . Char la ix and P. Tong, to be submitted (2011).


Yueh-Nan Chen (Department of Physics, National Cheng-Kung University; email: [email protected])


Research Activities on Quantum Entanglement and Quantum Transport

n the past year, my work was mainly focused on quantum entanglement and

quantum transport. First of all, we have found an e f f i c i e n t s c h e m e t o d e t e c t H i g h - O r d e r entanglement. Such a scheme is expected to be useful in real experiments. Second, we have also investigated how to generate remote entanglement between two quantum dots with the coupling to a nanowire surface plasmon. In addition, we have analyzed and “time-adjust” the photon-counting statistics of a Cavity QED system and showed that the photon statistics can be described by a simple “transport-like” non-equilibrium model. The details of my work are outlined in the followings.

Verifying Genuine High-Order Entanglement

We introduce a scheme to efficiently detect genuine highorder entanglement, such as states close to genuine qudit Bell, Greenberger-Horne-Zeilinger, and cluster states as well as multilevel multi-DOF hyperentanglement. All of them can be identified with two local measurement settings per

Fig. 1. Each measurement in a LMS is chosen by the cor respond ing qud i t ho lder fo r en tang lement verification. All the N qudits are measured locally by (a) t he f i r s t measu remen t , ( b ) t he second l oca l measurements. (a) and (b) together are used to detect N-qudit GHZ states with the criterion (3). (c) All the 2N LMSs for N-partite states are typically required by the kernel of Bell-type inequality.

DOF regardless of the qudit or DOF number. The proposed verifications together with further utilities such as fidelity estimation could pave the way for experiments by reducing dramatically the measurement overhead.

Surface plasmons in a metal nanowire coupled to colloidal quantum dots: Scattering properties and quantum entanglement

We have investigated coherent single surface-plasmon transport in a metal nanowire strongly coupled to two colloidal quantum dots. Remote entanglement of the wave functions of the two quantum dots can be created if the inter-dot distance is equal to a multiple half-wavelength of the surface plasmon. Furthermore, by applying classical laser pulses to the quantum dots, the entangled states can be stored in metastable states that are decoupled from the surface plasmons.

Fig. 2. Schematic diagram of a metal nanowire coupled to two QDs. A single surface plasmon injected from the left is coherently scattered by the dots.

Unified single-photon and single-electron counting statistics: from cavity-QED to electron transport

We analyze and “time-adjust” the photon-counting statistics of such a single-photon source, and show that the photon statistics can be described by a simple “transport-like” non-equilibrium model. We then show that there is a one-to-one correspondence of this model to that of non-equilibrium transport of electrons through a double quantum dot nanostructure, unifying the fields of photon counting statistics and electron t ranspor t s ta t is t ics . This correspondence


empowers us to adapt several tools previously used for detecting quantum behavior in electron transport systems (e.g., super-Poissonian shot noise, and an extension of the Leggett-Garg inequality) to single-photon-source experiments.

Fig. 3. (a) Schematic diagram of a QED system. Vacuum Rabi oscillations can occur if the atom-photon coupling strength g overwhelms the loss rate of cavity photons and the emission rate into other modes. (b) Normal photon counting: Periodic ultra-short laser pulses excite the atom faster than all other time scales. The single-photon detector records the arrival time tn of a photon decaying out of the cavity with respect to each pulse. The grey area in (b) means that no photon is detected due to detector inefficiency.

Publications[1] C. M. Li, K. Chen, A. Reingruber, Y. N.

Chen*, and J. W. Pan, Phys. Rev. Lett. 105, 210504 (2010).

[2] G. Y. Chen, N. Lambert, C. H. Chou, Y. N. Chen*, and F. Nori, Phys. Rev. B 84, 054310 (2011).

[3] N. Lambert, Y. N. Chen*, and F. Nori, Phys. Rev. A 82, 063840 (2010).

[4] J. Y. Lien, Y. N. Chen*, and C. H. Chou, New J. Phys. 13, 083036 (2011).

[5] W. Chen, G. Y. Chen, and Y. N. Chen*, Opt. Lett. 36, 3602 (2011);


Cheng-Wei Chiang ( Department of Physics, National Central University and Institute of Physics, Academia Sinica;

e-mail: [email protected])


Research Activities on Collider Physics

ince February 2011 as a Center Scientist at NCTS, my research has been focused

on hadron collider physics, particularly those issues related to LHC physics. Since then, I have been working on the three topics, as detailed in the following paragraphs.

The first project that my collaborators and I worked on is the study of the Drell-Yan processes at the LHC [1]. In this work, we study such processes mediated by a new bosonic resonance. The bosons of spin-0, 1, and 2 with the most general leading-order couplings to Standard Model fermions and gluons are considered, which provide a model-independent formulation for future exploration of the resonance properties, such as its spin, mass and couplings.

In the case of neu t ra l resonances , we demonstrate how the shapes of the kinematical distributions change as one varies the chiral couplings of the quarks and leptons, and show how to analyze the couplings by making use of the forward-backward asymmetry. In the case of charged resonances, we propose a novel technique to effectively reconstruct the angular distribution in the center-of-mass frame, to a large extent avoiding the two-fold ambiguity due to the missing neutrino. Similar to the case of a neutral resonance, the spin information of the resonance can be extracted unambiguously, and chiral couplings and the asymmetries can be explored in a statistical manner. With the current LHC data, we present bounds on the mass and cross section times branching fraction of the new resonance and estimate the future reach.

This paper has been submitted to PRD and is currently under review for publication.

The second project that my collaborators and I

worked on concerned a recent experimental anomaly of Wjj production by CDF at the Fermilab Tevatron. We explore a possible explanation within the framework of the two-Higgs doublet model for the anomaly. We find that a charged Higgs boson of mass ~140 Gev with appropriate couplings can account for the observed excess. In addition, we consider the flavor-changing neutral current effects induced at loop level by the charged Higgs boson on the B meson system to further constrain the model. Our study shows that the like-sign charge asymmetry Asl

b can be of O(10-3) in this scenario. In particular, unlike most other proposals based on gauge extension, this model has a suppression production of b jets due to the Yukawa coupling.

This paper has been submitted to PLB and is currently under review for publication.

The third and most recent project that my collaborators and I worked on, is to constrain the lepton coupling to a new heavy neutral gauge boson, generally referred to as the Z' boson. In this work, we explore a Z' boson with family-non-universal couplings to charged leptons. The general effect of Z-Z' mixing, of both kinetic and mass types, is included in the analysis. Adopting a model-independent approach, we perform a comprehensive study of constraints on the leptonic Z' couplings from currently available experimental data on a number of f lavor-conserving and flavor-changing transitions. Detailed comparisons are made to extract the most stringent bounds on the leptonic couplings. Such information is fed into predictions of various processes that may be experimentally probed in the near future.

This paper has been submitted to JHEP and is currently under review for publication.


References[1] C.W. Chiang, N.D. Christensen, G.J. Ding,

and T. Han, arXiv: 1107.5830 [hep-ph].

[2] C.H. Chen, C.W. Chiang, T. Nomura, and F.S. Yu, arXiv: 1105.2870 [hep-ph].

[3] C.W. Chiang, Y.F. Lin and J. Tandean, arXiv: 1108.3969.


Chung-Hsien Chou (Department of Physics, National Cheng Kung University; email: [email protected])

Center scientist, 2008/8/1~2009/7/31, 2010/2/1~2012/1/31

Research Activities on Quantum Information Science

n 2011 my research activity in NCTS has been focused on quantum information

science, especially quantum entanglement issues related to the macroscopic quantum phenomena and quantum devices.

Macroscopic quantum phenomena (MQP) is a relatively new research venue, with exciting experimental results and bright prospects, yet surprisingly little theoretical activity is found. What makes MQP intellectually stimulating is better understood from the traditional view that macroscopic means classical. This simplistic and h i ther to ra re ly cha l lenged v iew need be scrutinized anew and perhaps much conventional wisdoms repealed. In a series of papers we report on a systematic investigation into some key fundamental issues of MQP, with the hope of constructing a viable theoretical framework for this new endeavor [1,2]. The three major themes discussed in these essays are the large N expansion, the correlation hierarchy and quantum entanglement for systems of “large” sizes, with many components or degrees of freedom.

In the first paper [1] we use different theories in a variety of contexts to examine the conditions or criteria whereby a macroscopic quantum system may take on classical attributes, and more interestingly, that it keeps some of its quantum features. The theories we consider here are, the O(N) quantum mechanical model, semi-classical stochastic gravity and gauge/string theories; the contexts include that of a `quantum roll' in inflationary cosmology, entropy generation in quantum Vlasov equation for plasmas, the leading order and next-to-leading order large N behavior, and hydrodynamic/thermodynamic limits. The criteria for classicality in our consideration include the use of uncertainty relations, the correlation between classical canonical variables, randomization of quantum phase, environment-induced decoherence, decoherent history of

hydrodynamic variables, etc. All these exercises are to ask only one simple question: Is it really that surprising that quantum features can appear in macroscopic objects? By examining many well-known examples where theoretical analysis has been studied in detail for different systems, we find that there is no a priori good reason why quantum phenomena in macroscopic objects cannot exist.

In the second paper [2] we explore how macroscopic quantum phenomena can be measured or understood from the behavior of quantum correlations which exist in a quantum system of many particles or components and how the interaction strengths change with energy or scale, under ordinary situations and when the system is near its critical point. We use the nPI (master) effective action related to the Boltzmann-BBGKY / Schwinger-Dyson hierarchy of equa t ions a s a t oo l f o r sy s t emiz ing t he contributions of higher order correlation functions to the dynamics of lower order correlation functions. Together with the large N expansion discussed in our first paper we explore 1) the conditions whereby an H-theorem is obtained, which can be viewed as a signifier of the emergence of macroscopic behavior in the system. We give two more examples from past work: 2) the non-equilibrium dynamics of N atoms in an o p t i c a l l a t t i c e u n d e r t h e l a rg e N ( f i e l d components), 2PI and second order perturbative expansions, illustrating how N and N enter in these three aspects of quantum correlations, coherence and coupling strength. 3) the behavior of an interacting quantum system near its critical point, the effects of quantum and thermal fluctuations and the conditions under which the system manifests infrared dimensional reduction. We also discuss how the effective field theory concep t bea r s on mac roscop i c quan tum phenomena: the running of the coupl ing parameters with energy or scale imparts a


dynamical-dependent and an interaction-sensitive definition of “macroscopia”.

