E-APMN Vol5 No1.pdf

Asia PacificMathematics Newsletter

www.asiapacific-mathnews.com

January 2015 Volume 5 Number 1

Grothendieck (page 1) Wen-Ching Li (page 18) Tai-Ping Liu (page 22)

Advisory Board

Tony F ChanHong Kong University of Science and TechnologyHong [email protected]

Louis H Y ChenInstitute for Mathematical Sciences National University of Singapore [email protected]

Chi Tat Chong Department of MathematicsNational University of [email protected]

Kenji FukayaDepartment of MathematicsKyoto University, [email protected]

Peter HallDepartment of Mathematics and StatisticsThe University of Melbourne, [email protected]

Jungkai A ChenDepartment of MathematicsNational Taiwan [email protected]

Michio JimboRikkyo University [email protected]

Peng Yee Lee Mathematics and Mathematics EducationNational Institute of EducationNanyang Technological [email protected]

Yong Hoon Lee Pusan National UniversityBusan [email protected]

Ta-Tsien LiSchool of Mathematical SciencesFudan [email protected]

Ryo Chou1-34-8 Taito Taitou Mathematical Society [email protected]

Fuzhou GongInstitute of Appl. Math.Academy of Math and Systems Science, CASZhongguan Village East Road No. 55 Beijing 100190, [email protected]

Ivan GuoSchool of Mathematics and Statistics F07The University of SydneySydney NSW [email protected]

Le Tuan HoaVIASM (Vien NCCCT) 7th Floor Ta Quang Buu Library in the Campus of Hanoi University of Science and Technology 1 Dai Co Viet, Hanoi, Vietnam [email protected]

Shin-Shin Kao Department of Applied MathematicsChung-Yuan Christian UniversityNo. 200, Chung-Pei Road, Chung-Li,[email protected]

Jongwoo LeeDepartment of MathematicsKwangwoon UniversitySeoul, 139-701, [email protected]

Zhiming MaAcademy of Math and Systems ScienceInstitute of Applied Mathematics, [email protected]

Yeneng Sun Department of EconomicsNational University of Singapore [email protected]

Tang Tao Department of MathematicsThe Hong Kong Baptist UniversityHong [email protected]

Spenta WadiaDepartment of Theoretical PhysicsTata Institute of Fundamental Research [email protected]

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Editorial Board

San LingDivision of Mathematical SciencesSchool of Physical and Mathematical SciencesNanyang Technological [email protected]

Ramdorai SujathaSchool of MathematicsTata Institute of Fundamental Research Homi Bhabha Road, Colaba Mumbai 400005, India [email protected]

Chengbo Zhu Department of Mathematics National University of Singapore 10 Lower Kent Ridge Rd Singapore [email protected]

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Published byWorld Scientific Publishing Co. Pte. Ltd.5 Toh Tuck Link, Singapore 596224http://www.asiapacific-mathnews.com/

Print ISSN 2010-3484

January 2015

Asia PacificMathematics Newsletter

Volume 5 Number 1

Asia Pacific Mathematics Newsletter is listed in MathSciNet.

For submission of feature articles, news, conference reports and announcements, etc. please send to [email protected].

For advertisement please contact [email protected].

The views expressed in this Newsletter belong to the authors, and do not necessarily represent those of the publisher or the Advisory Board and Editorial Board.

Editor-in-Chief

Phua Kok Khoo

Editor

Y K Leong

Production

Tan Rok Ting

Elizabeth Lie

Artist

Jimmy Low

Editorial

Grothendieck and Algebraic Geometry .................................................................................1

Topology of Puzzle Rings .............................................................................................................6

The Indian Girls Guide to Science, Technology, Engineering and Math ....................9

Interview with Wen-Ching (Winnie) Li ................................................................................. 18

An Interview with Tai-Ping Liu ................................................................................................ 22

Australian Mathematical Sciences Institute ....................................................................... 29

Problem Corner ........................................................................................................................... 34

Book Reviews ................................................................................................................................ 36

News in Asia Pacific Region ..................................................................................................... 38

Conferences in Asia Pacific Region ....................................................................................... 47

Mathematical Societies in Asia Pacific Region .................................................................. 53

