Lucian M. Ionescu Illinois State University Contact Info & Links Department of Mathematics 1504 N Hershey Rd

Stevenson Hall 312J Bloomington IL 61704-1365 Normal IL 61790-4520 LMIones@ilstu.edu Ph.: 309-438-7167 www.ilstu.edu/~lmiones Fax: 309-438-5866

Education

•Ph.D. in Mathematics, Homological algebra, Kansas State University, August 2000, GPA 4.0, Advisor: Louis Crane; co-advisor: Yan Soibelman. •M.S. in Mathematics, Mathematical-Physics, Kansas State University, 1996, GPA 4.0, Advisor: Louis Crane. •Certified High School Teacher. •M.S. in Mathematics, Operator theory, Bucharest University, GPA 3.75, Thesis advisor: Dan Voiculescu •B.S. in Mathematics, Differential geometry, Bucharest University, GPA 3.4, Thesis advisor: Ion Chitescu •Certified computer analyst-programmer, Dr. Petru Groza High School for Informatics, GPA 3.4.

Teaching and other Work Experience

• Institute des Hautes Etude Scientifique (IHES), Bures-sur-Yvette, France, 2017

(Dec.9, 2017-Feb.9, 2018):

I was accepted for two month visit as a guest of Prof. Maxim Kontsevich (Fields Medalist); research topic: “Periods, Feynman Integrals and Venetiano Amplitudes”.

The research on the structure of Riemann zeros, via the present author’s approach through Weil zeros, led to a concrete project, considered interesting by Prof. Yuri Manin (Max Plank Institute, Germany), as well as by Prof. Maxim Kontsevich (IHES): to study Weil zeros as periods in the sense of Kontsevich, Zagier and Manin, using the global-to-local principle applied to String Theory’s Veneziano amplitudes which formally correspond to Jacobi sums of characters of finite fields.

• Illinois State University, Department of Mathematics, Normal IL, 8/2001- present,

Assistant Professor – Tenure-track appointment: 8/2001-5/2006;

Associate Professor with Tenure: 8/2006-8/2012;

Professor with Tenure: 8/2012-present.

I have taught lower and upper division courses (calculus, differential equations, advanced abstract algebra, advanced abstract analysis), and supervised various individual studies. I have used technology in the instructional process, including web based enhanced course resources.

I continued my research agenda, enhanced as a result of my visit to IHES, submitting internal and external grant proposals (see Grants) and published articles on various topics, some with internal/external collaborators (see Publications and Scholarly Papers).

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To involve faculty in the area of quantization, I organized and participated to the seminar on

TQFTs, focusing on the understanding of their relation with the theory of subfactors, topic of special interest to the Operator Algebra/Analysis Research Group. The seminar continued through the spring of 2002, contributing to the involvement of faculty in mainstream research, being also a place to brainstorm research ideas. The research associated with the faculty seminar resulted in the article submitted [15’], clarifying a subtle issue regarding the place of duality within the axiomatic of TQFT. During the one month of summer research sponsored by ISU (URG/NFIG), an “old dilemma” regarding the interpretation of the mappings associated with a parity quasi-complex was settled, and the relation with n-categories clarified. As another result, the continuation of the research on non-Abelian cohomology and their even closer relation with TQFT become clearer. As another immediate consequence of the above research, a new more involved project aiming to generalize TQFT was conceived. The targeted sponsor is NSF, and the proposal was submitted in November 2002. An essential part of this project represents the goal of the URG/PFIG proposal being submitted concomitantly.

During the academic year, I involved in my research an undergraduate student, namely Lucas Wiman. The collaboration focused on the problem of spectra in additive categories, which aims to implement a mathematical model for the physical idea that paths are the “points” of a space (spectrum) associated to the “category of Feynman diagrams”. Part of the outcome is Wiman’s presentation of the joint work in progress to the ISU Undergraduate Research

Workshop Spring 2002.

My research has been and will always be a source of examples of mathematical theories

applied to science, especially to physics and computer science. I have discussed Maxwell’s equation for electromagnetism with my Calc III students, encouraging interested students in further expanding their knowledge with applications of mathematical models to physics. I have helped another undergraduate student (Sathyam Ravishankar) glimpse to the exciting area of quantum phenomena, including quantum computing and teleportation. Although based on an isolated case, I am confident claiming that students are very receptive and eager to prospect these two applications.

I was a member of the fall 2002 analysis search committee and chair of the fall 2003 search committee, resulting in two successful recruitments for the mathematics department. I am presently member of the Math-Ed Search committee.

I am preoccupied of the continuous improvement of the mathematics curriculum through several course proposals, both for changes as well as for new courses towards the improvement of the quality of the education provided by the mathematics department.

I served as a member of the department council and the mathematics sequence committee.

Besides my past and continuing collaborations with Gabriel Pripoae from Bucharest University and Florin Balasa from University of Chicago, I have fruitful collaborations with my colleagues Fusun Akman and Papa Sissokho from the mathematical-physics group and discrete group, as well as ongoing collaborations with Domenico Fiorenza, University of Rome, Italy. I am prospecting new collaborations, including on a topic of L-infinity algebras with Michael Penkava from University of Wisconsin at Eau Claire.

I wrote a book during the 2005-2006 academic year, The Digital World Theory v.1: An

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Invitation, sketching the mathematical-physics implementation of a quantum theory capable of unifying the standard model and gravity, based on a quantum physics and computer science unifying point of view.

I designed new courses, as part of the graduate program of the Mathematics Department, to update the curriculum in view of the recent progress in science, e.g. nanotechnology, quantum computing: Introduction to Quantum Computing (Mat 389.68), Introduction to Topology and

Differential Geometry, Topics in Mathematics with Applications to Mathematical-Physics and

Computer Science. I also taught Mat 389.68 and the students were interested and enjoyed the pictorial and intuitive aspects, characteristic to topology and geometry.

During 2006-2007 I wrote the second volume from DWT series, “Q++ and a Non-standard model”, explaining the need for a more systematic development of a mathematical-physics language to program quantum physics (Q++), together with implementation considerations for a new paradigm for the physics of elementary particles, as a prospective alternative to the current Standard Model. The book was self-published at Lulu and at Trafford Publishing Co.

There are two reviews for the first volume, but it is too soon to expect feedback regarding the 2nd volume.

Between 2007 and 2010 I developed QID, explained the relation with the standard model and proposed a new paradigm for a Grand Unified Theory based on the Hopf monopole bundle as a gauge “group” with Gravity as a deformation of “Electromagnetism” (QID/electro-weak theory) as a result of charge violation due to the non-triviality of the bundle structure.

• ISU, Summer Research Academy, June 25-29, 2012.

Another successful integration of mathematics, physics, biology and technology during the annual research academy, was this time achieved largely because of a group of enthusiastic high school students, eager to learn way above their required level:

http://my.ilstu.edu/~lmiones/Summer%20Research%20Academy/Summer%20Research%20Academy%202012.html

Checkout the website they have developed and how they have explained their work:

http://cemast2012.webs.com/

• ISU, Summer Research Academy, June 20-26, 2011.

http://cemast.illinoisstate.edu/students/high_school/isra/index.shtml

http://tv10.illinoisstate.edu/wp/tag/illinois-summer-research-academy/

It is time to integrate Mathematics with Sciences at the current level attained by technology: Quantum Computing, non-linear optics etc. Invited by the Center for Mathematics, Science and Technology, I taught the Mathematical-Physics component of the Summer Research Academy 2011.

http://my.ilstu.edu/~lmiones/Summer%20Research%20Academy/Summer%20Research%20Academy%202011.html)

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• Institut des Haute Etudes Scientifiques (IHES), Bures-sur-Yvette, France,

Visitor, 10/9-11/9, 2009.