Recently, the concept of plasmonics, in analogy to photonics, has received much attention since surface plasmons reveal strong analogies to light propagation in conventional dielectric components. Motivated by the recent development in plasmonics and quantum information science, we propose a new scheme that can entangle two remote quantum dots (QDs) coupled to a metal nano-wire [3]. We investigate coherent single surface-plasmon transport in a metal nano-wire strongly coupled to two colloidal quantum dots. We use a real-space Hamiltonian to treat the coherent surface-plasmon transport in the wire coupled to two dots. Analytical expressions are obtained for the transmission and reflection coefficients by solving the corresponding eigenvalue equation. Remote entanglement of the wave functions of the two quantum dots can be created if the inter-dot distance is equal to a multiple of half-wavelength of the surface plasmon. Furthermore, by applying classical laser pulses to the quantum dots, the entangled states can be stored in metastable states that are decoupled from the surface plasmons.

The quantum phase transition has been widely studied to understand the quantum nature of many-body systems at zero temperature and to manipulate the ground states through tuning the parameters of the system Hamiltonian. The quantum phase transition of photons between the Mott-insulating and superfluid states can take place in a periodic array of nano-cavities, where the photons are strongly coupled to a two-level system inside each cavity. In this regime, the Jaynes–Cummings–Hubbard (JCH) model is used to describe the Hamiltonian of a cavity-array structure, where photons effectively interact with each other through the coupling to individual two-level systems. To realize the photonic phase transition, one important issue is measuring the global quantities of the macroscopic states of photons, such as the compressibility and the order parameter. In this work [4], we study how a weakly coupled single defect inside a JCH lattice

reflects the global signatures of the lattice, and propose a scheme to detect the transition through this defect by using electron transport techniques. For a large enough JCH lattice, the defect reasonably has minor affection to the lattice. The defect cavi ty is found to provide enough information on the phase transition, which can be detected by coupling the cavity to a non-equilibrium electron transport device, i.e. a transport qubit.

Reference[1] C . H. Chou, B . L . Hu and Y. Subas i ,

Macroscopic quantum phenomena from the large N perspective, J. Phys.: Conf. Ser. 306, 012002 (2011).

[2] C . H. Chou, B . L . Hu and Y. Subas i , Macroscopic Quantum Phenomena from the Corre la t ion, Coupl ing and Cri t ica l i ty Perspectives, J. Phys.: Conf. Ser. (in press) [arXiv: 1107.3008].

[3] G. Y. Chen, N. Lambert, C. H. Chou, Y. N. Chen, and F. Nori, Surface plasmons in a metal nanowire coupled to colloidal quantum dots: scattering properties and quantum entanglement, Phys. Rev. B 84, 045310 (2011).

[4] J. Y. Lien, Y. N. Chen, and C. H. Chou, Detecting quantum phase transitions of photons through a defect cavity, New J. Phys. 13, 083036 (2011).


Ming-Chiang Chung (email: [email protected])

Assistant research scholar, 2010/2/1~ 2013/1/31

Research Activity on Bose-Einstein Condensate and Quantum Information Applied in Condensed Matter Physics

n 2011 my research activity in NCTS has been focused on two main topics: Bose-

Eins te in condensate (BEC) and quantum information applied to condensed matter theory. In the aspect of BEC I have been interested in a one-dimensional spin-2 BEC loaded in an optical lattice, quench dynamics of solvable models and macroscopic quantities of BEC. For quantum information applied in condensed matter I have ma in ly focused on t he en t ang l emen t o f subsystems.

Trimerized and dimerized phases for for spin-2 Bosons in a one-dimensional optical lattice

We study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using non-Abelian density matrix renormalization group (DMRG) method we identify three possible phases: ferromagnetic, dimerized, and trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate two methods for identifying the�phases.�The�first�method�is�based�on�the�spin-spin correlation function while in the second method one observes the excitation gap as a dimerization or a trimerization superlattice is imposed. The advantage of the second method is that i t can also be easi ly implemented in experiments. By using the scattering lengths in the literature we estimate that 83 Rb, 23 Na, and 87 Rb be ferromagnetic, dimerized, and trimerized respectively. [1]

Thermalization and Quantum Correlations in Exactly Solvable Models

The generalized Gibbs ensemble introduced for describing few body correlations in exactly solvable systems following a quantum quench is related to the way in which operators sample, in

the limit of infinite time after the quench, the quantum correlations present in the initial state. The emergence of the generalized Gibbs ensemble is thus analytically demonstrated for the quantum Ising and XX chains in the thermodynamic limit. For these models and a broad class of initial states, which includes both translationally and non-translationally invariant states, the validity of the generalized Gibbs ensemble for simple correlation functions of both local and nonlocal operators is established [2].

Bogoliubov structure in Bose-Einstein condensate

Based�on�a�unified�theoretical�treatment�of�the�1D Bogol iubov-de Genes equa t ions , the dephasing effects due to nonlinear interaction in Bose-Einstein condensates loaded into a trapped optical lattice are studied. Within the perturbation regime, an all-analytical framework is presented enabling a straightforward phenomenological mapping of the oscillation character. This is performed by scanning a wide parameter window where� available� experimental� configurations� also�fit�[3].

On the relation between entanglement and subsystem Hamiltonians

The reduced density is an important concept for entanglement. We define a reduced density matrix as follows: if a initial density matrix ρ0 is obtained by a eigenstate of a system containing the system A and the environment B. The reduced density matrix is defined as ρA = TrB ρ0. The reduced density is important not only because the entanglement entropy SA can be written as SA�=�−�Tr ρA log2 ρA, but also because the entanglement Hamiltonian HeA� =�−� ln�ρA. HeA is related to the entanglement spectra and it can be used to


investigate the topological systems, for example, topological insulators or fractional quantum Hall effects. In our paper we investigate the conditions w h e n t h e e n t a n g l e m e n t H a m i l t o n i a n i s proportional to the Hamiltonian of a subsystem. This observation can be used to the thermalization mentioned above [4].

My research plan of the future is based on the ongoing research of mine: one is the development on the theory of cold atoms and the other on the quantum information applied to condensed matter theory. The quantum dynamics of cold atomic systems and the spinor bosons are two important topics of my study on cold atoms and I am also focusing on topological properties and quantum quench of entanglement - an aspect of quantum information applied to condensed matter theory (see the overview of the research). I plan to work on different systems of those essential topics. Quantum quench of exactly solvable models, which can be mimicked by the cold atomic experiments, will be one of my essential study. My expertise on the low dimensional systems provides me a tool to study different one- or two-dimensional systems. The question, how the systems thermalize after a sudden quench, has become a major topic of dynamical prop-erties. This problem can be verified by the cold atomic experiments. I will be focusing on those problems in the near future. For the spinor BEC we are in the middle of the research. Even for spin-1 and spin-2 bosons, except some of the phases found by us and by others, there are still a lot of unknown phases. I will be concentrating on finding those phases and convincing the experimentalists to work on those systems.

Another important thema for me is the topological properties in quantum information. Topolog ica l sys tems such as g raphenes , topological insulators and quantum Hall effects have been significantly discussed recently in the literature. The relation between topological systems and quantum information has also attracted a lot of attentions. We have already developed a method to detect the entanglement of topological effects, such as zero energy modes and

edge states. The final goal is to find a way to detect the entanglement properties such as entanglement entropy and entanglement spectra using experiments . This wil l be the most challenging part of my study on the quantum information applied to condensed matter theory.

References[1] Dimerized and trimerized phases for spin-2

Bosons in a onedimensional optical lattice, P.C. Chen, Z.L. Xue, I. P. McCulloch, M.-C. Chung and S.K. Yip, arXiv: 1004.3707 (submitted to PRL).

[2] Thermalization and quantum correlations in exactly solvable models, M.A. Cazalilla, A. Iucci and M.-C. Chung, arXiv: 1106.5206 (submitted to PRA)

[3] I n t e r m o d u l a t i o n i n B o s e - E i n s t e i n condensates, C. Trallero-Giner, V. Lopez-Richard, M.-C. Chung, N. Nurez- Fernadez and M. Oliva, arXiv: 1107.4899 (submitted to PRA)

[4] On the relation between entanglement and subsystem Hamiltonian, I. Peschel and M.-C. Chung, arXiv: 1105.5206 (submitted to EPL)


Kazuyuki Furuuchi (email: [email protected])