Electronic ISSN 2010-3492

Editorial

Asia Pacific Mathematics Newsletter welcomes contributions on the following areas:

Expository articles on mathematical topics of general interest

Articles on mathematics education

Introducing centres of excellence in mathematical sciences

News of mathematical societies in the Asia Pacific region

Introducing well-known mathematicians from the Asia Pacific region

Book reviews

Conference reports and announcements held in Asia Pacific countries

Letters from readers on relevant topics and issues

Other items of interest to the mathematical community

With all the accolades and medals duly presented at the International Congress of Mathematicians 2014, mathematicians are presumably starting 2015 with their usual determination and unswerving perseverance in tackling the multitudes of unsolved open problems, both old and new. It used to be that one could cogitate and meditate on outstanding problems in apparent oblivion of others, at least in pure mathematics. This seems possible even recently, as in the case of the breakthroughs achieved by Andrew Wiles for Fermats Last Theorem and by Yitang Zhang for the Twin Prime Problem. What seems to have changed is the style and mind set of mathematical research from glorious individual isolation in the pre-Internet era to collective sharing and participation in the Internet age. Shortly after the by-now well-known dramatic story of Zhangs breakthrough, Terry Tao (Fields Medallist 2006) initiated the so-called bounded gaps between primes Polymath8 project to garner the collective efforts of mathematicians to push Zhangs idea to its final conclusion for a long-standing problem in number theory. In his 30 September 2014 post in his blog, Tao declares and summarises the success of this project with the participation of ten fellow researchers. Perhaps this will serve as a forerunner of more projects that will be launched in the future with an equally high degree of success.

In this issue, we are fortunate to be able to feature two English translations of a French article on Grothendieck and his original ideas on algebraic geometry and a Japanese article on the topology of puzzle rings. We also have an original interview of Wen-Ching Winnie Li and a reprint of an interview with Tai-Ping Liu. Both of them are distinguished mathematicians working in Taiwan, and the former is an inspiring example of what women mathematicians can and have achieved. As an encouragement and reminder of the role that women can play in science, technology, engineering and mathematics we reprint an Indian girls guide on this topic. Finally, our Australian colleagues share with us some information

on the activities of the Australian Mathematical Sciences Institute in Melbourne.

So APMN begins 2015 on an optimistic note and we hope that the months to come will bring us more encouraging and inspiring news for the mathematical community in this region.

Y K Leong

Editor

Grothendieck and Algebraic GeometryLuc Illusie and Michel Raynaud

1

Grothendieck and Algebraic GeometryLuc Illusie and Michel Raynaud

Grothendiecks thesis and subsequent publica-tions in the early 1950s dealt with functionalanalysis. This was remarkable work, which isattracting new attention today.a Still, his mostimportant contributions are in algebraic geometry,a field which occupied him entirely from the late1950s on, in particular during the whole time hewas a professor at the Institut des Hautes EtudesScientifiques (IHES) (19591970).

Algebraic geometry studies objects defined bypolynomial equationsb and interprets them in ageometric language. A major problem faced byalgebraic geometers was to define a good frame-work and develop local to global techniques.In the early 1950s complex analytic geometryshowed the way with the use of sheaf theory.Thus, a complex analytic space is a ringed space,with its underlying space and sheaf of holomor-phic functions (Oka, H Cartan). Coherent sheavesof modules over this sheaf of rings play an impor-tant role.c In 1954 Serre transposed this viewpointto algebraic geometry for varieties defined overan algebraically closed field. He employed theZariski topology, a topology with few open sub-sets, whose definition is entirely algebraic (withno topology on the base field), but which is welladapted, for example, to the description of a pro-jective space as a union of affine spaces, and givesrise to a cohomology theory which enabled him,for example, to compare certain algebraic andanalytic invariants of complex projective varieties.