During my visit I made substantial progress with the implementation of the Digital World Theory; it is a universal mathematical-physics language for modeling complex evolving systems, classical or quantum, from a computer science perspective. I had the occasion to interact with my host professors Maxim Kontsevich and T. Damour, and also with other visitors present at IHES, notably with Graeme Segal.

• University of Rome, La Sapienza, Rome, Visitor, 10/30-11/2/2006. I was a guest of my collaborator D. Fiorenza. The presentation raised a considerable interest in

Feynman Processes.

• Institut des Haute Etudes Scientifiques (IHES), Bures-sur-Yvette, France,

Visitor, 8/27/2006-10/27/2006.

Various discussions with young researchers allow establishing new contacts with possibly future collaborators. M. Kontsevich seemed interested in the new ideas around Feynman Processes.

• Bucharest University, Bucharest, Romania, Visitor, 6/15/2006-7/15/2006 The conference on Feynman Processes suggested the need of a one week future workshop (summer school) to allow a more detailed exposition of the subject (Plan for 2007).

• Bucharest University, visitor, 5/10/2004-6/10/2004. I was a guest of the Geometry Department of the mathematics department. The visit centered on the connections between deformation quantization and space-time geometry models. I was invited to present my current work and I have presented the above topic to interested faculty members, in view of a possible collaboration; ample discussions followed the presentation, notably with the internationally renowned professor of mathematical-physics Prof. Costache Teleman on the different approaches to quantization, including the C*-algebra / French school trend. I have participated to the conference series by Jean-Pierre Serre. Together with G. Pripoae, we have planed a collaboration aiming to study the Hopf algebra structure in deformation theory with techniques imported from Lie group theory.

• Institut des Haute Etudes Scientifiques - IHES Bures-sur-Yvette, France,

Visitor, 9/15/2002-11/15/2002.

I have worked on a research project on the mathematical structures of renormalization centered on the Hopf algebra approach initiated by D. Kreimer and developed in collaboration with A. Connes (see bibliography). The project was started together with M. Marsalli and benefited from discussions with K. Kremnizer.

I have also started a study of the coefficients of deformation formulas (L∞-morphisms) with applications to perturbative QFT (Feynman expansions). The idea was found interesting by M. Kontsevich, and includes an algebraic approach to his generalization of periods on algebraic varieties (see bibliography). We have also discussed my current projects on generalized cobordism categories and TQFTs (see NSF grant proposal 2002). I have participated to IHES seminars (the mathematics, physics) and various workshops at IHES, and Institute Henri Poincare, Paris.

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• University of Northern Colorado, Mathematical Sciences Department, Greeley, CO,

8/2000-5/2001, Assistant Professor in the Department of Mathematical Sciences.

I have taught lower and upper division courses (calculus, topics in calculus, numerical analysis, seminar in mathematics). I have used technology in the instructional process. I used Mathematica in the Calculus course as computational software for the laboratory projects. The implementation of the major algorithms corresponding to the numerical analysis lab was done in Mathematica as well. The students understood that a broader programming experience will help them in the future, although the aim was a better understanding of the algorithms and not just the ability to execute them. The natural hierarchical structure was emphasized, justifying a top-down design approach to implementations. I also used WWW located resources to enhance teaching efficiency (course related information, study guides, sample tests, “virtual office hours” etc.). I proposed the implementation of an automated homework grading, testing and practice system to further assist students and offer them additional and immediate feed-back. As a byproduct it enhance instructor’s productivity, allowing more quality time spent for teaching and one-to-one student help. I enjoyed managing and maintaining a set of LAN laptops, technology destined to be integrated into pertinent courses. I used them as additional student resources for the numerical analysis lab, allowing the students to work outside the lab, resulting in a broader time-window to work on their projects, as well as an other opportunity to experience the use of technology. I participated to the training of the Putnam competition team and to the math-education seminar. I am planning a mathematical-physics and computer science seminar for the Spring semester, aiming applications of path quantization and Feynman diagrams to quantum computing. I have contributed with service to the department, and continued my research agenda. I initiated a “restoration project” of “Pursuing Stacks” by A. Grothendieck into a TeX file as part of a collaboration with an undergraduate student. My interests on non-abelian cohomology directed me towards homotopy theory and weak n-categories. I also planed a visit to Max-Planck-Institute to the summer workshop on algebraic geometry organized by Professor A. Rosenberg.

• Kansas State University, Mathematics Department, Manhattan, KS, 1994-2000,

Teaching Assistant, Organizational Assistant and Master GTA.

My teaching experience is very broad, continually achieving high scores on student evaluations, confirming my ability to communicate effectively with students. I have taught both upper and lower level classes as well as high school courses.

I have extensive instructor experience. I taught various undergraduate courses: College algebra, Trigonometry, Calculus (205, 210, 220-222), Elementary differential equations.

I have successfully designed and directed lower division courses, including lecture and recitation: Calculus, General calculus and Linear Algebra, Technical Calculus and Elementary Differential Equations.

I have experience using technology in mathematics courses. I used MatLab and WWW based Java scripts in the E.D.E. laboratory to assist students in the understanding of differential equations, being comfortable with technology-based mathematics education.

I have continually achieved high scores on the student evaluation process.

As a Master GTA, I served as a resource for mathematics graduate students who have questions about teaching and I helped the Department Head implement the speakers program, which includes colloquia, conferences, and endowed lectures. I also helped the Director of

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Undergraduate Studies coordinate the daily and final help sessions. I was also a member of the mathematics Olympiad committee.

I designed and implemented in C++ a PC version of the student evaluation tabulation program. It incorporates a database with faculty, GTA and courses information leading to a faster and easier processing of the evaluations. Subsequently adapted to fit the GTA communication surveys, allowed to administer, tabulate and follow-up these surveys in-house, as well as cutting costs and eliminating delays due to having to have Planning and Analysis process/tabulate the questionaire results.

• National Institute for Research and Development in Informatics (I.C.I.), Bucharest,

Romania, 1988-1994 - Principal Research Scientist III.

I conducted and participated in various computer science research projects in solid modeling, finite element method, computer assisted design. I also participated in mechanical engineering and robotics projects (design, specifications and implementation).

• Designed and implemented a formal computational system with numerical and graphical capabilities, for the study of the curvature of Lagrangean systems.

• Coordinated and participated in a project consisting in the implementation in C++ of the graphical standard PHIGS (Programmers Hierarchical Interactive Graphical System)

I was director of the research teams on the following projects:

• Dynamical systems simulation;

• Toolbox for 3D modeling and visualization;

• Simulation of ergodic systems;

• Integration of CSG models into PHIGS standard.

Throughout this appointment, I have continually improved my background in quantum theories and I have participated in international summer schools of physics, on operator methods in quantum mechanics and string theory.

• Institute for Computational Technology (I.T.C.), Bucharest, Romania, 1985-1988 -

Research Scientist. I have extensive research experience with algorithmic and computational mathematics as a

researcher in a computer science research institute. I worked in a computer graphics department, participating to various projects in CAD and CAM. We developed modules for graphical interfaces, solid modeling and 3-D geometric relational data bases.

In 1986 I presented several lectures on semi-Riemannian geometry in the Gheorghe Vranceanu mathematics seminar at Bucharest University. I was interested in general relativity and the applications of semi-Riemannian geometry to cosmology, particularly to causality and singularity theorems.

• High School, Romania, 1982-1985, Teacher. I taught high school level mathematics and physics. I was interested in operator theory

applications to quantum mechanics.

Research interests

Currently (2014-2015) I am investigating the duality between prime numbers and Riemann

zeros (Riemann spectrum). After (re)discovering the POSet structure of the prime numbers [33]

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(related to Pratt trees1975, in his work on primality tests), I investigated the correlation between Riemann zeros, which led to the idea that these are related to Weil zeros (see Weil Conjectures). During 2015, I gathered strong evidence of the (suspected) link between Riemann zeros and Weil zeros (while enjoying learning the basics of algebraic number theory). The resulting main question is: in what sense the (co) POSet of splitting of rational primes, which is controlled by the POSet of primes, is dual to the latter?