Staff scientist, 2007/8/1~2012/7/31

Research Activities on Particle Physics

his academic year, I devoted myself to the construction of a model which realizes

gauge-Higgs unification in spontaneously created fuzzy extra dimensions. This work was done in collaboration with Prof. Takeo Inami at Chuo University and Prof. Kazumi Okuyama at Shinshu University, and the results have been announced in the e-print [2]. This study was partially motivated by my earlier work with Prof. Okuyama I reported last year, which was published in a journal in this academic year [1]. In [1] we constructed a class of configurations of D-branes wrapped on fuzzy del Pezzo surfaces, and studied its implications to the structure of the Yukawa couplings in Grand Unified Theories. In [1] the naturalness problem regarding the mass of the Higgs field (extremely small mass of the Higgs field compared with the theoretically expected natural value due to the quantum cor rec t ions) was taken care by supersymmetry. While such set up is quite natural in the model building based on string theory, there is another possibility for solving the naturalness problem, which is particularly natural in the setting of [1]. In [1], a component of a gauge field in the direction of the fuzzy del Pezzo surface was a candidate of the Higgs field. On the other hand, when the Higgs field originates from the extra-dimensional component of a gauge field in higher dimensions, it is known that the naturalness problem can be solved. This is the so-called gauge-Higgs unification scenario. However, as far as we had noticed, there had been no detailed study of the gauge-Higgs unification in fuzzy extra dimensions. Thus it was important to study this new possibility and clarify its basic features. Furthermore, in the ordinary gauge-Higgs unification the extra dimensions are a-priori given. On the other hand, fuzzy extra dimensions can be described by four-dimensional quantum field theory. The fuzzy extra dimensions are described as a vacuum of the four-dimensional quantum field theory which spontaneously breaks the gauge

symmetry of the four-dimensional model. The mass spectrum on the vacuum mimics the low-lying Kaluza-Klein modes of ordinary extra dimensions, but deviates at higher modes and is truncated at finite level. This is an interesting point , and thus we concentra ted on such spontaneously created fuzzy extra dimensions. Another important point is that such fuzzy extra dimensions are ubiquitous in string theory, and thus this scenario can be generically realized in string vacua. In [2] we studied a model with fuzzy torus extra dimensions in detail in the framework of effective field theory and clarified the basic features of the model: We showed that the Higgs naturalness problem can be solved. We pointed out that the size of the gauge group which describes the fuzzy torus cannot be arbitrary large in order for the effective field theory description to be valid. We also pointed out the size of the gauge group need not be very large in order to solve the Higgs naturalness problem. This means the fuzzy extra dimensions need not look close to ordinary extra dimensions at all. We explained that a region for a parameter which is required for the existence of fuzzy torus vacuum is quite natural. We also comment on a realization of the model on the worldvolume of D-branes. In [2] we concentrated on the simple case of fuzzy torus extra dimensions, but we believe many of the features would be similar if one considers other type of extra dimensions.

Since our model solves the naturalness problem regarding the Higgs mass, the evidences for our scenario might be found at the Large Hadron Collider, which is expected to probe the mechanism that solves the Higgs naturalness problem. Since our study clarified the basic theoretical structure of the model, it will provide the basis for the construction of a variety of more de ta i l ed mode ls which may be t es ted in experiments.


References[1] K. Furuuchi , K. Okuyama, “D-branes

Wrapped on Fuzzy del Pezzo Surfaces”, JHEP 1101, 043 (2011) [arXiv: 1008.5012 [hep-th]].

[2] K. Furuuchi, T. Inami, K. Okuyama, “Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions,” [arXiv: 1108.4462 [hep-ph]].


Chao-Qiang Geng (National Tsing Hua University; email: [email protected])



t is well known that the standard model (SM) of the strong and electroweak

interactions has had enormous success in explaining all relevant existing experimental data. However, in addition to the large number of free parameters, the SM leaves too many fundamental problems unanswered. For instance, why are there three families? What is the origin of CP violation? It is generally anticipated that there is new physics in higher energy regions. On the other hand, it is well established that the evolution of the universe is described by the standard hot big bang model. Its early stage offers a common field for particle physics, astrophysics and cosmology. Various observations in laboratories have led to some clues as well as new ideas to understand what occurred in the early universe. However, there are still many fundamental questions answered. In particular, the recent data indicates that more than 95% of the total energy density of the universe is dark, referred as dark matter and dark energy, but we still do not know the real nature of them. My research during 2011 at NCTS has been studying these fundamental and important problems in particle physics, astronomy and cosmology. My research results during 2011 at NCTS are listed as follows:

[1] “Dark Matter in Inert Triplet Models”, Takeshi Araki, C.Q. Geng, Keiko I. Nagao, Phys. Rev. D83 (2011) 075014.

[2] “Phantom crossing in viable f(R) theories”, Kazuharu Bamba, Chao-Qiang Geng, Chung-Chi Lee, Int. J. Mod. Phys. D20 (2011) 1339-1345.

[3] “Thermodynamics in Modified Gravity Theories”, Kazuharu Bamba, Chao-Qiang Geng, Shinji Tsujikawa, Int. J. Mod. Phys. D20 (2011) 1363-1371.

[4] “Signatures of Dark Matter in Inert Triplet

Models”, Takeshi Araki, C.Q. Geng, Keiko I. Nagao, Int. J. Mod. Phys. D20 (2011) 1433-1440.

[5] “Gravitational Waves in Viable f(R) Models”, Louis Yang, Chung-Chi Lee, Chao-Qiang Geng, JCAP 1108 (2011) 029.

[6] “Localizing fields on brane in magnetized background”, Shih-Hao Ho and C.Q. Geng, Eur. Phys. J. C71, 1738 (2011).

[7] “Semileptonic B- ppe-e decay”, C.Q. Geng, Y.K. Hsiao, Phys. Lett. B704 (2011) 495.

[8] “Large 13 from finite quantum corrections in quasi-degenerate neutrino mass spectrum”, Takeshi Araki, Chao-Qiang Geng, JHEP1109 (2011) 139.

[9] “'Teleparallel' Dark Energy”, C.Q. Geng, C.C. Lee, E.N. Saridakis and Y.P. Wu, Phys. Lett. B704 (2011) 384.

[10] “Large-scale magnetic fields from inflation due to a CPT-even Chern-Simons-like term with Kalb-Ramond and scalar fields”, Kazuharu Bamba, C.Q. Geng, S.H. Ho, W.F. Kao, arXiv: 1108.0151 [astro-ph.CO].

[11] “Thermodynamics of cosmological horizons in f(T) gravity”, K. Bamba and C.Q. Geng, arXiv: 1109.1694 [gr-qc].

[12] “Study of ”, C.Q. Geng and Y.K. Hsiao, arXiv: 1109.3032 [hep-ph].

[13] “Observational Constraints on Teleparallel Dark Energy”, C.Q. Geng, C.C. Lee and E.N.Saridakis, arXiv: 1110.0913 [astro-ph.CO].

[14] “ P r i m o r d i a l F l u c t u a t i o n s w i t h i n Teleparallelism”, Y.P. Wu and C. Q. Geng, arXiv: 1110.3099 [hep-th].


Jae-Sik Lee (Department of Physics, National Tsing Hua University; email:[email protected])

Assistant research scholar, 2008/7/1– 2011/7/31


et me begin with our efforts to go beyond the Minimal Supersymmetric extension

of the Standard Model (MSSM). The MSSM has a weak point known as the mu problem. For a supersymmetric model to be phenomenologically viable, the size of the mu parameter should be a round the sca le o f 1 Tev. The min imal supersymmetric model achieves this goal by going to Next-to-Minimal Supersymmetric Standard Model (NMSSM) which adds one more gauge singlet to the MSSM. Furthermore, it is well known that the strong first-order phase transition, which is needed for the mechanism of the electro-weak baryogenesis to explain the matter-dominance of our Universe, can be realized in the NMSSM more comfortably.

We have made a team for the NMSSM phenomenology with explicit CP violation. The team consists of Prof. Kingman Cheung, Dr. Tie-Jiun Hou, Dr. Eibun Senaha, and me. We have done the calculation of the Higgs mass spectrum and the mixing by including the higher-order corrections beyond the one-loop level [1]. Now we are working on the constraints from the non-observation of the electric dipole moments on the CP phases in the NMSSM, the electro-weak phase transition, relevant B- and K-meson observables with high tanβ values, etc.

We believe that Top-quark Physics will be one of the most important topics in the LHC era and it is likely for any New Physics to show through the productions and decays of the top quark. Motivated by a possible anomaly in the forward-backward asymmetry of top quark observed at the Tevatron, we perform a model independent analysis using an effective Lagrangian with dim-6 four-quark operators [2]. We derive necessary conditions on new physics structures and the couplings that are consistent with the top-quark pair production cross section and the forward-backward asymmetry measured at Tevatron, and discuss possible new physics scenarios that could generate such dim-6 operators. We are extending our study to include the top-quark pair invariant

mass and rapidity-gap distributions, resonance productions of new particle(s) at the LHC, top-quark polarizations in general, and impacts on the low-energy flavor observables. We emphasize the importance of the LHC as a top-quark factory as well as a New-Physics discovery machine.

On the other hand, with my UK colleagues, we present a new geometric approach to the flavor d e c o m p o s i t i o n o f a n a r b i t r a r y s o f t supersymmetry-breaking sector in the MSSM [3]. Our approach is based on the geometry that results from the quark and lepton Yukawa couplings, and enables us to derive the necessary and sufficient conditions for a linearly-independent basis of matrices related to the completeness of the internal [SU(3) x U(1)]5 flavor space. In a second step, we calculate the effective Yukawa couplings that are enhanced at large values of tanβ for general soft supersymmetry-breaking mass parameters. We highlight the contributions due to non-universal terms in the flavor decompositions of the sfermion mass matrices. We present numerical examples illustrating how such terms are induced by renormalization-group evolution starting from universal input boundary conditions, and demonstrate their importance for the flavour-violating effective Yukawa couplings of quarks.

We also analyze the constraints imposed by experimental upper limits on electric dipole moments wi th in the Maximal ly CP- and Minimally Flavour-Violating version of the MSSM [4]. Since the MCPMFV scenario has 6 non-standard CP-violating phases, in addition to t h e C P - o d d Q C D v a c u u m p h a s e θ Q C D, cancellations may occur among the CP-violating contributions to the three measured EDMs, those of the Thallium, neutron and Mercury, leaving open the possibility of relatively large values of the other CP-violating observables. We develop a novel geometric method that uses the small-phase approximation as a starting point, takes the existing EDM constraints into account, and enables us to find maximal values of other CP-violating observables, such as the EDMs of


the Deuteron and muon, the CP-violat ing asymmetry in b -> sγ decay, and the Bs mixing phase. We apply this geometric method to provide upper limits on these observables within specific benchmark supersymmetric scenarios, including extensions that allow for a non-zero θQCD.