Inspired by this, Grothendieck introducedschemes as ringed spaces obtained by gluing (forthe Zariski topology) spectra of general com-mutative rings. Furthermore, he described theseobjects from a functorial viewpoint. The languageof categories already existed, having appeared inthe framework of homological algebra, followingthe publication of CartanEilenbergs book (Ho-mological Algebra, Princeton Univ. Press, 1956). But

aSee [G Pisier, Grothendiecks Theorem, Past and Present, Bull.Amer. Math. Soc. (N.S.) 49(2) (2012) 237323].bHowever, we seldom saw Grothendieck write an explicitequation on the blackboard; he did it only for basic, crucialcases.cCf. Cartans famous theorems A and B.

it was Grothendieck who showed all its wealthand flexibility. Starting with a category C, to eachobject X of C one can associate a contravariant func-tor on C with values in the category of sets, hX :C Sets, sending the object T to HomC(T,X). By aclassical lemma of Yoneda, the functor X hX isfully faithful. To preserve the geometric language,Grothendieck called hX(T) the set of points of Xwith values in T. Thus, an object X is known whenwe know its points with values in every object T.Grothendieck applied this to algebraic geometry.This was revolutionary as, until then, only fieldvalued points had been considered.

As an example, suppose we have a system ofequations

f1(x1, . . . , xn) = = fN(x1, . . . , xn) = 0, (1)where the fis are polynomials with coefficients inZ. Let A be the opposite category of the categoryof rings, and let F be the (contravariant) functorsending a ring A to the set F(A) of solutions(xi), xi A, of (1). This functor is nothing but thefunctor hX for X the object of A corresponding tothe quotient of Z[x1, . . . , xn] by the ideal generatedby the fis: the functor F is represented by X, anaffine scheme. Points of X with values in C arepoints of a complex algebraic variety that onecan possibly study by analytic methods whilepoints with values in Z, Q, or in a finite fieldare solutions of a diophantine problem. Thus thefunctor F relates arithmetic and geometry.

If the fis have coefficients in a ring B insteadof Z, the analogous functor F on the category Aopposite to that of B-algebras, sending a B-algebraA to the set F(A) of solutions of (1) with valuesin A, is similarly represented by the spectrumX of a B-algebra (quotient of B[x1, . . . , xn] by theideal generated by the fis), a scheme over thespectrum of B. In this way a relative viewpointappears, for which the language of schemes isperfectly suited. The essential tool is base change,a generalisation of the notion of extension ofscalars: given a scheme X over S and a basechange morphism S S, we get a new schemeX over S, namely, the fiber product of X and S

January 2015, Volume 5 No 1 1

Asia Pacific Mathematics Newsletter

2over S. In particular, X defines a family of schemesXs parameterised by the points s of S. The abovefunctor F then becomes the functor sending aS-scheme T to the set of S-morphisms from T toX. A number of useful properties of X/S (suchas smoothness or properness) can nicely be readon the functor hX. The two above mentionedproperties are stable under base change, as isflatness, a property that plays a central role inalgebraic geometry, as Grothendieck showed. In1968, thanks to M Artins approximation theorem,it became possible to characterise functors thatare representable by algebraic spaces (objects veryclose to schemes) by a list of properties of thefunctor, each of them often being relatively easyto check. But already in 1960, using only thenotion of flatness, Grothendieck had constructed,in a very natural way, Hilbert and Picard schemesas representing certain functors, at once super-seding by far all that had been written onthe subject before.

Nilpotent elementsd in the local rings ofschemes appear naturally (for example in fiberproducts), and they play a key role in questionsof infinitesimal deformations. Using them system-atically, Grothendieck constructed a very generaldifferential calculus on schemes, encompassingarithmetic and geometry.

In 1949 Weil formulated his conjectures onvarieties over finite fields. They suggested thatit would be desirable to have at ones disposala cohomology with discrete coefficients satisfyingan analogue of the Lefschetz fixed point formula.In classical algebraic topology, cohomology withdiscrete coefficients, such as Z, is reached by cut-ting a complicated object into elementary pieces,such as simplices, and studying how they overlap.In algebraic geometry, the Zariski topology is toocoarse to allow such a process. To bypass thisobstacle, Grothendieck created a conceptual rev-olution in topology by presenting new notions ofgluing (a general theory of descent,e conceived al-ready in 1959), giving rise to new spaces: sites andtopoi, defined by what we now call Grothendiecktopologies. A Grothendieck topology on a categoryis the datum of a particular class of morphismsand families of morphisms (Ui U)iI, called

dAn element x of a ring is called nilpotent if there exists aninteger n 1 such that xn = 0.eThe word descent had been introduced by Weil in the caseof Galois extensions.