Computational investigations were done using a self-made tool-box of SAGE programs. In the 2010-2013 transitional period, following the formulation of the DWT [20], [25], my

research aimed to reformulate QFT, CFT, string theory etc. as Quantum Information Dynamics on Feynman categories modeling causality, and using methods of homotopical and homological algebra. Around 2013 I finally realized, in a concrete way, that the “Ultimate Physics Theory” is Number Theory, in a broader sense, with the world of p-adic numbers dominating the landscape. Soon after, I realized that the key fact to be explained by an “ultimate unifying theory” is the fine structure constant (approx. 1/137), which I conjectured should be a square-average of sizes of finite strings (primes; size of the “total Foch-space” of basic finite fields), explaining at the same time the structure of the spectrum of the Hydrogen atom.

This led to (the never-ending?) story of chasing the Riemann Hypothesis … In the period 2013-2016 I studied the Riemann Hypothesis from the Analytic point of view,

and then realized there is a better approach via Algebraic Number Theory, specifically via Weil zeros (Weil Conjectures; RH was proved in finite characteristic).

In 2017 I started the study of Periods, following the work of Kontsevich, Zagier, Schnetz, F.

Brown and others. This is a new direction in Mathematics, yet strongly connected with Quantum Physics and, most likely connected to RH too. This topic will be pursued at the upcoming visit to IHES, benefiting from advise from M. Kontsevich, A. Connes and CNSR researchers.

…… My general mathematics research interests and “tools”, include deformation theory and its

applications in mathematical-physics (geometric and deformation quantization, renormalization). I have research interests in category theory and homological algebra. I am interested in applications of ideal theory to additive categories and to spectra of categories, with application to physics and TQFTs.

I have done research on singular connections and foliations semi-Riemannian manifolds and

I have been interested in applications of semi-Riemannian geometry to cosmological models, causality and singularity problems in general relativity. I also have interests in formal computational systems and in mathematical modeling in computer science.

In my doctoral dissertation I proposed a definition of nonabelian group cohomology spaces

in all dimensions, and coinciding in low dimensions with the usual cohomology spaces. It is based on the notion of parity quasi-complex: a sequence of objects and pairs of morphisms, thought of as the positive / negative boundary, and verifying a technical condition. The parity quasi-complex associated with a group is obtained from the corresponding free semi-simplicial group. In the abelian case, taking the difference of the boundary maps yields the bar construction. It is proved that parity quasi-complexes give the cohomology of monoidal

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categories. I constructed a functorial correspondence between groups and monoidal categories, compatible with the corresponding parity quasi-complexes. This constructive approach suggested some relations to homotopy theory, via categorification and classifying space of a category. They are discussed in my research statement. A time list of research topics follows next.

The “Bigger Picture” Research

2016-2020: Jacobi sums are discrete Veneziano amplitudes … but concrete results and published articles are needed: “Publish or Perish”! So, this line of research was set on hold! Going to Paris to get advise from the Masters! Periods are generic at the core of Riemann Zeros (Motives as universal cohomology summands). At the same time I understood how Gravity as a deformation of EM can be obtained from “fractional charges” of the Electro-Weak Theory; but is it quantum Slq(2;C) at roots of unity, or changing coefficients to cyclotomic integers (quantizing the natural way the qubit) also yields what quark flavors are!? Must learn the Standard Model meanwhile!

2011-2015: The essay on Gravity clarified that one needs to understand the modes of vibration of the qubits: should be prime “stringy” modes, and somehow related to finite fields Fp … do these form the Riemann Spectrum!? The research into the structure of Spec Z (rational primes) and their dual spectrum (Riemann Hypothesis) begun. The weil zeros should be the “local picture”, hence the importance of studying Jacobi sums.

2009-2010: Incorporating Gravity as a deformation of QID; the correspondence between QID, as an SU2-Yang-Mills Gauge Theory with the electroweak model of Weinberg and Salam. Proposed the Hopf monopole bundle (one of the many conceptual faces of the qubit) as the unifying gauge “group”; it fits naturally with the idea that Gravity is a deformation of Electromagnetism (or electro-weak theory).

2007-2009: Developing Quantum Information Dynamics as a theory/language describing a unified picture of classical and quantum physics. The concept of Infotronics was introduced.

Summer 2007: I have wrote the 2nd volume for The Digital World Theory, representing the documentation specification phase: quantum programming language and implementation considerations.

Fall 2006 & Spring 2007: Quantum Information Dynamics (see current research statement and publications);

Spring 2006: The connections between mathematical-physics and computer science regarding QFT, graphs homology etc., start to bloom: DWT v.1 is ready (“beta release“, on a web site near you ☺). Looking forward to the IHES visit …

Postgraduate School

2005: Fruitful internal and external collaborations (see publication lists).

Fall 2004: The combinatorial approach to coefficients project gained another member within the department: Papa Sisshoko. Several joint articles are under preparation.

On the homological/homotopical algebra side, the problem of constructing L-infinity structures from higher derived brackets is under joint investigation with Fusun Akman. The work with the my other two collaborators mentioned below is benefiting from discussions on these deeply related problems.

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Spring & Summer 2004: I continued the investigation of Feynman cocycles, which provide the right coefficients of a star-product in deformation quantization, adopting a combinatorial point of view within the Hopf algebra framework. The web published article attracted Domenico Fiorenza as a collaborator. We are currently preparing a joint article on star-products built on graphs without circuits.

Fall 2003 & Spring 2004: Applying Hopf algebra techniques to deformation quantization; Spring & Summer 03: I have completed two articles concerning non-abelian cohomology, including results sponsored by ISU/URG, and finished two projects started at IHES. The first project, which I regard as a a continuation of Kontsevich work on deformation quantization of Poisson manifolds, proposes an “axiomatic” of Feynman integrals, obtaining a result relating the cohomology of Feynman graphs and L-infinity morphisms. The second article, on renormalization, relates two main avenues towards quantum field theories: the one based on bialgebra deformation quantization and the one based on Feynman integrals (via renormalization).

F03: Cohomology of Feynman graphs and perturbative QFT (see list of publications).

S03: Focused on perturbative QFT, L-infinity algebras and non-abelian cohomology (see publications).

F02: I have worked on a research project on the mathematical structures of renormalization centered on the Hopf algebra approach initiated by D. Kreimer and developed in collaboration with A. Connes (see bibliography). The project was started together with M. Marsalli and developed in collaboration with K. Kremnizer.

I have also started a study of the coefficients of deformation formulas (L∞-morphisms) with applications to perturbative QFT (Feynman expansions). The idea was found interesting by M. Kontsevich, and includes an algebraic approach to his generalization of periods on algebraic varieties (see bibliography). We have also discussed my current projects on generalized cobordism categories and TQFTs (see NSF grant proposal 2002).

U02: A research project to implement TQFTs corresponding to a categorical version of deRham theory was proposed as an NSF grant.

S02: Clarifying the concept of duality within the framework of TQFTs yielded a symmetrical reformulation of Frobenius algebras.

F01: Started to study subfactors as a source of tensor categories for TQFTs.

S01: I discovered a homotopical interpretation of the nonabelian cohomology based on parity quasi-complexes.

F00: @#$! (i.e. no time for research)

Graduate School

S:00: Research break (Job hunt instead)

F’99: I begun studying the spectra of additive categories in terms of ideals and the relation with the existing definitions, advised by A. Rosenberg.

My future research plans on the possible use of Quillen’s techniques of homotopy theory to nonabelian cohomology were included as part of a grant proposal with Yan Soibelman as principal investigator.

A former project on non-associativity as curvature and an alternative approach to noncommutative geometry through formal differential geometry [12] was finished, benefiting

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from the remarks of J. Stasheff.