At the time of writing this Annual Report, we have two preprints. The first one [5] is a sequel to the paper published previous year. In the paper, we provide a comparative study of the Higgs boson mass measurements based on two approaches to the dileptonic decay of W-bosons produced by the Higgs boson decay, one using the kinematic variable M_T^true and the other using the MT2-assisted on-shell reconstruction of the invisible neutrino momenta. We found that these two approaches can determine the Higgs boson mass with a similar accuracy for both of the two main production mechanisms of the SM Higgs boson at the LHC, i.e. the gluon-gluon fusion and the weak vector boson fusion. It is noticed also that the efficiency of both approaches might be improved with an appropriate MT2 cut. The second preprint [6] is a mathematical note related to our geometric approach to CP Violation [4]. The note presents an analytic construction of the optimal unit-norm direction that maximizes or minimizes the objective linear expression which is under a system of linear constraints. We have submitted it to the mathematical journal of "Linear Algebra and Its Applications" and are waiting for a constructive referee report.

Lastly, I report our invited contribution to Summary document Pre-SUSY 2009 has been published as in Ref[7].

I am closing my Annual report by accounting that the preprints mentioned in my contribution to the 2009 Annual Report have been published as Refs.[8,9].The first one [8] is on a possibility of dimension-five operators with strong couplings in the superpotential as an alternative origin of the particle masses. And the second one [9] is on the exotically decaying MSSM Higgs bosons at hadron colliders.

References[1] Kingman Cheung, Tie-Jiun Hou, Jae Sik Lee,

Eibun Senaha, The Higgs Boson Sector of the Next-to-MSSM with CP Violation,To appear

in Phys. Rev. D, arXiv: 1006.1458 [hep-ph].

[2] Dong-Won Jung, P. Ko, Jae Sik Lee, Soo-hyeon Nam, Model independent analysis of the forward-backward asymmetry of top quark production at the Tevatron, Phys. Lett. B691, 238-242 (2010).

[3] John Ellis, Robert N. Hodgkinson, Jae Sik Lee, Apostolos Pilaftsis, Flavour Geometry and Effective Yukawa Couplings in the MSSM, JHEP 1002:016, 2010.

[4] John Ellis, Jae Sik Lee, Apostolos Pilaftsis, A Geometr ic Approach to CP Violat ion: Applications to the MCPMFV SUSY Model, To appear in JHEP, arXiv: 1006.3087 [hep-ph].

[5] Kiwoon Choi, Jae Sik Lee, Chan Beom Park, Measuring the Higgs boson mass with transverse mass variables, arXiv: 1008.2690 [hep-ph].

[6] John Ellis, Jae Sik Lee, Apostolos Pilaftsis, N o t e o n a D i f f e r e n t i a l - G e o m e t r i c a l Construction of Optimal Directions in Linearly-Constrained Systems, arXiv: 1009.1151 [math.OC].

[7] P. Nath et al., The Hunt for New Physics at the Large Hadron Collider, Nucl. Phys. Proc. Suppl. 200-202, 185-417 (2010).

[8] Dong-Won Jung, Otto C.W. Kong, Jae Sik Lee, Holomorphic Supersymmetric Nambu-Jona-Lasinio Model, Phys. Rev. D81, 031701 (2010).

[9] J . S . L e e , Y. P e t e r s , A . P i l a f t s i s , C . Schwanenberger, Strangephilic Higgs Bosons in the MSSM, Eur. Phys. J. C66, 261-269 (2010).


C.-J. David Lin (Institute of Physics, National Chiao-Tung University)


Research Activities on Lattice Gauge Theory in Physics of the Large Hadron Collider

Introduction

rom August 2010 to August 2011, I made progress in projects in physics related to

the Large Hadron Collider using large-scale numerical simulations in lattice field theory. This is reflected in three main research avenues that I am pursuing. First, I am studying the scenario of electroweak symmetry breaking via a strongly coupled gauge theory at TeV scale, namely, the “walking technicolour” scenario. Second, I am performing calculations for matrix elements of baryons containing a b quark, which is the main subject of the LHC-b experimental project. Finally, I started working on a project in non-perturbative computation for the Higgs-Yukawa model in the strong-Yukawa regime.

Walking TechnicolourWalking technicolour is one of the candidates

that generate the electroweak symmetry breaking at TeV scale without the need for the Higgs particles. It is a strongly-coupled gauge theory, hence lattice gauge theory can play an important role in this research avenue. In the walking-technicolour scenario, the coupling constant in the gauge theory increases over a range of scale when the energy is decreased, then it becomes “frozen”. At the very low energy regime, it starts increasing again, such that conformal symmetry and chiral symmetry are broken dynamically. The system then develops an energy gap which generates the spectrum.

The reason why such a scenario is required is due to the need to dynamically suppress the flavour-changing neutral currents (FCNC) in physics beyond the Standard Model. A walking theory is likely to produce large anomalous dimensions for the operators that generate the Standard Model fermion masses. This can then

lift the scale at which flavour emerges, hence suppress the FCNC. It is not easy even just to find a theory which has the “walking” feature and dynamical symmetry breaking at low energy. My postdoc, Kenji Ogawa, and I have formed a collaboration with physicists in Japan centred around Professor Tetsuya Onogi at Osaka University. In 2009, we published a paper proposaing new methods in studying technicolour models on the lattice [1] via defining the coupling constant in the string-type renormalization scheme. This year, we finished a numerical calculation, using this method, for the SU(3) gauge theory coupled to 12 flavours of massless fermions [2]. The most important result of this work is summarized in Fig. 1, in which we show the ratio between the “step-scaling function” and the coupling constant “u” as a function of the coupling constant. The step-scaling function is defined as the “output coupling constant” after inputting a value of the coupling constant and enlarging the length scale by a factor of 1.5. This ratio becomes one when the theory exhibits scale-invariance behavior and the β-function becomes zero. From Fig. 1, it is clear this theory is conformal both in the UV (asymptotic freedom) and in the IR (IR fixed point). The corresponding behavior of the coupling constant itself against the renormalization scale is shown in Fig. 2.Fig. 1


Fig. 2

We have also studied the SU(2) gauge theory with 8 flavors of massless fermions and found similar behavior [3].

Physics of the B-BaryonA b-baryon is composed of three valence

quarks, namely, a b-quark and two light quarks. The rare decay channels in which a non-stranged b-baryon decays into a stranged baryon plus a photon or a lepton pair are sensitive to new physics effects involving the mixing of quarks via right-handed coupling structure that is absent in the Standard Model. This structure cannot be probed by existing experiments performed with the B mesons which do not carry spin. With William Detmold, Stefan Meinel and Matthew Wingate, I have set up a program to pin down the relevant matrix elements in the above decay channel as our final goal.

In our program, we use the dynamical gauge configurations generated and kindly lent to us by the RBC Collaboration. The lattice size is 24-cube times 64, with lattice spacing around 0.1 fm. The 2+1 flavors of dynamical quarks in these RBC configurations are domain wall fermions. We also use the same fermions for our valence light quarks. For the heavy quark, we use the static approximation where the heavy-quark mass is infinite. In 2009, we published our first paper in this program [4]. The results are summarized in Fig. 3. There we pinned down the spectrum of hadrons containing one single valence b quark. Our result for the Omega-b baryon helped resolve a discrepancy in experimental measurements from the CDF and the D0 collaborations. This year we

finished a complete determination for the axial couplings in heavy-hadron chiral pertuerbation theory (HHChPT), starting from a one-loop HHChPT calculation [5], to the actual lattice numerical computation for these couplings [6,7]. These coupling are very important quantities in b-hadron physics, since they dominate the strong decays of certain b-baryons, and they appear in all the chiral extrapolations in lattice computation for b-hadron matrix elements and spectrum. Our calculation is the first such calculation for two of the three axial couplings using lattice QCD, and the main numerical results are summarized in Fig. 4.Fig. 3

Fig. 4

Strong Yukawa ModelsWith the LHC producing more data, there has

been a recent resurrection of the search for extra generation of (heavy) fermions. Such fermions are coupled to the scalar particles, the Higgs, via strong Yukawa coupling, and their masses could be well above 700 Gev. The existence of strong


Yukawa couplings can lead to very interesting f i e l d t h e o r e t i c f e a t u r e s , a s w e l l a s phenomenological consequences. First, the strong Yukawa coupling may lead to the condensates of these heavy fermions, hence a new mechanism for dynamical electroweak symmetry breaking. Second, these extra generation fermions can form bound states which will saturate the unitarity bound for the W-W scattering process.

The above scenario involves strongly-coupled field theory and the lattice is the only reliable tool in performing calculations. Together with the HEP group at National Taiwan University, led by Professor George, W.-S. Hou and the lattice group at DESY Zeuthen, centred around Professor Karl Jansen, I started working on this research avenue this year.

After setting up a powerful PC cluster at National Taiwan University, we have accumulated data for studying the scaling behavior for the existence of a new phase in the Higgs-Yukawa model at the strong-Yukawa regime. Such a phase was observed in previous studies using Wilson and staggered fermions. Our work is first investigation of this theory using fermions with exact chiral symmetry on the lattice. This allows us to define the Yukawa couplings without any ambiguity. By studying the susceptibility of the magnetization, we found a phase transition at the strong-Yukawa regime. In Fig. 5, we plotted the susceptibility for a particular choice of the bare scalar mass and the bare scalar quartic coupling (which is set to infinity), obtained at various finite volumes. We performed a global fit to all these data points according to the finite-size behavior as predicted by solving the renormalization group equation under the assumption that the theory is close to a second-order phase transition in this corner of the parameter space. The fit works very well and the perfect scaling behavior is shown in Fig. 6. From these plots, our data are clearly indicating that the theory has a second-order phase transition in the large bare Yukawa coupling regime and this can be identified as a new continuum limit. We are currently generating more data at larger volumes to further confirm this picture, and to study the spectrum in this regime. The above was presented at the Lattice 2011 conference and the proceedings will appear soon [8].

Fig. 5

Fig. 6

References [1] E.Bilgici, A.Flachi, E.Itou, M.Kurachi, C.-J.