covering, satisfying a small number of properties,similar to those satisfied by open coverings intopological spaces. The conceptual jump is thatthe arrows Ui U are not necessarily inclusions.fGrothendieck developed the corresponding no-tions of sheaf and cohomology. The basic exampleis the etale topology.g A seminar run by M Artinat Harvard in the spring of 1962 started its sys-tematic study. Given a scheme X, the category tobe considered is that of etale maps U X, andcovering families are families (Ui U) such thatU is the union of the images of the Ui s. The defi-nition of an etale morphism of schemes is purelyalgebraic, but one should keep in mind that if X isa complex algebraic variety, a morphism Y Xis etale if and only if the morphism Yan Xanbetween the associated analytic spaces is a localisomorphism. A finite Galois extension is anothertypical example of an etale morphism.

For torsion coefficients, such as Z/nZ, oneobtains a good cohomology theory Hi(X,Z/nZ),at least for n prime to the residue characteristicsof the local rings of X. Taking integers n of theform r for a fixed prime number , and pass-ing to the limit, one obtains cohomologies withvalues in Z = limZ/

rZ, and its fraction fieldQ. If X is a complex algebraic variety, one hascomparison isomorphisms (due to M Artin) be-tween the etale cohomology groups Hi(X,Z/rZ)and the Betti cohomology groups Hi(Xan,Z/rZ),h

thus providing a purely algebraic interpretation ofthe latter. Now, if X is an algebraic variety overan arbitrary field k (but of characteristic ) (ak-scheme of finite type in Grothendiecks lan-guage), k an algebraic closure of k, and Xk de-duced from X by extension of scalars, the groupsHi(Xk,Q) are finite dimensional Q-vector spaces,and they are equipped with a continuous action ofthe Galois group Gal(k/k). It is especially throughthese representations that algebraic geometry in-terests arithmeticians. When k is a finite field Fq, inwhich case Gal(k/k) is generated by the Frobeniussubstitution a aq, the Weil conjectures, whichare now proven, give a lot of information aboutthese representations. Etale cohomology enabledGrothendieck to prove the first three of these

fMore precisely, monomorphisms, in categorical language.gThe choice of the word etale is due to Grothendieck.hBut not between Hi(X,Z) and Hi(Xan,Z): by passing tothe limit one gets an isomorphism between Hi(X,Z) andHi(Xan,Z) Z.

January 2015, Volume 5 No 12


3conjectures in 1966.i The last and most difficultone (the Riemann hypothesis for varieties over finitefields) was established by Deligne in 1973.

When Grothendieck and his collaborators(Artin, Verdier) began to study etale cohomology,the case of curves and constant coefficients wasknown: the interesting group is H1, which is es-sentially controlled by the Jacobian of the curve. Itwas a different story in higher dimension, alreadyfor a surface, and a priori it was unclear how toattack, for example, the question of the finitenessof these cohomology groups (for a variety overan algebraically closed field). But Grothendieckshowed that an apparently much more difficultproblem, namely a relative variant of the question,for a morphism f : X Y, could be solved simply,by devissage and reduction to the case of a familyof curves.j This method, which had already madeGrothendieck famous with his proof, in 1957, ofthe GrothendieckRiemannRoch formula (althoughthe devissage, in this case, was of a differentnature), suggested a new way of thinking, andinspired generations of geometers.

In 1967 Grothendieck defined and studied amore sophisticated, second type of topology, thecrystalline topology, whose corresponding coho-mology theory generalises de Rham cohomology,enabling one to analyse differential properties ofvarieties over fields of characteristic p > 0 orp-adic fields. The foundations were written up byBerthelot in his thesis. Work of Serre, Tate, andGrothendieck on p-divisible groups, and problemsconcerning their relations with Dieudonne theoryand crystalline cohomology launched a wholenew line of research, which remains very activetoday. Comparison theorems (solving conjecturesmade by Fontainek) establish bridges betweenetale cohomology with values in Qp of varietiesover p-adic fields (with the Galois action) onthe one hand, and their de Rham cohomology(with certain extra structures) on the other hand,thus providing a good understanding of thesep-adic representations. However, over globalfields, such as number fields, the expected prop-erties of etale cohomology, hence of the associated

iThe first one (rationality of the zeta function) had already beenproved by Dwork in 1960, by methods of p-adic analysis.jAt least for the similar problem concerning cohomology withproper supports: the case of cohomology with arbitrary supportswas treated only later by Deligne using other devissages.kThe so-called Ccris, Cst, and CdR conjectures, first proved infull generality by Tsuji in 1997, and to which many authorscontributed.