U’99: Some thoughts on the difficulties of quantizing gravity and the relationships between noncommutative geometry and quantum physics were gathered in the essay [11].

S’99: After finishing writing the Ph.D. thesis, I investigate the relationship between parity quasi-complexes and homotopy theory, with support from J. Maginnis. The research on the correspondence between set theoretical notions and category theory concepts, motivated by the correspondence between the cohomology of monoidal categories and nonabelian group cohomology, was finalized as [1,13]. It benefited from the discussions with Saunders MacLane. The homological algebra point of view regarding parity quasi-complexes and the relationship to Giraud-Grothendieck approach to nonabelian cohomology is addressed in [14].

1998: The preliminary report [15] on the parity principle and its application to nonabelian cohomology of monoidal categories and group cohomology proves the compatibility with the usual definition of nonabelian group cohomology in low dimensions and constitutes the core of the Ph.D. thesis. The category theory support was provided by my Ph. D. advisor Luis Crane. Discussions with D. Yetter are appreciated.

1997: The research project on deformation of Poisson manifolds and the formality conjecture suggested by my coAdvisor Yan Soibelman is abandoned (I wasn’t ready I guess!).

1996: A categorical approach to quantization of UEAs through deformation of braidings is investigated. The correspondence between the categorical coherence conditions and their simplicial interpretation is investigated under the supervision of Louis Crane, as thesis advisor. The goal is to understand the Pachner moves on the topological side and the corresponding coherence conditions on the categorical side, and involved in the construction of TQFTs and quantum invariants of manifolds.

1992 Singular distributions on semi-Riemannian manifolds were investigated. For a regular distribution, several classes of associated linear connections are known. These connections contain intrinsic information concerning properties of the distributions: integrability, integral manifolds etc. It is the aim of [3] to investigate what part of this theory survives in the case of singular distributions.

1990: Non-differential foliations in semi-Riemannian manifolds are also investigated. Some preliminary results are obtained in [5]. In [4] a muti-tasking implementation of the GKS graphic standard is presented. The portability on various graphical platforms is analyzed.

1985-1990 I have done research in computer science, particularly in solid modeling with applications to computer graphics. I have designed and implemented mathematical models as part of various software projects in CAD, CAM, CAE. I participated at the implementation of the graphical standards GKS and PHIGS.

1982-1985: A continuous calculus in two variables for a pair of self-adjoint operators commuting modulo trace class operators is investigated [20]. I was interested in the applications of operator theory techniques to quantum mechanics.

1981: Differentiable vector-valued measures are studied in [21], in relationship to the Krein-Milman property. A class of Banach spaces without the Radon-Nycodim property is identified.

Ph.D. Level Courses Completed

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•Low dimensional Topology - David Yetter.

•Representation theory; BN-pairs - Zongzhu Lin.

•Algebraic Topology - John Magginis.

•Riemann Surfaces - Zongzhu Lin

•Homological Algebra (I, II) - Zongzhu Lin.

•Cohomology, sheaves and categories - David Yetter.

•Spin geometry; Atiyah-Singer index theorem - Fan-Bing Wu.

•Quantum Groups - Yan Soibelman.

•Knots, Invariants and Braided Categories - David Yetter.

•Topics in Geometric and Deformation Quantization - Yan Soibelman.

•Topological Quantum Field Theory; Topics in Geometry and Quantum Gravity - Louis Crane.

•Introduction to Algebraic Geometry (I, II)- Yan Soibelman.

•Topics in Deformation Theory - Yan Soibelman.

•Topics in mathematical-physics: KP-equations and τ functions; 2D-gravity; - Yan Soibelman.

Post Graduate School Courses Taken Phys 387 Topics in Mathematical Physics, Instr. Niel Christensen, Fall 2017.

Publications (Published or Pending)

2017-Present

[1]* L. M. Ionescu, R. Sumitro, Periods and Applications, https://arxiv.org/abs/1708.09277; *submitted to the journal Involve, Aug. 2017.

[2]* L. M. Ionescu, A statistical study of the Riemann zeta function zeros, *submitted to Crelle’s

Journal, Aug. 2017. [3] L. M. Ionescu, On Prime Numbers and The Riemann Zeros, Journal of Advances in Applied

Mathematics, Volume 2, Number 4, October 2017, PP. 208-219, Pub. Date: Aug. 17, 2017, DOI:10.22606/jaam.2017.24002

[4] L. M. Ionescu, A holistic approach to quantum physics, article 9401292, American Association for Science and Technology Communications, Vol.4 , No. 4, pp. 19-26, Sep. 14, 2017; http://www.aascit.org/journal/archive2?journalId=940&paperId=5323

[5] L. M. Ionescu, Quantum Relativity: an Essay, Physics Essays, Vol. 30, Issue 4, Pages 308-313, 2017, http://physicsessays.org/browse-journal-2/product/1591-15-lucian-m-ionescu-quantum-relativity-an-essay.html .

[6] L. M. Ionescu, A discrete analog of de Rham cohomology on finite abelian groups as manifolds, accepted for publication in JP Journal of Algebra, Number Theory and Applications, (ISSN: 0972-5555), Ref. No.: PPH-1705128-ANT, Aug. 18, 2017.

[7] L. M. Ionescu, On the Arrow of Time, Scientific Pub., Theoretical Physics, Vol.2, No.3, Sept. 2017, pp.115-123, DOI: 10.22606/tp.2017.23002

[8] L. M. Ionescu and Mina M. Zarrin, Lattice Models of Finite Fields, Advances in Pure Mathematics, Vol.7 No.9, September 2017, PP. 451-466.

Between 2006-2016

[1] “A natural partial order on the prime numbers”, Notes on Number Theory and Discrete

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Mathematics, Volume 21, 2015, Number 1, Pages 1-9; arxiv.org/abs/1407.6659, 2015 [2] “Remarks on Physics as Number Theory”, Proceedings of the 19th National Philosophy Alliance

Vol. 9, pp. 232-244; http://gsjournal.net/Science-Journals/Essays/View/3617, 2011. [3] “On Super-Symmetry, Anti-Gravity and Free-Energy”, 2011,

http://www.virequest.com/Ionescu_SuperSymmetry-AntiGravity-FreeEnergy.v3.pdf, Proceedings of the National Philosophy Alliance Vol.8, pp.283-288.

[4] “From Lie Theory to Deformation Theory and Quantization”, Int. J. for Pure and Applied Mathematics, Vol. 58, No.2 (2010), pp.209-230; arXiv:0704.2213.

[5] “The Feynman Legacy”, Int. J. Pure and Appl. Math., Vol.48, No.3, 2008, pp.333-355. [6] “Perturbative quantum field theory and integrals on configuration spaces”, Surveys in

Mathematics and Its Applications, Vol.3 (2008), 79-110. [7] “A Hopf algebra deformation approach to renormalization”, with M. Marsalli, Applied Sciences,

Vol. 10 (2008), pp.107-114. [8] “Q++ and a Non-Standard Model”, ed. Lulu & Trafford, ISBN: 978-1-4251-3492-1, pp. 133,

2007 (self-published). [9] “A canonical semi-classical star-product”, with Papa Sissokho, J. Generalized Lie Theory and

Appl., Vol.1 (2007), No.2, pp.117-128 [10] “The search for a new equivalence principle”, Scientific Journal International, Journal of

Physical Sciences, Vol.1, No.1, 2007, pp.1-12; arXiv:0705.1116v1. [11] “A Survey of Huebschmann and Stasheff's Paper: Formal solution of the master equation via

HPT and deformation theory”, with F. Akman, Int. J. Pure and Applied Mathematics, Vol. 37, No.3, pp.367-394, 2007; arXiv:0704.0432.

[12] “From operads and PROPs to Feynman processes”, JP Alg. Number Theory and Applications, Vol. 7, No.2, pp.261-283, 2007; math.QA/0701299

[13] “The Digital World Theory v.1: An Invitation!”, Olimp Press, ISBN: 973-7744-39-x, pp.225., 2006 (self-published).