D.Lin, H.Matsufuru, H.Ohki, T.Onogi, E.Shintani, T.Yamazaki, arXiv:0902.3768 [hep-lat], Phys. Rev. D80 034507 (2009).

[2] T.Aoyama, H.Ikeda, E.Itou, M.Kurachi, C.-J.D.Lin, H.Matsufuru, K.Ogawa, H.Ohki, T.O n o g i , E . S h i n t a n i , T . Ya m a z a k i , arXiv:1109.5806 [hep-lat], submitted to Phys. Rev. Lett. for publication.

[3] H.Ohki, T.Aoyama, E.Itou, M.Kurachi, C.-J.D.Lin, H.Matsufuru, K.Ogawa, T.Onogi, E.Shintani, T.Yamazaki, arXiv:1011.0373 [hep-lat], PoS LATTICE 2010 06 (2010).


[4] W.De tmo ld , C . - J .D .L in , M.Winga t e , arXiv:0812.2583 [hep-lat], Nucl. Phys. B818 17-27 (2009).

[5] W. D e t m o l d , C . - J . D . L i n , S . M e i n e l , arXiv:1108.5594 [hep-lat], accepted for publication in Phys. Rev. D.

[6] W. D e t m o l d , C . - J . D . L i n , S . M e i n e l , arXiv:1109.2480 [hep-lat], submitted to Phys. Rev. Lett. for publication.

[7] W.Detmold, C.-J.D.Lin, S.Meinel, to appear. 8 . J .Bulava , P.Gerho ld , G .W.-S .Hou, K.Jansen, B.Knippschild, C.-J.D.Lin, K.-I. Nagai, A.Nagy, K.Ogawa, B.Smigielski, to appear in PoS LATTICE 2011 (2011).


Baruch Rosenstein (Department of Electrophysics, National Chiao Tung University)

Center scientist, 2010/9/1-2011/8/30

Research Activities on Condensed Matter Physics

I. Research Type II superconductors in magnetic fields

distinctive remarkable feature of a superconduct ing s ta te , a quantum

mechanical macroscopic coherent state, is its rigidity. This robust rigidity (even a certain amount of nonmagnetic impurities does not spoil this feature due to the Anderson theorem) leads to the absence of dissipation. This is a result of the energy�gap�Δ�in�the�spectrum�of�excitations�of�the�many body system around the Fermi level observed early on both in measurements of microwave absorption and of tunneling density of states. Unfortunately, the magnetic field always destroys this property. In type II superconductors it creates Abrikosov vortices with cores of radius ξ (coherence length), in center of which the superfluid density vanishes due to a nonzero vorticity. This feature is of topological nature and therefore unavoidable. In the vortex core center the material resembles a normal metal in the sense that the spectrum of the fermion excitations is almost continuous. In fact, the spectrum is discrete since the charge ±e quasiparticles are “confined” by Andreev reflection inside the vortex core with typically small inter-level spacing and the minimal excitation�(the�mini-gap):�Eμ=Δ²/EF.

The influence of the core excitations (Andreev bound states) on local DOS was first observed in the clean superconductor NbSe2 using scanning t u n n e l i n g s p e c t r o s c o p y ( S T M ) . R e c e n t developments of the STM technique allow identification of the core states in a wide variety of materials. The core excitations lead to dissipation when the vortices move or vibrate. The dynamics of the vortex motion, very important for applications, depends therefore essentially on the excitation spectrum of the vortex core.

The above theories considered unpinned vortices although vortices are seldom free in real superconductors. Usually they are weakly pinned by spatial inhomogeneities. It is expected that spectrum of a vortex pinned on metallic defects is not modified significantly due to the proximity effect. However, in addition to inhomogeneities, superconducting material can also tolerate small insulating inclusions and even holes. In fact, an early method to ensure pinning of vortices was irradiation that creates such an insulating columnar defect.

Recently a more efficient method, the ultrafast laser and electron-beam lithography, was realized experimentally in thin films to produce arrays of dielectric inclusions or holes. It has an advantage over the randomly distributed intrinsic or columnar defects since the pinning centers can be periodically arranged into an array. An even more important feature of the artificial pinning is that the diameter of the hole can be made of order of the coherent length. In these cases the effect on the core excitation spectrum might be stronger.

We ascertained, by solving the BdG equations numerically, that the artificial pinning by an array of holes changes dramatically the excitation spectrum: while the mini-gap, that in the spectrum of unpinned vortex (or captured by a metallic defect)� is� small,� it� becomes�of� the�order�Δ.�The�work done in collaboration with colleagues in Bar Ilan University (using their CRAY machine operated by Dr. I. Shapiro) whom I visited was reported on conferences and is in press in

[1] B. Rosenstein, I. Shapiro, E. Deutch, B. Ya. Shapiro. “Microwave absorption in the cores of the Abrikosov Vortices Pinned by Artificial Insulator Inclusion”, Phys. Rev. B (2011).

In addition I completed the previous research on transport in periodic arrays of such inclusions in collaboration with the same group.


[2] B. Rosenstein, I. Shapiro and B.Ya. Shapiro, “Transport current carrying superconducting film with periodic pinning array under strong magnetic fields”. Phys. Rev. B83, 064512 (2011).

Electric transport in graphene

Electronic mobility in graphene, especially one suspended on leads, is extremely large, so that a graphene sheet is one of the purest electronic systems. The relaxation time of charge carriers due to scattering off impurities, phonons, ripplons, etc., in suspended graphene samples of submicron length is so large that the transport is ballistic. The extraordinary physics appears right at the Dirac point at which the density of states vanishes. In particular, at this point graphene exhibits a quasi - Ohmic behaviour, J=σE, even in the purely ballistic regime.

Determination of the value of the minimal DC conductivity at Dirac point in the limit of zero t e m p e r a t u r e h a d u n d e rg o n e a p e r i o d o f experimental and theoretical uncertainty. After the value in graphene on substrate was measured to be about σ=4e²/h,� it�was� shown� in� experiments� on�suspended samples that the zero temperature limit was not achieved and in fact that these early samples had too many charged “puddles”, so that they represented an average around the neutrality or the Dirac point. The value in early suspended samples was half of that and most recently settled around σ2=(π/2)e²/h� in� best� samples� at� 2K�temperature. Theoretically several different values fo r in f in i t e sample appeared . The va lue σ1=(4/π)e² /h� had� been� considered� as� the�“standard” one for several years and appeared as a z e r o d i s o r d e r l i m i t , a l t h o u g h d i f f e r e n t regularizations within the Kubo formalism resulted in different values. The value σ2 is equal to the AC value calculated however under the condition ω>>T/ℏ�at�finite�temperatures.

The dynamical approach to transport was applied to the tight binding model of graphene was developed in collaboration with Lewkowicz (Ariel University) to resolve this “regularization ambiguity”. It consists of considering the ballistic evolution of the current density in time after a sudden or gradual switching on of the electric field. The electric field creates electron - hole excitations in the vicinity of the Dirac points

similar to the Zener tunneling effect in narrow gap semiconductors or electron - positron pair creation in Quantum Electrodynamics. Importantly, in graphene the energy gap is zero, thus the pair creation is possible at zero temperature and arbitrary small E, even within linear response. The result within linear response is that the current settles very fast, on the microscopic time scale on the value of σ2. Deeper analysis of the “quasi - Ohmic” graphene system beyond the leading order in perturbation theory in electric field performed in collaboration with H.C. Kao of Taiwan Normal University revealed that on the time� scale� tnl=√((ℏ/(eEvg))),� the� linear� response�breaks down due to intensive Schwinger's pair creation and leads to a linear increase. It turns out tha t the energy is radia ted away and the calculation was published in

[3] M. Lewkowicz, H. C. Kao and B. Rosenstein, “Signature of the Schwinger pair creation rate via radiation generated in graphene by a strong electric current”, Phys. Rev. B84, 035414 (2011).

Alternative and independent approach to ballistic transport in mesoscopic, importantly to finite length L, graphene samples was pioneered byBeenakker’ group. They applied the Landauer - Buttiker formula for conductance derived for transport in (quasi) one dimensional channels. The approach hinges on description of leads in terms of a potential barrier of certain nonzero potential barrier potential U(r) (the height actually assumed to be very large

It looks that the physical picture behind this calculation is almost “orthogonal” to the one of ultra - relativistic pair creation above. We used our dynamical approach to study rigorously transport in mesoscopic samples and show that indeed the physics behind the two values is different.

[4] M. Lewkowicz, B. Rosenstein and D. Nghiem, “Two distinct ballistic processes in graphene at the Dirac point”, Phys. Rev. B84, 115419 (2011).

II. Organization of a workshopWorkshop on Physics of low dimensional electronic systems 30-31 October 2011


The workshop included 11 local speakers in addition to the following foreign visitors:

•��Prof.�B.�Altshuler,�Columbia�University,�New�York, USA,

•��Prof.�A.�Varlamov,�University�of�Rome,�Italy•��Prof.�D.�P.�Li,�Peking�University,�Beijing,�China

First day (superconductivity) took place in NCTU library, while the second day at Physics Dept. of NTNU (Taipei). Budget was on target (below 50.000$NT), paid by the focus group.

This was followed by discussions with Profs. Altshuler and Varlamov both in NCTU and NTU about their nanophysics group proposals with members of education committees in both Universities.

III. VisitorProf. Chen Qing-Hu (Department of Physics,

Zhejiang Normal University, Jinhua, China) visited for a period of two weeks In July. He is an expert in theory of superconductivity (and heads a new center), but is also active in MC simulations in statistical physics. Both of us were co chairs of the First Chinese International Workshop on vortex physics in superconductors in Jinhua (China) in May, 2011.

IV. Work group and course focusing on the physics of grapheme and topological insulators

The course took place at NCTU during the second semester and became an informal seminar on the topic of graphene and topological insulators and its relation to the relativistic (Dirac) physics.