Galois representations, are still largely conjectural.In this field, the progress made since 1970 owesmuch to the theory of automorphic forms (theLanglands programme), a field that Grothendiecknever considered.

In the mid 1960s Grothendieck dreamed ofa universal cohomology for algebraic varieties,without particular coefficients, having realisa-tions, by appropriate functors, in the cohomolo-gies mentioned above: the theory of motives. Hegave a construction, from algebraic varieties andalgebraic correspondences between them, relyingon a number of conjectures that he called stan-dard. Except for one of them,l they are still open.Nevertheless, the dream was a fruitful source ofinspiration, as can be seen from Delignes theoryof absolute Hodge cycles, and the construction byVoevodsky of a triangulated category of mixedmotives. This construction enabled him to provea conjecture of BlochKato on Milnor K-groups,and paved the way to the proof, by Brown, of theDeligneHoffman conjecture on values of multi-zeta functions.

The above is far from giving a full ac-count of Grothendiecks contributions to alge-braic geometry. We did not discuss RiemannRoch and K-theory groups, stacks and gerbes,m

group schemes (SGA 3), derived categories andthe formalism of six operations,n the tannakianviewpoint, unifying Galois groups and Poincaregroups, or anabelian geometry, which he developedin the late 1970s.

All major advances in arithmetic geometryduring the past forty years (proof of the Rie-mann hypothesis over finite fields (Deligne), ofthe Mordell conjecture (Faltings), of the ShimuraTaniyamaWeil conjecture (TaylorWiles), worksof Drinfeld, L Lafforgue, Ngo) rely on the founda-tions constructed by Grothendieck in the 1960s.He was a visionary and a builder. He thoughtthat mathematics, properly understood, shouldarise from natural constructions. He gave manyexamples where obstacles disappeared, as if

lThe hard Lefschetz conjecture, proved by Deligne in 1974.mThese objects had been introduced by Grothendieck toprovide an adequate framework for non abelian coho-mology, developed by J Giraud (Cohomologie non abelienne,Die Grundlehren der mathematischen Wissenschaften 179,Springer-Verlag, 1971). Endowed with suitable algebraic struc-tures (DeligneMumford, Artin), stacks have become efficienttools in a lot of problems in geometry and representationtheory.nCurrently used today in the theory of linear partial differen-tial equations.



4Alexander Grothendieck at the IHES in 1960s during his famous Seminar of Algebraic Geometry. [Photo courtesy IHES]

by magic, because of his introduction of the rightconcept at the right place. If during the lastdecades of his life he chose to live in extremeisolation, we must remember that, on the contrary,between 1957 and 1970, he devoted enormousenergy to explaining and popularising, quite suc-cessfully, his point of view.

****************

Grothendiecks three major works in algebraicgeometry are:

EGA: Elements de geometrie algebrique, redigesavec la collaboration de J. Dieudonne, Pub. Math.IHES 4, 8, 11, 17, 20, 24, 28 et 32.

FGA: Fondements de la geometrie algebrique, Ex-traits du Seminaire Bourbaki, 19571962, Paris,Secretariat mathematique, 1962.

SGA: Seminaire de Geometrie Algebrique du Bois-Marie, SGA 1, 3, 4, 5, 6, 7, Lecture Notes inMath. 151, 152, 153, 224, 225, 269, 270, 288, 305,340, 589, Springer-Verlag; SGA 2, North Holland,1968.

Acknowledgements

We thank Jean-Benot Bost, Pierre Deligne, andJean-Pierre Serre for their remarks on a prelimi-nary French version of this text. The first authorthanks Robin Hartshorne, Nicholas Katz, WilliamMessing, and Arthur Ogus for their help with itstranslation into English.