Before Tenure (2001-2005) [1] “Higher Derived Brackets and Deformation Theory I”, with Fusun Akman, Journal of y,

Homotopy and Related Structures, Vol. 3 (2008), No.1, pp. 385-403; math.QA/0504541. [2] “On deformation theory and graph homology”, with Fusun Akman and Papa Sissokho, J. Algebra

Vol. 310/2 (2007), pp.730-741; math.QA/0507077. [3] “Graph complexes in deformation quantization”, with Domenico Fiorenza, Letters in

Mathematical Physics, Vol. 73, No.3, September 2005, p.193-208. Extended version: http://xxx.lanl.gov/abs/math.QA/0505410.

[4] “A combinatorial approach to coefficients in deformation quantization”, Annals of Bucharest University, Proceedings of the G. Vranceanu conference, 2005, editor G. Pripoae, p.77-96; http://xxx.lanl.gov/abs/math.QA/0404389.

[5] “Perturbative Quantum Field Theory and L∞-Algebras”, Advances in Topological Quantum Field Theory, Proceedings of the NATO ARW on New Techniques in Topological Quantum Field Theory, editor J. Bryden, Kluwer Academic Publishers, 2004, p. 243-252.

[6] “A note on duality and Frobenius algebras”, J. Knot Theory and its Ramifications, 2004, Vol. 13. No. 8 (December 2004), 1-8.

[7] “Non-abelian cohomology via parity quasi-complexes”, Homology, Homotopy and Applications, Vol. 6, No.1, pp. 49-58, March, 2004; xxx.lanl.gov/abs/math.CT/0108147

[8] “Remarks on quantum theory and noncommutative geometry”, Int. J. Pure and Applied Math., Vol.11, No.4, 2004, pp.363-376.

[9] “Cohomology of Feynman graphs and perturbative Quantum Field Theory”, Focus on Quantum

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Field Theory, Nova Publishers Inc., O. Kovras (editor), ISBN: 1-59454-126-4, 2004, 17 pages; math.QA/0506142

[10] “Red-Black Interval Trees in Device-Level Analog Placement”, in collaboration with F. Balasa, S. Maruvada, K. Krishnamoorthy, IEICE Transactions, Vol.E86-A No.12 pp.3127-3135, 2003/12.

[11] “Categorifying the bar resolution”, JP Journal of Algebra, Number theory and Applications, Vol. 3(3) 2003, pp.337-350.

[12] “Non-associative algebras: a Framework for Differential Geometry”, Int. J. Math. Math. Sci.., Vol. 2003, No.60.

[13] “Categorification and Group Extensions”, Appl. Cat. Str. 10 (2002), 35-47; math.CT/9906038 [14] “On ideals and homology in additive categories”, Int. J. Math. Math. Sci, Vol. 29, No.8, 2002;

lanl.arXiv.org/abs/math.CT/9906039. [15] G. Pripoae, L. Ionescu, “Singular Distributions and Associated Connections”, Classical analysis

(Kazimierz Dolny, 1991), 219-223, World Sci. Publishing, River Edge, NJ, 1992. [16] L. Ionescu, C. Pribeanu, “A multi-tasking implementation of the GKS standard”, Romanian

review of informatics, No.2, 1991. [17] L. Ionescu, G. Pripoae, “Some Aspects Concerning Non-differentiable Foliations in semi-

Riemannian Manifolds”, Proc. 21-st Conf. on Differential Geometry and Topology, Craiova, Romania, 1990.

[18] I. Cimpeanu, L. Ionescu, “Spaces analysis techniques based on bodies illumination”, Proc. Conf. CAD, I.C.I., Bucharest, 1986.

[19] I. Cimpeanu, C. Ionescu, L. Ionescu, V. Ionescu, “BUILDSTAR: An interactive graphical system for CAD in architecture and constructions”, Proc. Conf. on CAD, I.C.I., Bucharest, 1985.

Publications - Scholarly Papers or Submitted for Publication

Since Tenure

[1] L. M. Ionescu, N. Christensen, BCFW recursion method and Hopf algebras of graphs, work in progress, 2017.

[2] “A SAGE Exploration of Riemann zeros”, presentation and SAGE programs, 2015.

[3] On Riemann Zeros and Weil Polynomial, 2015 [4] On Weil Zeros, 2015

[5] On Weil Conjectures, 2014 … (Several other drafts – TBA; together with 7 boxes of annotated research articles and hand-written notes) …

[9] “On a Generalized Lorentz Force”, General Science Journal, 2011, http://www.wbabin.net/Science-Journals-Papers/Author/471/Lucian%20M.,%20Ionescu

[10] “On some points of mathematical-physics from a computer science perspective”, 2010, The Journal of General Science: http://gsjournal.net/ntham/ionescu.pdf .

[11] “Infotronics: Theory and Experiment”, self-published at Lulu.com, Aug. 2009.

1981-2000 [5] “Cohomology of monoidal categories and nonabelian group cohomology”, Ph.D., 2000. [4] “State Sum Invariants of 3-Manifolds”, MS report, KSU, 1996. [3] “PHIGS versus GKS for CAD systems”, I.C.I. report, Bucharest, Romania, 1989. [2] “Pairs of Operators Commuting modulo C1”, M.S. thesis, Bucharest University,1982. [1] “Banach Spaces with the Radon-Nicodym Property”, B.S. thesis, Bucharest University, 1981.

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Presentations (Internal Events – for details please see my homepage at ISU)

ISU Undergraduate Colloquium

• Complex Analysis and Applications, Oct., 2017 (link: ISU Web page).

ISU Mathematics-Physics Seminar, 2010-present, http://my.ilstu.edu/~lmiones/MathPhysics_seminar.html see also ISU Webpage. ISU Algebra Seminar, 2011-2014, http://my.ilstu.edu/~lmiones/alg_sem.html ISU Algebra Seminar, Fall 2011

• Oct. 4 & Oct. 7 Multiplicative Number Theory and Algebraic Quantum Groups.

• Nov.15 Algebraic Quantum Group of Rationals.

ISU DiscMath Seminar Fall 2011

• Oct. 27 On the Structure of Prime Numbers ISU Mathematical-Physics Seminar, Spring 2011

• 2/10 The "Biggest" Question in Physics & Flows on Graphs from a Homological Algebra viewpoint"

• 2/17 Introduction to Electric Circuits (or whatever else "flows") (scanned notes) • 2/24 Primer of homological algebra; main example: graphs and Kirchoff's Laws (see 3rd Talk)

• 3/3 Linear resistive circuits, and conceptual links (serial-parallel graphs, boolean functions, Mobius transformations etc.)

• 3/24 Review and 12.1 continued (Maxwell's methods);

• 4/7 Hodge decomposition of electric circuits • 4/14 Discrete Laplacian and discrete Poisson equation

• 4/21 Some MS-Thesis level questions of discrete mathematics: relating Hodge star operator and Maxwell's Methods for EC

• 4/28 EC / Maxwel Methods: conclusions and interpretations; planning for next semester (last MP-seminar for Spring).

ISU Algebra Seminar Fall 2010 • Sept.14 Hodge Theory on Projective Manifolds and physics motivation.

• Oct. 12 Overview of Hodge Theory. ISU Algebra Seminar Spring 2009

• 4/2 Algebraic Graph Theory - Ch. 4: Cycles and Cuts, and their relation with homological algebra and dynamics.

ISU Algebra Seminar Fall 2008

• 8/26 On a few points of homological algebra

• 11/11 Overview of Deformation Quantization, Part I.