V. Visiting (July 13 – September 30, 2011)I visited Technion (Haifa, Israel) to continue

cooperation with Prof. T. Maniv and Bar Ilan University to continue collaboration and to write papers on vortex physics. Prof. Maniv visited NCTS for one month three years ago.

In Beijing, I continue a collaboration with former NCTS postdoc and visitor Prof. Dingping Li.


Eibun Senaha (Korean Institute for Advanced Study, email: [email protected])


he cold Dark Matter (DM) and the baryon asymmetry of the Universe (BAU) are

open questions in particle physics and cosmology. The former issue can be naturally solved by assuming that the DM is identified with the so-called the WIMP (weakly-interacting-massive-particle) whose couplings to the standard model (SM) particles are the same size of the gauge couplings and whose masses are the electroweak scale (~GeV). Therefore, the electrically neutral and stable particles in the extension of the SM can be the natural candidates for the cold DM.

For the latter problem, many scenarios have been proposed so far, which are basically classified into the two: (1) the baryon number generation above the electroweak phase transition (EWPT) scale which is about O(100) GeV, (2) the baryon number generation during the EWPT. One of the examples of the scenario (1) is leptogenesis which is attractive in the sense that the scenario can be related to the neutrino mass generation mechanism. It is, however, unclear how we test the scenario by the current and/or experiments in the near-future. On the other hand, the scenario (2) which is called electroweak baryogenesis (EWBG) exclusively relies on the known physics and physics that will be tested in the collider, such as the Tevatron and LHC and the low energy experiments such as electric dipole moments (EDMs) measurements that can probe CP violation. (More precisely, it is T violation that is equivalent to CP violation under the CPT conservation.)

My principal research activities at the NCTS in 2010-2011 are on the DM and CP violation that is one of the necessary ingredients for the successful baryogenesis.

In [1] we consider a scenario in which a DM can couple only to the top quark. The analysis is conducted by using the effective Lagrangian approach. By taking the latest phenomenological

constraints on the DM into consideration, we obtain the possible size of the DM-top quark coupling, . If the DM is thermally produced,

0.3-0.6 should hold to be consistent with the observed DM relic density. This limitation is relaxed by assuming that the DM is non-thermally produced. Since the DM exclusively couples to the top quark, the constraint coming from the direct search experiment is rather weak. We found that 30 is allowed. The indirect search, however, give a severer upper bound on , that turned to be around 4-5 in the light of the antiproton flux data of the PAMELA experiment.

We also s tudied the phenomenological consequences of this model.The distinctive signature at the LHC was found to be the +missing transverse energy. By using the appropriate missing ET cut, the significance of the signal , can be substantial ly improved. Therefore, with a O(1), the model can be testable at the LHC.

In [2] the EDMs of the Thallium, neutron, Mercury, deuteron and Radium in the next-to-minimal supersymmetr ic s tandard model (NMSSM) are investigated in connection with the EWBG scenario.

The conventional wisdom says that the complex phase of the coupling λ , which corresponds to the phase of the μ parameter in the MSSM, are severely constrained by the current experimental upper bounds of the EDMs while the phase of κ is basically free of such experimental constraints. However, there is no comprehensive analysis of the EDMs at the 2-loop level.

Here, we conduct the 2-loop analysis by assuming that the phase of κ is the only source of CP violation. This phase appears in the singlino and the singlet Higgs couplings. For the detailed analysis of the NMSSM Higgs sector with CP violation, see , for example, Ref. [3].

Research Activities on Dark Matter and CP violation


At the 1-loop level, the diagrams which involve the charginos or gluinos do not contribute to the EDMs since κ does not enter.

On the other hand, the diagrams in which the neutralinos are participating in loop can yield the nonzero EDMs. However, they would be suppressed if the soft SUSY breaking masses of the 1st and 2nd generation sfermion are greater than about 300 GeV. This observation may be the source of the conventional wisdom that we state above.

At the 2-loop level, we find that the so-called Barr-Zee diagrams can modify the 1-loop results significantly, especially the contributions of the crhomo Barr-Zee diagrams to the down quark can be sizable even in the low β scenario. Because of such contributions, the EDMs of the Mercury, Deuteron and Radium can exceed the current upper bound or the projected bounds (See Fig5 in [2] ) . Impor tan t ly, such EDMs cannot be suppressed in the large sfermion mass limit. In the case of the Mercury EDM, however, there is a significant uncertainty coming from the Schiff-moment calculation. Taking this into account leads to some relaxation of the tension between theoretical prediction and experimental upper bound. Still, it should be noted that the constraint can be marginal in some parameter sets.

In conclusion, there is no definitive EDM constraints on the phase of κ at the moment. However, the 2-loop Barr-Zee corrections can be sizable and cannot be neglected in the EDM calculations. Our analysis shows that the predicted value of the Mercury EDM can reach the current experimental upper bound in some parameter space.

We also find that the future planned EDM searches of the Deuteron and Radium can definitely probe the phase of κ that may be

related to the BAU observed today. The devoted study of the BAU calculation will be given elsewhere [4].

References[1] “The top window for dark matter”, Kingman

Cheung, Kentarou Mawatari, Eibun Senaha, Po-Yan Tseng and Tzu-Chiang Yuan, JHEP 1010, 081 (2010) [arXiv:1009.0618 [hep-ph]].

[2] “Higgs-mediated electric-dipole moments in the next-to-minimal supersymmetric standard model : An appl icat ion to electroweak baryogenesis”, Kingman Cheung, Tie-Jiun Hou, Jae Sik Lee and Eibun Senaha, Phys. Rev. D 84, 015002 (2011) [arXiv:1102.5679 [hep-ph]].

[3] “The Higgs Boson Sector of the Next-to-MSSM with CP Violation”, Kingman Cheung, Tie-Jiun Hou, Jae Sik Lee and Eibun Senaha , P h y s . R e v . D 8 2 , 0 7 5 0 0 7 ( 2 0 1 0 ) [arXiv:1006.1458 [hep-ph]].

[4] Kingman Cheung, Tie-Jiun Hou, Jae Sik Lee and Eibun Senaha, in preparation.


Shulin Sun (email: [email protected])


Research Activities on Plasmonic Metamaterials

am a postdoctoral fellow of the physics division of NCTS at NTU under the

supervision of Prof. Guang-Yu Guo from May, 2010.

I. Summary of my workI will describe my work done in last year in

three sections:

1. We have developed a numerical method based upon the finite element method to calculate the dispersion relation for dispersive, anisotropic, and arbitrary 2D/3D systems. It is a powerful tool to analysis the eigenstates, coupling effect of surface plasmon polarition (SPP) modes in arbitrary systems. This topic is theoretically and experimentally hot. Later we will apply this method to different systems.

Fig.1. Dispersion and electric field patterns of eight SPP modes in double nano metallic cylinder system

2. I have also established a collaboration with Prof. Din-Ping Tsai on some simulation and experimental works. A work about a 3D upright plasmonic “meta-molecules” has been published in Optics Express [1]. It is a breakthrough in this area because they developed a new technique to design 3D metamaterials in optical region. It ensures that people have more powerful ability to realize people's idea in plasmonic metamaterial region. Cons ide r ing tha t I can f ind exce l l en t experimental supports from Prof. Tsai's group, I developed my gradient metamaterial from microwave to optical region. My collaborators and I have designed the gradient samples work ing a t 1 .55um and 750nm. Some interesting experimental results have been measured. Based on this idea, we can design a new kind of SPP coupler with ultra-high efficiency and definite momentum. These advantages are hard to reach for the traditional methods.

Fig.2. Photograph of gradient meta-surface working at 750nm

3. Crystalline microstructures with regular shape as optical microcavities have been attracting


great interests due to potential applications in optical devices [2]. My collaborators with researchers in Fudan University have designed single crystalline ZnO multilayer hexagonal microplates and observed Fabry-Pérot modes in UV and visible spectral range at room temperature. Furthermore, strong UV lasing was obtained in experiments. Considering that it is difficult to distinguish the resonance types and hard to figure out the filed patterns in experiments, FDTD simulation will be a powerful tool to solve all these problems [3].

Fig.3. Reflection spectra based on a slab model (green line) and the real hexagonal microcavity (blue line) calculated by FDTD simulat ion. They per fect ly match the experimental results (red line).

References

[1] Wei Ting Chen, Chen Jung Chen, Pin Chieh Wu, Shulin Sun, Lei Zhou, Guang-Yu Guo, Chinh Ting Hsiao, Kuang-Yu Yang, Nikolay I. Zheludev, and Din Ping Tsai, “Optical magnetic response in three-dimensional metamaterial of upright plasmonic meta-molecules”, Opt. Express 19, 12837 (2011).

[2] F. Qian, Y. Li, S. Gradecak, H-G. Park, Y. Dong, Y. Ding, Z. L. Wang and C. M. Lieber, “ M u l t i - q u a n t u m - w e l l n a n o w i r e heterostructures for wavelength-controlled lasers”, Nat. Mater., 2008, 7, 701.

[3] Hongxing Dong, Shulin Sun, Liaoxin Sun, Weihang Zhou, Lei Zhou, Xuechu Shen, Zhanghai Chen, Jun Wang, and Long Zhang, “Thermodynamic effect induced growth and UV lasing of hierarchical ZnO Fabry-Pérot resonators”, submitted to Journal of Materials Chemistry.