Luc IllusieUniversit de Paris-Sud, France

[email protected]

Luc Illusie, born 1940, is an honorary professor of mathematics at the Universit de Paris-Sud. He was a student of Grothendieck in the 1960s. His main contributions are on the theory of the cotangent complex and deforma-tions, crystalline cohomology and the de Rham-Witt complex, Hodge theory, and logarithmic geometry.

Michel RaynaudUniversit de Paris-Sud, France

[email protected]

Michel Raynaud, born 1938, is an hononary professor of mathematics at the Universit de Paris-Sud. He was a student of Grothendieck in the 1960s. His main poles of interest are group schemes, Nron models and rigid geometry. He proved Abhyankars conjecture on the fundamental group of the affine line on an algebraically closed field of positive characteristic.



Topology of Puzzle RingsKouki Taniyama

1

Topology of Puzzle RingsKouki Taniyama

1. Introduction to Topology and Knot

Theory

Here we treat plane figures and solid figures as

topological spaces. A plane figure is a subset of

the 2-dimensional Euclidean space R2 and a solid

figure is a subset of the 3-dimensional Euclidean

space R3. In general, a figure is a subset of the n-

dimensional Euclidean space Rn for some natural

number n.

Two figures X and Y are homeomorphic if there

exists a continuous bijection f : X Y such that

the inverse map f1 : Y X is also continuous.

Then we denote it by X Y. Such a map f is said

to be a homeomorphism from X to Y.

=

= = = = =

= = = =

= = =

= =

= =

Fig. 1.1

For example, we consider the 26 alphabet cap-

ital letters as plane figures. Here we think that

each of them is a finite union of line segments and

curves. Namely they are 1-dimensional and have

no areas. Then they are classified up to home-

omorphism as illustrated in Fig. 1.1. In Fig. 1.1,

a real line rectangle describes a homeomorphism

class and a dotted line rectangle describes a ho-

motopy equivalence class. Here we omit the def-

inition of homotopy equivalence. But we note

here that the homotopy equivalence classification

of these 26 letters is in one to one correspon-

dence with the homeomorphism classification of

26 boldface alphabet capital letters as illustrated

in Fig. 1.2. Here each boldface letter is a regular

neighbourhood of the corresponding letter and is

=

= = = = =

= = = =

== = =

= == =

=

=

= ==

Fig. 1.2

a compact planar surface with boundary. They are

completely classified by the Euler characteristic or

the first Betti number.

For figures in the same n-dimensional Eu-

clidean space Rn, there is an equivalence relation

that is stronger than the homeomorphism. Let X

and Y be subsets of Rn. We say that X and Y

are ambient isotopic if there exists an orientation

preserving homeomorphism f : Rn Rn such that

f (X) = Y. Then we denote it by X Y.

Two mutually homeomorphic plane figures

that are not mutually ambient isotopic in R2 are

illustrated in Fig. 1.3. Note that if we think them

as solid figures, then they are ambient isotopic

in R3.

=

Fig. 1.3

A knot is a simple closed curve in R3. Knot

theory studies whether or not two given knots

are ambient isotopic in R3. By definition, any two

knots are mutually homeomorphic. Two mutually

non-ambient isotopic knots, 01 and 31, are illus-

trated in Fig. 1.4.

=

0101 31

Fig. 1.4



22. Topology of Puzzle Rings

There are many studies on puzzle rings. However

it seems to me that not so many studies on them

from topological viewpoint are done yet. Here

we consider a puzzle ring with hard part and soft

part. A hard part is rigid and made of metal for

example. A soft part is pliable and made of string

for example. This can be formulated as follows.

Let Xi = Hi Si be a subset of R3 with Hi Si =

for i = 1, 2. We say that X1 and X2 are equivalent

if there exist an orientation preserving isometry

f : R3 R3 with f (H1) = H2 and an orientation

preserving homeomorphism g : R3 R3 that is

pointwisely fixed on H2 such that g(f (S1)) = S2.

Below we consider the case that X = H S is a

finite graph embedded in R3. Then we can apply

spatial graph theory to puzzle ring problem. Now

we consider the following problem. From now

on we do not stick to using only mathematically

defined terminologies.

Problem 1. In Fig. 2.1, remove the soft part from

the hard part.

Fig. 2.1

To be more mathematical, we reformulate the

problem as follows. The dotted line in Fig. 2.1 is

an imaginary line.