ISU Algebra Seminar Spring 2008

• 4/10 From Lie Theory to Deformation Theory, Part I: Lie Theory

• 1/31 Rota-Baxter Algebras and Lie groups decompositions

ISU Algebra Seminar Fall 2007

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• 9/6 Rota-Baxter Algebras

• 9/20 Spitzer’s identity

ISU Physics Seminar 9/7/2007: Discrete Models in Quantum Physics ISU Algebra Seminar Spring 2007

• 3/31 Universal differential forms I

• 4/11 Universal differential forms and higher order differential operators.

ISU Algebra Seminar Fall 2006

• 11/30 The Feynman Legacy: past, present and future

• 12/7 Introduction to PROPs and operads, with applications to physics.

ISU Algebra Seminar Spring 2006

• 2/23/06 On quantum groups and quantization

• 4/6/06 From Lie theory to quantum dynamics

• 4/20/06 Review of Heisenberg groups and their representations (I)

• 4/27/06 The m-representation of a Heisenberg group, r-matrices and bialgebra quantization.

ISU Algebra Seminar Fall 2005

• 9/22/05 & 9/29/05 On general cohomology theories I & II

• 11/3/05 Deformation theory via DGLAs by M. Manetti (math.AG/0507284)

ISU Algebra Seminar Spring 2005

• 2/23/05 On quantum groups and quantization (braided tensor categories and some math/phys motivation)

• 4/6/05 1) From Lie theory to quantum dynamics? 2) Hopf algebra structures on Heisenberg algebra and relations with bialgebra quantization

• 4/20/05 Review of Heisenberg groups and their representations (I)

• 4/27/05 The m-representation of a Heisenberg group, r-matrices and bialgebra quantization. Disc Math Seminar, Mathematics Department, ISU, 2004

• 4/1/04 Deformation quantization as a problem about composition of graphs.

ISU Analysis Seminar Summer 2003, Fall 2003 & Spring 2004

• 7/8/04 "Fusion like" Hopf algebras • 7/15/04 Connes-Kreimer Hopf algebra and categorical interpretation (categorification)

• 10/28/04 Lucian: On VOAs, QG and quantization • 11/4/04 Lucian: On deformation theory

• 11/11/04 Lucian: L-infinity algebras from higher derived brackets

ISU Analysis Seminar Fall 2003 & Spring 2004

• 8/20/03 Two "applications" of configurations space integrals • 8/27/03 Formality and star-products

• 9/3/03 Properties of the weights in Feynman-Taylor expansions

• 10/1/03 L.I. & W.Z Relations between QFT, L-infinity morphisms and renormalization

• 10/29/03 Connes-Kreimer renormalization and deformation quantization

• 11/5/03 Renormalization after Borcherds with Kontsevich notations

• 1/14/04 Bernoulli graphs and graph cohomology; W.Z.: A state sum on graphs. • 2/11/04 Star-products and the Hopf algebra of graphs

• 2/18/04 A problem about composition of graphs (undergraduate seminar)

• 2/25/04 A canonical semi-classical star-product

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ISU Analysis seminar Fall 2002 & Spring 2003 • 8/22/02 Perturbative renormalization, Riemann-Hilbert problem

• 8/30/02 Hopf algebra of Feynman graphs

• 9/5/02 Feynman rules and renormalization

• 9/12/02 Renormalization and Birkhoff decomposition

• 1/18/03 Deformation of Poisson structures and quantization

• 2/28/03 Weyl quantization, Duflo isomorphism

• 3/07/03 Wigner distribution and Weyl-Wigner correspondence

• 3/21/03 Weyl quantization as deformation

• 4/25/03 Quantization of Lie bialgebras

ISU Analysis seminar Fall 2001 & Spring 2002 • 10/23/01Simplicial sets, triangulations, Pachner moves

• 10/30/01 Quantum 6j-symbols

• 11/7/01 Recoupling theory

• 11/13 The 2-3 condition (3-cocycle condition)

• 11/20/01 State-sums independence on order, bases and triangulations.

• 11/27/01 Ionescu: state-sums invariance

• 01/29/02 & 02/05/01 Duality and ribbon categories

• 02/12/02, 19 Marsalli: Frobenius reciprocity

• 04/16/02 Sources of TQFTs - QG & subfactors; derived categories

UNCo Mathematics Seminar, Spring 2000 • 01/18, 01/25: Hilbert spaces (Ch.1)

• 02/01 Fourier Transform (Ch.2)

• 02/08 Windowed Fourier Transform and Wavelets

• 02/15 IWT, signal processing and constructive filed theory

• 02/22 Linear operators in Hilbert spaces (Ch.III) (I)

• 03/01 Spectral theory; eigenvalues/eigenvectors; examples (II)

• 03/08 Examples; the number of particles operator (III)

• 03/15 Extensions and completions: generalized functions

• 04/05 Classical mechanics and Hamiltonian systems

• 04/12 Postulates of quantum mechanics

• 04/19 Quantum computing I (automata, logical gates, quantum bits and registers)

• 04/26 Quantum computing II (quantum gates, q. evaluations of functions, copying)

• 05/03 Student presentations: 1) Kevin Stump: Shor's quantum algorithm 2) Tara Hart: An undergraduate approach to Bell's Inequalities.

Communications and Presentations (External)

* “A partial order on the set of primes”, Number Theory at Illinois, Conference in memory of Batemans and Heini Halberstam, June 5, 2014.

* “Tesla waves, Biofields and Aetheric energy (Part II)”, Tesla Extraordinary Conference, Albuquerque, NM, July 25-28, 2013;

* “Fundamental Physics as Number Theory”, 19th Annual Conference of the NPA, July 25-28, 2012, Albuquerque, NM;

* “Tesla waves, Biofields and Aetheric energy (Part I)”, Tesla Extraordinary Conference, Albuquerque, NM, July 26-29, 2012;

* “On Super-Symmetry, Anti-Gravity and Free-Energy, 18th Annual Conference of the NPA, July 6-9, 2011, at College Park, MD (in absentia).

* “From Feynman amplitudes to qubit model: Infotronics”, CSUI Research Conference, Argonne National Laboratory, Nov. 7-8, 2008,

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http://www.dep.anl.gov/p_undergrad/ugsymp/2008abstracttimes.htm#session17. * From Feynman amplitudes to the Qubit Model, poster, “The Clock and the Quantum: Time in

Quantum Foundations”, Perimeter Institute, Oct.2, 2008, http://www.perimeterinstitute.ca/Events/The_Clock_and_the_Quantum/Posters/

* Graph complexes in deformation quantization and the Feynman Legacy, Bucharest University, Bucharest, Romania, 6/29/2006, http://www.ilstu.edu/~lmiones/Buc.pdf; and University of Rome, La Sapienza, Rome, Italy, 10/31/2006, http://www.ilstu.edu/~lmiones/ Rome.pdf.

* Higher derived brackets and deformation theory, together with F. Akman, AMS Bard College Oct 8-9 2005, delivered by F. Akman

* Feynman graphs and deformation theory, Bucharest University, Romania, 6/8/04. * A canonical semi-classical star product, Rider University, AMS Conference at Lawrenceville,

NJ, 4/16/2004. * Cohomology of Feynman graphs and L-infinity morphisms, AMS UNC Chapel-Hill,

10/24/03. * The nonabelian bar resolution, AMS Meeting, Lawrence, KS, 03/31/01. * Wavelets in Signal Processing and Conformal Field Theory", Fort Hays State University,

Hays, KS, February 26, 2001. * On nonabelian Cohomology, University of Northern Colorado, March 2000. * The Fundamental Theorem of Calculus, Penn State Haezlton, March 2000. * Ideals and homology in additive categories, Joint Mathematics Meetings, Washington D.C.,

January 19, 2000. * Maurer Cartan equation and quasi-complexes, The University of Chicago, March 25, 1999. * On categorification, The University of Chicago, March 23, 1999. * Categorifying groups, KSU, March 17, 1999. * Parity quasicomplexes, KSU, February 1999. * Group extensions with abstract kernel, after S. Mac Lane, KSU, February 1999. * Parity quasicomplexes and non-abelian cohomology, Joint AMS-MAA meeting, San Antonio,

January 16th 1999. * Non-associative algebras and categorical constraint equations, KSU, May 1998. * Gauge theory on Riemann surfaces, after N. J. Hitchin, KSU, Spring 1997. * State sum invariants of 3-manifolds, KSU, May 1996. * Raster graphics techniques for CAD systems, workshop on CAD, Sinaia, Romania, 1987. * Semi-Riemannian coverings and orbit manifolds, after B. O’Neill, G. Vranceanu seminar,

Bucharest University, 1986. * Warped products and semi-Riemannian submersions, after B. O’Neill, G. Vranceanu seminar,

Bucharest University, 1986.