II. Research plan in the coming yearIn recent years, there are two hot areas in

physics community: metamaterials and surface plasmon polariton (SPP). Meta-materials are man-made electromagnetic materials composed of sub-wavelength local resonance structures of electric and/or magnetic type. Now people have more tools to manipulate electromagnetic waves because metamaterials can possess arbitrary values of permittivity and permeability in principle. Now tunable, wide-band, and high frequency plasmonic metamaterials are the dream of people. Following the trend, my work will focus on two topics:

1. Gradient metamaterial working in optical region.

The famous gradient metamaterials are cloaking [1]. The idea is to construct a gradient -index system around the target object which can guide the incident light around it. So far the theory is only applicable to change the propagation direction of a pure PW or a pure SPP. We have developed an idea to convert propagating waves to SPP waves 100% based on a specially-designed gradient system [2]. It has been demonstrated in microwave experiments. Now we plan to apply this idea in optical region. Many applications can be expected, such as an SPP coupler, optical invisibility and absorber;

2. Hybrid-surface-plamon mode.

S u r f a c e p l a s m o n p o l a r i t o n s a r e electromagnetic (EM) excitations coupled with charge oscillations bounded at metal/dielectric interfaces. Its sub-wavelength and local field enhancement effects stimulate many applications such as optical imaging, bio- and chemical- sensors, enhanced Raman and nonlinear optics effect, etc. In the past, people mainly focus on the pure SPP system. The coupling state between SPP and other optical modes will be a new and interesting direction [3, 4]. I have done some work on some semiconductor micro/nano cavities [5, 6]. It might be interesting to put them on the metal surface because the optical modes and SPP happens at the same frequency region. So I plan to study the hybrid-mode coupled between SPP and whispering gallery modes.


References

[1] J. B. Pendry, D. Schurig, D. R. Smith, “Controlling Electromagnetic Fields”, Science 312, 1780 (2006).

[2] Shulin Sun, Qiong He, Shiyi Xiao, Qin Xu, C. T. Chan, and Lei Zhou, “Covert propagating waves to surface plasmon polaritons using gradient meta-surfaces”, to be submitted to Nature Physics.

[3] Rupert F. Oulton, Volker J. Sorger, Thomas Zentgraf, Ren-Min Ma, Christopher Gladden, Lun Dai, Guy Bartal, and Xiang Zhang, “Plasmon lasers at deep subwavelength scale”, Nature 461, 629 (2009).

[4] Xuejin Zhang, Pengwei Wang, Xinzheng Zhang, Jun Xu, Yongyuan Zhu, and Dapeng Yu, “Surface Exciton-Plasmon Polariton Enhanced Light Emission via Integration of Single Semiconductor Nanowires with Metal Nanostructures”, Nano Res 2, 47 (2009).

[5] Hongxing Dong, Shulin Sun, Liaoxin Sun, Wei Xie, Lei Zhou, Xuechu Shen, and Z h a n g h a i C h e n , “ S i n g l e - c r y s t a l l i n e Polyhedral In2O3 Vertical Fabry-Pérot Resonators”, Appl. Phys. Lett. 98, 011913 (2011).

[6] Hongxing Dong, Liaoxin Sun, Shulin Sun, Wei Xie, Lei Zhou, Xuechu Shen, and Zhanghai Chen, “Indium oxide octahedra o p t i c a l w h i s p e r i n g g a l l e r y m o d e microcavities”, Appl. Phys. Lett. 97, 223114 (2010).

III. Attending Conferences2011/08 OCPA7 (Kaohsiung, Taiwan): Oral

2011/05 ICNP2011 (Shanghai, China): Poster

2011/03 APS March Meeting 2011 (Dallas, USA): Oral

IV. Publications[1] Hongxing Dong, Shulin Sun, Liaoxin Sun,

Weihang Zhou, Lei Zhou, Xuechu Shen, Zhanghai Chen, Jun Wang, and Long Zhang, “Thermodynamic effect induced growth and UV lasing of hierarchical ZnO Fabry-Pérot resonators”, submitted to Journal of Materials Chemistry.

[2] Wei Ting Chen, Chen Jung Chen, Pin Chieh Wu, Shulin Sun, Lei Zhou, Guang-Yu Guo, Chinh Ting Hsiao, Kuang-Yu Yang, Nikolay I. Zheludev, and Din Ping Tsai, “Optical magnetic response in three-dimensional metamaterial of upright plasmonic meta-molecules”, Opt. Express 19, 12837 (2011).

[3] Hongxing Dong, Shulin Sun, Liaoxin Sun, Wei Xie, Lei Zhou, Xuechu Shen, and Z h a n g h a i C h e n , “ S i n g l e - c r y s t a l l i n e Polyhedral In2O3 Vertical Fabry-Pérot Resonators”, Appl. Phys. Lett. 98, 011913 (2011).

[4] Hongxing Dong, Liaoxin Sun, Shulin Sun, Wei Xie, Lei Zhou, Xuechu Shen, and Zhanghai Chen, “Indium oxide octahedra o p t i c a l w h i s p e r i n g g a l l e r y m o d e microcavities”, Appl. Phys. Lett. 97, 223114 (2010).


Dan Tomino (Department of Physics, Tunghai University; email: [email protected])

Assistant research scholar, 2008/8/1~2011/7/31

Research Activities on String Theory

uring the period of 2010-2011, my research activity has been devoted to

investigate on a supersymmetric gauge theory based on Lie 3-algebra, and a Yang-Mills type matrix model.

Gauge theory in six-dimension with (2,0) supersymmetry based on Lie 3-algebra

The Lie 3-algebra is an extension of the ordinary Lie 2-algebra. There has been much attention on this algebraic structure in study of M-theory recently. The M-theory is the strong coupling limit of type II A superstring. It is known that the M-theory includes the eleven-dimensional supergravity in its classical limit. And the strong coupling limit of strings in superstring becomes M- theo ry membranes (M2-b ranes ) . The 3-algebraic structure appeared in construction of a low energy effective model of multiple M2-branes with desirable symmetries.

Except for the M2-brane, there is another extended object that has six-dimensional world volume, called as M5-brane. Multiple (non-Abelian) M5-brane system is also important to describe low energy limit of the M-theory as well as the multiple M2-branes. However, it has been known that the world volume theory of multiple M5-branes is difficult to write down. Because the low energy excitation of multiple M5-branes must be a in terac t ing gauge theory wi th (2 ,0) supersymmtry, that contains self-dual 2-form gauge field whose non-Abelian generalization had not succeeded until recently. Last summar, Lamber and Papageorgakis succeeded to write down a non-Abelian generalization (2,0) on-shell supersymmet ry a lgebra in re f . [1 ] . Th i s deve lopment was ach ieved by us ing the 3-algebraic structure.

The on shell supersymmetry algebra provides a

set of field equations on M5-brane world volume. I investigate these field equations by using a 3-ablgebra of infinite dimension, in collaboration with Dr. Shoichi Kawamoto (NTNU) and Dr. Tomohisa Takimi (NTU). We find that the set of field equation has many different interpretations as multiple-Dp-branes, NS5-branes in superstring.theory, and M5-branes in M-theory. We also find that known duality relations among these branes can be reproduced as re-labelings of parameters that describe solutions of the field equation of ref.[1]. At same time, we also observe that in order to get physical interaction between M5-branes, we still need to introduce some new ingredient like non-locality.

This work is published as “Branes from non-Abelian (2,0) tensor multiplet with 3-algebra”, Shoichi Kawamoto, Tomohisa Takimi, Dan Tomino, J Phys A 389304, arXiv: 1103.1223 [hep-th].

Critical behavior of Yang-Mills type matrix model (on going project)

A proposal of non-perturbative definition of superstring theory has been formulated using a Yang-Mills type matrix model, called as IKKT model. In the IKKT model, the spacetime picture dose not exist in its formulation, and this is expected to be an emergent phenomenon in various large N limit (N is the size of matrices) of the matrix model. Therefore it is important to study large N dynamics in the IKKT model. One of basic questions about the large N dynamics is existence of the critical behavior of the matrix model. In the case of one-matrix model that describes a 2D system couples to the 2D gravity, the model is exactly solvable. Once the exact solution is known, the critical behavior of the matrix model is subsequently extracted. On the other hand, IKKT-type matrix model is not


solvable in general. Thus we need to use some approximation method to extract non-analytic behavior of the model.

Currently, I investigate this problem by using matrix renormalization group (RG) approach proposed in ref [2], with Dr. Shoichi. Kawamoto (NTNU). We will apply the matrix RG to Yang-Mills type two-matrix model with a mass term, as a toy model of IKKT-type model. So far, several evidences of non-analytic behavior have been observed. We also apply the matrix RG method to one-matrix model with the φ-4 interaction to compare out results to the known exact solution.

References [1] “Nonabelian (2,0) Tensor Multiplets and

3-algebras” ,Neil Lambert, Constantinos Papageorgakis, JHEP 1008:083, 2010. arXiv: 1007.2982 [hep-th].

[2] “Renormalization group approach to matrix models”, E.Brezin, J. Zinn-Justin, Phys Lett. B 288 (1992) 54, arXiv: hep-th/9206035.


Daw-Wei Wang (Department of Physics, National Tsing Hua University; email: [email protected])


Research Activities on Atomic Physics

s being the NCTS Center Scientist, I have benef i ted f rom the resources and

flexibility of this position to work deeper in my research. Below I outline some important works and/or activities I have done so far since the last summer.

I. Personal ResearchConfinement induced quantum melting and polarization cooling for a 2D dipolar crystal:

My student and I investigate the confinement effects on a two-dimensional mesoscopic self-assembled dipolar crystal trapped in a harmonic potential. The ground-state wave function and energy are calculated by diagonalizing the position fluctuations to second order within the strong-interaction limit. We find that the entropy of a trapped dipolar crystal can be much larger than the entropy in the liquid state at zero dipole moment, indicating a polarization cooling mechanism during the formation of dipolar crystal when the external field is increased adiabatically. Our results therefore have significant applications to the experimental preparation of a self-assembled dipolar crystal using ultra-cold polar molecules.

Quantum Criticality from in-situ Density Imaging:

We perform large-scale quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a two dimensional optical lattice trap and conf i rm an excel lent agreement wi th the benchmarking in situ density measurements by the Chicago group. We further present a general finite-temperature phase diagram for both the uniform and the trapped systems, demonstrating how the universal scaling properties near the

superfluid-to-Mott insulator transition can be observed from the in situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present experiments.

Superfluidity and dimerization in a multilayered system of fermionic polar molecules:

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. We construct an effective Ising-XY-lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized “pseudogap” state with only short-range phase coherence.