Courses Taught

Calculus I, II, III, Technical calculus, General calculus and linear algebra, Trigonometry, College algebra, Differential equations I & II, Numerical Analysis, Elementary Abstract Algebra, Advanced Abstract Algebra, Elementary Real Analysis, Advanced Abstract Analysis, Advanced Linear Algebra, Advanced Calculus, Seminars in Mathematics, History of Mathematics:1600-present, History of Mathematics: past-1600, Topics in Mathematical-Physics, MAT 389.60 Introduction to Topology and Differential Geometry, Mat 447 Advanced Analysis I.

Conferences and Workshops Attended

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• 3rd International Symposium on Riordan Arrays and Related Topics, IWU, Bloomington, IL, June 20-23, 2016.

• Tesla Extraordinary Conference, July 26-30, 2012, Albuquerque, NM.

• 19th Annual Conference of the National Philosophy Alliance, July 25-28, 2012, Albuquerque, NM.

• Joint Conferences: “4th Conference on Future Energy” (COFE) and “3rd Space, Propulsion & Energy Sciences International Forum (SPESIF), March 15-17, 2011, University of Maryland, College Park, MD.

• BEER, ISU, Sept. 2010.

• Joint Mathematics Meeting Washington DC, Jan. 5-8, 2009.

• AMS Short Course “Introduction to Quantum Computing, Washington DC, Jan. 3-4, 2009.

• “The Clock and the Quantum: Time in Quantum Foundations”, Perimeter Institute, Waterloo, Canada, Oct.2, 2008.

• CSUI Research Conference, Argonne National Laboratory, Nov. 7-8, 2008

• AMS Meeting, Northwestern University, Evanston/Chicago, 10/14/04.

• Workshop on the Jacobian Conjecture, Il.St.U., April 27, 2004.

• AMS Meeting, Rider University, April 14-16, 2004.

• MAA Meeting at Roosevelt University-Schaumburg Campus, Schaumburg, IL, 4/4, 2004.

• AMS Meeting, University of North Carolina at Chapel-Hill, October 23-24, 2003.

• University Teaching Workshop: Teaching and Electronic Portfolios, May/14-15, 2003.

• International colloquium in the memory of Michael Herman, Institute Henry Poincare, Paris, November 04-08, 2002.

• Blaise Pascal Conference on String/Brane Cosmology, IHES, France, October 23-27, 2002.

• Workshop on renormalization, I.H.E.S., France, October 14-18, 2002.

• Workshop on Classroom Assessment and Classroom Research, ISU, May 21-23, 2002.

• 2002 Summer Proposal Writing Workshop, ISU, May 13-17, 2002.

• University Teaching Workshop: Teaching portfolios and Course redesign, 5/15-16, 2002.

• August University Teaching Workshop, August 14-16, 2001.

• AMS meeting, Lawrence, KS, March 30-31, 2001.

• Web design workshop, UNC, Oct. 2000.

• Grant Writing Workshop, UNC, Sept. 2000.

• Mathematical Challenges of the 21st Century, August 7-12, UCLA, August 7-12, 2000.

• Kansas Section of the MAA, Baker University, 03/31-4/1/2000.

• Grant Writing Workshop, KSU, Feb. 9, 2000.

• Joint Mathematics Meeting, Washington D.C., January 19-23, 2000.

• Workshop on “Cooperative Learning, Featuring Academic Controversy”, KSU, Jan 12, 2000.

• 9-th Midwest Geometry Conference, The University of Missouri-Columbia, Nov. 5-7, 1999.

• Swap Session: Teaching Portofolios, KSU, Sept. 28, 1999.

• Joint Mathematics Meeting, San Antonio, January 12-16, 1999.

• Workshop on deformation quantization and E-theory, Dartmouth College, 1997.

• 10th IAMP Congress of Mathematics and Physics, Leipzig, 1991.

• New Developments in Quantum Mechanics, International Summer School in Theoretical Physics, Poiana Brasov, 1989.

• Conformal Invariance and String Theory, International Summer School in Theoretical Physics, Poiana Brasov, 1987.

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Host for ISU Visitors

* Florin Balasa, Assistant professor, University of Illinois at Chicago, 22-23/02/03. * Donseok Kim, University of California at Davis, Graduate student, 6/18/03. * John Bryden, Associate professor, Southern Illinois University at Edwardsville, 6/27-28/03. * Yan Soibelman, Professor, Kansas State University, 2/21/2006.

Visitor as a Guest of (Short visits):

* Alexei Abrikosov, 2003 Nobel Price in physics, Argonne National Lab, Aug. 26, 2009.

External Reviewer

* Mathematical work of John Bryden, Associate professor, Southern Illinois University at Edwardsville, 8/2003.

* Gabi Mihalcea, Physics instructor, Benedictine University, 06/2002. * D. Bullock, Boise State University, Computations in quantum topology, NSF GP, 4/2003. * G. Pripoae, manuscript RB757, Balkan J. of Geom. And its Applications, 08/2008.

Collaborations

Internal

Collaborations with colleagues from the mathematical department started fall 2004 already yielded three articles: Publications [18], [19] and [16’]. The Analysis seminar will play a catalytic role in maintaining the current collaborations and possibly expanding to another level, working as a Focused Research group (see FRG NSF grants). Trying “to recruit” students in my research, e.g. in a computer search of solutions of graph equations, which would provide solutions of the deformation quantization problem, did not (yet) succed. External

1) Gabriel Pripoae, Associate professor, Mathematics department, Bucharest University, Bucharest,

Romania We have collaborated in the past on topics of semi-Riemannian geometry and we have projects for future collaborations to incorporate geometrical concepts in the theory of representation of Hopf algebras of graphs. Outcomes: Publications [3], [5]; see also [16]. 2) Florin Balasa, Assistant Professor, Computer science department, University of Chicago,

Chicago, USA.

I am a consultant and contributor regarding the mathematical theory behind computer science theory and algorithms. We worked on a project on “Counting integral points of convex polyhedra”. Outcomes: Publication [10]; 3) Domenico Fiorenza, Assistant professor, Mathematics Department, Institute “Guido

Castelnuovo”, University of Rome “La Sapienza”, Roma, Italy. He wrote several articles centered on the mathematical aspects of Feynman graphs and we are collaborating on graph expansions of L-infinity morphisms, extending some of my results on deformation quantization, as a continuation of the corresponding work of Maxim Kontsevich. A new project “Grand configuration spaces, Feynman path integrals and Connes-Kreimer renormalization” is under planning.

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Outcome: Publication [17]. 4) Michael Penkava, Associate Professor, Mathematics Department, University of Wisconsin, Eau

Claire, WI, USA After several discussions at previous conferences I was invited to collaborate on topics of L-infinity algebras. We met in October at the AMS meeting at Northwestern University, Evanston, IL and discussed in more detail various possibilities of collaboration. 5) Collaborations with doctoral students recommended by Professor Jim Stasheff are potential at this time.

Grants and Scholarships

Invited Speaker to Tesla Extraordinary Conference, July 26-30, 2012, $500. ISU sabbatical, Fall 2009. Center for Mathematics-Science-Technology, 2009, $5000. Visiting IHES, France, 10/9-11/9, 2009, $1000. Discrete homological algebra methods in physics, Grant Writing Initiative Award, $1000, 2008. Feynman Processes and Quantum Information Dynamics, URG – SFF $3000, 2008. Visiting IHES, France, 2006, $2000. Visiting University La Sapienza, Rome, Italy, $500. Visiting BU/Romania and IHES/France, ISU Travel Grant, 4/2006, $1,000. Geometry of grand configuration spaces, cohomology of Feynman graphs and Connes-Kreimer renormalization, Grant Writing Initiative Award, 4/2006, $3,000. Feynman processes, ISU URG – Research Enhancement Award, 04/2006, $3,500. A combinatorial approach to Kontsevich coefficients in deformation quantization of Poisson manifolds, ISU URG/PFIG, Summer 2004, $2,500. The Comparison Theorem for Parity Quasi-complexes, ISU URG/NFIG, ISU, Summer 2002, $2,500. I.H.E.S., Bures-sur-Yvette, France, visiting grant, 9/15-11/15/2002. UNC-SPARC Travel grant, Lawrence AMS meeting, March 2001. KSU travel grant, Joint Mathematics meeting, Washington D.C., January 19-23, 2000. UMC travel grant, 9-th Midwest Geometry Conference, UMC, Nov. 5-7, 1999. KSU travel grant, The University of Chicago, March 22-26, 1999. KSU travel grant, Joint Mathematics Meeting, San Antonio, January 13-16, 1999. KSU/Dartmouth College travel grant, Dartmouth College, 1997. Eileen Hostinski Scholarship, 1995.

Honors and Affiliations

AMS Lifetime Member, 1996; National Science Teachers Association 2008; National Public Employee Association, 2017; National Philosophy Alliance 2011; Tesla-Tech Association 2011; American Association of University Professors, 2008. Mathematical Association of America – 1996; Institute des Hautes Etude Scientifique – 2002; Institute of Electrical and Electronics Engineers 2008;

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ISU Research Initiative Award for 2004-2005 ISU Award for Department’s 2004 Pre-tenure Outstanding Research. KSU Award for Outstanding Graduate Student in Academics - 1995. Kappa Phi Kappa Honor Society – 1996; US Tennis Association, Lifetime Member since 2004; US Figure Skating Association, 2013.

Additional Information

Languages: Romanian, English, French. Computer languages: HTML, C++, Pascal, Lisp, Prolog, FORTRAN, COBOL, Basic. Operating systems: Windows 98/00/ME/XP/Vista, MS_DOS, UNIX, RSX-11M+. Word procesors: TeX, MS-Word, SciWord, Wordperfect, Wordstar, Ventura. Mathematical Software: Mathematica, SAGE, Maple, MatLab Software tools: Excel, Paradox, DBMSx, AutoCAD, MatCad, Coreldraw, etc. (multimedia and communication).

Professional References

* Louis Crane / Advisor, Associate Professor, Mathematics Department, 111 Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-6750, e-mail: crane@math.ksu.edu

* Yan Soibelman / coAdvisor, Professor, Mathematics Department, 214 Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-0584, e-mail: soibel@math.ksu.edu

* James Stasheff, Professor, Mathematics Department, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599. Tel.: (215) 822-6707, jds@math.upenn.edu.

* Tom Muenzenberger, Associate Professor, Director of Undergraduate School, Mathematics Department, 137A Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-0557, e-mail: muenz@math.ksu.edu

* Forrest Miller, Professor, Mathematics Department, 233 Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-0575, e-mail: frm@math.ksu.edu

* John Maginnis, Associate Professor, Mathematics Department, 114 Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-0574, e-mail: maginnis@math.ksu.edu

* Alexander Rosenberg, Associate Professor, Mathematics Department, 215 Cardwell Hall, KSU, Manhattan, KS 66502 Tel.: (785) 532-0578, e-mail: rosenber@math.ksu.edu

* Richard Grassl, Chair / Professor, Mathematics Department, University of Northern Colorado, Ross Hall 3200, Greeley, CO 80639. Tel.: 970-351-7595, rmgrassl@aol.com.

* John Bryden, Associate professor, Mathematics Department, Department of Mathematics and Computer Science, NSU, Thibodaux, LA 70310, U.S.A., ph: 618-650-2156, fax: 618-650-3771.

* Michael Marsalli, Professor, Mathematics Department, Illinois State University, Stevenson Hall, Normal IL 61790-4520. Tel.: (309)-438-7976, e-mail: mmarsalli@avemaria.edu

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* Fusun Akman, Assistant Professor, Mathematics Department, Illinois State University, Stevenson Hall, Normal IL 61790-4520. Tel.: (309)-662-0186, e-mail: fusun@coastal.edu

* Michael Penkava, Associate Professor, Mathematics Department, University of Wisconsin at Eau Claire, 622 Eau Claire, WI 54701, Tel.: (715)-836-4970, e-mail: penkavmru@uwec.edu

* Alberto Cattaneo, Professor, Institut fur Mathematik, Universitat Zurich, Winterthurerstr 190, CH-8057, Zurich, Germany; 41-(0)44-63 55877, alberto.cattaneo@math.unizh.ch

* Yuri I. Manin, Max Plank Institute, Bohn, Germany, manin@mpim-bonn.mpg.de

List of Reviewers

• Alberto Cavicchioli, Professor, Department of Pure and Applied Mathematics, University of Modena and Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy; cavicchioli.alberto@unimo.it

• Manuel Bullejos Lorenzo, Professor, Department of Algebra, University of Granada, Av. Fuentenueva s/n , E18071 Granada, Spain; bullejos@ugr.es

• Dimitry A. Leites, Docent Full Professor, Mathematics Department, Stockholm University, Roslagsv. 101, Kraftriket HUS 6, S-106 91, Stockholm, Sweden; Head of the Laboratory "Supersymmetry theory", Inst. of New Technologies of Education, Moscow, http://www.matematik.su.se/~mleites/, Dimitry.Leites@mis.mpg.de

• Pilar Carrasco Carrasco, Professor, Department of Algebra, University of Granada, Av. Fuentenueva s/n , E18071 Granada, Spain; mcarrasc@ugr.es

• Dominique Manchon, Professor, Laboratoire de Mathématiques de l'université Blaise Pascal de Clermont-Ferrand (UMR 6620), 24 avenue Landais F63177 Aubiere Cedex, France, (0033)473 40 76 98, Fax: (0033)473 40 70 64, manchon@math.univ-bpclermont.fominique

Short List of References

James Stasheff – Internationally renowned mathematician working in the area of Homotopy theory and contributor to “Cohomological Physics”, introducing one of the key generalization of the algebraic structures: strong homotopy (Lie) algebras (homotopical algebras). Authored more than 70 publications, including monographs on modern mathematics etc.

John Bryden - Pier and expert in quantum topology, and collaborator of V. Turaev (prominent figure in quantum algebra). We had fruitful discussions regarding the algebraic and topological method used in quantum physics.

Michael Penkava - Specialist in homotopical algebra and potential future collaborator; we had fruitful discussions regarding our mutual work on several occasions.

Alberto Cattaneo – Renowned mathematician, specialist in the mathematical-physics of quantization, especially deformation quantization; we have met at Institut des Hautes Etudes Scientifique, Bures-sur-Yvette, France.

Alberto Cavicchioli and/or Pilar C. Carrasco -Reviewers of my work on non-abelian cohomology and categorical methods.

Manuel Bullejos Lorenzo - Reviewer of my work applying homological algebra methods to quantum physics.

Lucian Ionescu CV

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Dimitry Leites - Docent full professor and head of the Laboratory "Super-symmetry theory”, Moscow. Reviewer of my work generalizing the key point of departure in algebraic geometry. Dominique Manchon, Professor and Researcher at University Blaise-Pascal, France, reviewer of my work with Domenico Fiorenza on Graph Complexes and Deformation Quantization.