Few-Body Bound States in Dipolar Gases and Their Detection:

We consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intra-tube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to many tubes and layers, and outline the implications on many-body physics.

II. ServiceI served as the coordinator of AMO focus

group of NCTS and have conducted the following activities and host following visitors:


Activities

In the May 2011, we held an International Workshop on Ultra-cold Atoms and Molecules in National Tsing-Hua University, organized by Daw-Wei Wang, Shih-Chuan Guo, and our visitor, Miguel Cazalilla. We invited several leading world-class theorists and experimental groups to describe their work on ultra-cold atoms and molecules.

Visitor

I have invited two long term visitors in this year. One is Prof. Miguel Cazalilla, to stay in NCTS from Feb. 15 to May 15. His visit brought a great impact to the AMO community in various ways : Fo r example , P ro f . Caza l i l l a ha s c o l l a b o r a t i o n w i t h m e o n t h e a n a l y t i c renormalization group theory of anisotropic superfluidity at zero and finite temperatures, compared to the numerical quantum Monte Carlo results. We will also continue to collaborate on different subjects in the future.

The second long-term visitor is Dr. Bo Xiong from Institute of Physics of Chinese Academy of Science. Prof. Xiong collaborates with me on exotic Rydeberg atom states in fermionic cold atoms.

III. International CollaborationProf . E . Demler (Harvard , USA) , G .

Shyalpnikov (LPTMS, France), Cheng Chin (Chicago U., USA), and Nikolaj Zinner (Aarhus U., Demark).

IV. Publications[1] Yi-Ya Tian and Daw-Wei Wang*, Europhys.

Lett. 91, 66006 (2010).

[2] Shiang Fang*, Chia-Ming Chung, Ping Nang Ma, Pochung Chen, and Daw-Wei Wang, Phys. Rev. A 83, 031605(R) (2011).

[3] Andrew C. Potter*, Erez Berg, Daw-Wei Wang, Bertrand I. Halperin, Eugene Demler, Phys. Rev. Lett. 105, 220406 (2010).

[4] B. Wunsch*, N. T. Zinner, I. B. Mekhov, S.-J. Huang, D.-W. Wang, and E. Demler, Phys. Rev. Lett. 107, 073201 (2011).


Dr. Yu-Kuo Hsiao

Dr. Wen-Ming Huang

Assistant research scholar (Ph.D., National Taiwan University)

email: [email protected]

Postdoctoral researcher (Ph.D., National Tsing Hua University)


Introducing New Members

am starting from this fall as an assistant research scholar in the physics division of

NCTS after previously being a postdoctoral fellow at the institute of physics, Academia Sinica.

My research interest is mainly focused on high energy physics phenomenology, in particular weak decays and CP violation in B mesons. I am skillful

at programming and numerical analysis with Mathematica and C++. I also pay attention to collider physics related to the Large Hadron Collider at CERN. Currently, I study a series of topics about the semileptonic B decays into a baryon pair, which can be used to test new physics.

fter graduating from department of physics, National Tsing-Hua University in

2008, and two years postdoctoral research under the supervision of Professor Hsiu-Hau Lin, I become a new postdoctoral researcher in the phys ics d iv i s ion o f Na t iona l Cen te r fo r Theoretical Sciences in Jan. 2011.

Currently my interests are in the correlated c o n d e n s e d m a t t e r s y s t e m s , i n c l u d i n g superconductivity, low-dimensional materials and graphene. For research on the superconductivity, I focus on the paring mechanism in unconventional s u p e r c o n d u c t o r s . R e c e n t d i s c o v e r y o f superconductivity in iron pnictides has reignited intense investigations on the unconventional superconductivity. To understand the underlying pa i r ing mechan i sm in th i s new c l a s s o f superconductors, it is important to know the pairing symmetry.

The key to find the pairing symmetry is to understand the effective interactions in iron p n i c t i d e s . I t i s g e n e r a l l y b e l i e v e d t h a t

renormalization group (RG) is a powerful tool to determine the effective interactions for complex systems in low energies. However, due to the lack of analytic solutions for these coupled non-linear differential equations, it is rather subtle to tell which couplings are relevant or irrelevant.

Recently, we propose a new classification scheme to build up the hierarchy of the relevant couplings by a scaling Ansatz found numerically in RG equations. The scaling Ansatz can classify the relevant couplings in hierarchical order without any ambiguity. Next, we would like to develop the functional RG coding to test the scaling Ansatz and building up the effective interaction in iron pnictide superconductors.

In the low-dimensional system part, I recently collaborate with Professor Chung-Hou Chung in NCTU to study the transport problem in quantum dot systems with helical liquid. We hope we can solve the problem in the non-equil ibrium condition.

Introducing New Members -›› III-100

Dr. Hirotaka IriePostdoctoral researcher (Ph.D., Kyoto University, Japan)


started this January 2011 as a new post-doctoral researcher in the physics division

of NCTS after a post-doctoral fellow at National Taiwan University under the supervision of Professor Pei-Ming Ho.

My research areas are string theory and its relevant mathematical physics. String theory was proposed as a universal framework for quantum grav i ty and i s expec ted to un i fy a l l t he fundamental forces in our universe. Although this theory experienced two revolutions in i ts fundamental understanding, it still relies on the perturbative formulation and is not completely formulated from non-perturbative points of view. In particular, our current formulations are not good enough to derive the particle-physics standard model and to predict physical laws for observational cosmology, including dark matter and dark energy. Therefore, my main purpose of th i s research i s to t ry to ge t a comple te fundamental understanding of string theory and eventually find a direct connection with the real world from the first principle.

Motivated by these fundamental objectives, I recently focus on Stokes phenomena in string theory. Mathematically, this is the information which enables us to reconstruct a complete function from a given perturbative series with their all possible non-perturbative effects. In fact, in our current understanding, we know how to

define the all-order perturbative series (from the wor ld-shee t formula t ion) and the i r non-perturbative effects (mostly originated from D-branes and instantons). Therefore, the Stokes phenomenon is the last step toward the non-perturbative completion of string theory, and I expect that this should be a key understanding which binds all the string-theory vacua together to solve the string-theory landscape problem. Along this direction, in collaborations with Prof. Chuan-Tsung Chan in Tunghai University and Mr. Chi-Hsien Yeh in National Taiwan University (i.e. [1,2]), we are now discovering new intriguing results and opening a new direction of string theory!

References[1] C.-T. Chan, H. Irie, C.-H. Yeh, “Stokes

Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models”, Nuclear Physics, Section B 854 (2012) pp. 67-132 [arXiv: 1011.5745 [hep-th]].

[2] C.-T. Chan, H. Irie, C.-H. Yeh, “Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory,” [arXiv: 1109.2598 [hep-th] (43pp)]; a talk in the Gong Show session, Strings 2011, Uppsala, Sweden, June 27-July 2, 2011.

III-101 ‹‹- Introducing New Members

Dr. Yong Tang

Dr. Hiroshi Yokoya

Postdoctoral researcher (Ph.D., Institute of Theoretical Physics, Chinese Academy of Sciences, China)

Email: [email protected]

Assistant research scholar (Ph.D., Hiroshima University, Japan)


started Aug. 2011 as a new Postdoc in the P h y s i c s D i v i s i o n o f N C T S a f t e r

graduating from Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, under the supervision of Professor Yue-Liang Wu. My research interests include Higgs production at the LHC, one-loop correction in many physical processes, gravitation and cosmology.

My past work focused on the one-loop corrections in some physical processes for Higgs particle production at the LHC and also on the gravitational contributions to gauge couplings. Search for Higgs particle is one of the most important goals of LHC at CERN, and it will give us the answer about how the mass is generated. Since there are many theoretical models involving Higgs particles with similar feature, high precision

experiment may play the role to distinguish these models. High precision requires higher loop calculation in quantum field theory and the higher loop involves more Feynman diagrams. Luckily, computer program, such as FeynArts, FormCalc and LoopTools, can speed up the calculation. Gravitational contributions can change the running behaviors of gauge coupling running near Planck scale. This issue can be investigated by t r a d i t i o n a l b a c k g r o u n d f i e l d m e t h o d , diagrammatic calculation, and Vilkovisky-DeWitt’s formalism, using various regularization schemes. Since the gravitational effects on the gauge couplings will dominate over others' contribution, it may unify all gauge couplings with asymptotic freedom.

joined the physics division of NCTS in January 2011, as a visiting research

fellow. Since then I have been working on phenomenological studies for high-energy collider experiments mainly the LHC, in collaboration with Prof. W.S. Hou and Prof. X.G. He of National Taiwan University. My interests are to perform a phenomenological study based on perturbative QCD for various processes, such like top-quark pair production, the 4th generation quark product ion, and the scalar par t ic le production at the LHC.

I have been work ing on the Coulomb summation in the production of colored heavy particles at hadron colliders. For the top-quark pair production, the Coulomb summation brings significant deformation on the production cross-section near the threshold, and a broad resonance formation below the threshold. I developed a Monte-Carlo tool to simulate the top-quark

produc t ion inc lud ing a l l -o rder Coulomb c o r r e c t i o n , w h i c h i s a p p l i e d f o r t h e phenomenological study of the top-quark events near threshold, as well as the background analysis in Higgs-boson production in dilepton+missing-momentum+jets events.

4th generation quarks are, if they exist, expected to have large Yukawa couplings with the Higgs-boson and also the Nambu-Goldstone boson according to their large mass.

Therefore, they can form a bound-state via the Yukawa force. We studied the spectrum of such bound-states and their phenomenology at the LHC; the production cross-section, the decay branching ratio and the possible signature, by assuming degenerated 4th generation quarks. This study would be more emphasized after the experimental survey of 4th generation quarks goes further beyond the unitarity bound.

Introducing New Members -›› III-102

Documents

Words from the Directorncts.ncku.edu.tw/files/Annual_Report/2011_Annual_Report.pdfWords from the Director ‹‹- 2 I which attracted many mathematicians and physicists. Promoting