Problem 2. How many times does the soft part

need to go across the dotted line to be away from

the hard part as illustrated in Fig. 2.1?

Note that Problem 2 can be graded as illus-

trated in Fig. 2.2.

Fig. 2.2

The answer for level n is 2n. In particular

the answer for Problem 2 is 23 = 8. An actual

deformation that shows 8 is sufficient is illustrated

in Fig. 2.3.

However it will be unclear that the answer is

2n in general. Here we think the situation fully

topologically. Namely we suppose that the hard

part is also soft. Then we have a deformation

as illustrated in Fig. 2.4. It is clear by the final

illustration in Fig. 2.4 that the soft part bounds a

disk that intersects the dotted line transversally at

8 points. This fact is common for all illustrations

in Fig. 2.4 if we allow the disk to be topologi-

cal. Then we can shrink the soft part along the

topological disk. Then the soft part will become

sufficiently small and away from the hard part

after going across the dotted line 8 times.

It will be easy to image the solution for level

n from this solution for n = 3.

Fig. 2.3

Fig. 2.4

It is necessary to show that 2n is necessary.

It is shown in [1] by group theoretic argument.



3Recently the author found a geometric proof us-

ing covering space theory. It may be essentially

the same but at least for the author it is very

understandable. It will appear in [2] together with

certain generalisations.

A way to make a puzzle ring with hard part

and soft part is illustrated in Fig. 2.5. In such a

way we can produce a variety of puzzle rings

Fig. 2.5

with hard part and soft part as illustrated in

Fig. 2.6.

Fig. 2.6

References

[1] J. Przytycki and A. Sikora, Topological insightsfrom the Chinese rings, Proc. Amer. Math. Soc. 130(3)(2002) 893902.

[2] K. Taniyama, Site-specific Gordian distances of spa-tial graphs, in preparation.

Kouki Taniyama has been a professor in mathematics at Waseda University since 2004. He received a PhD from Waseda University in 1992. He has held positions at Tokyo Womans Christian University and has been a trus-tee of the Mathematical Olympiad Foundation of Japan since 2012. He received a Takebe Prize from MSJ in 1997 for his work in knot theory and spatial graph theory.

Kouki TaniyamaWaseda University, [email protected]

Translated from Sugaku Tushin, Vol. 18 (4) (2013)



The Indian Girls Guide to Science, Technology, Engineering and Math (STEM)

Deepika Sarma



Intro: As children and young adults, women in India enjoy and excel at science. But as studies progress to careers, fewer and fewer women stay on. How can we change the complex factors that keep women out of STEM? And just as importantly, why does Indian science need women?

On October 14 this year Ada Lovelace Day a handful of people assembled in a caf near Bangalores Ulsoor lake, typing away on their laptops to add mate-rial on Indian women scientists to what is possibly the worlds most read encyclopedia: Wikipedia. Three days before, a much larger group had gathered at the LotkaVolterra computer teaching lab at the Indian Institute of Sciences Centre for Ecological Studies with the same purpose. A handful of organisers, 15 participants from the institute, and around 10 more participants online, but elsewhere proceeded to enter names, dates, career achievements and biographical details. It may sound like a mundane activity, but the organisers, who included the all-women team of a non-profit science outreach initiative, had been working for two months to organise this Wikipedia edit-a-thon. And at the end of Ada Lovelace Day, material on around 40 Indian women had been added names we have not grown up with but should have. Anandibai Joshee, who in 1886 became the first Indian woman to get a degree in Western medicine; Janaki Ammal, a path-breaking botanist during the Second World War and Anna Mani, a pioneering physicist who published five single-authored papers while working in CV Ramans lab between 1942 and 1945.

Last month, this trio joined the women whose profiles were freshly created or updated on Wikipedia their place made firm on the Internet, while they continue to be absent from history textbooks. Read the carefully composed but Wiki-standard objective profiles and you get the beginnings, the barest glimpse into the enormous endurance, intelligence and suffering of these early scientists. Hear about the love and energy poured into the edit-a-thon and you get a sense of the

search contemporary Indian women scientists are on both for their place in the present and for their forgotten ancestors.

Delhi-based non-profit Feminist Approach to Technology published a study in 2014 which examined the performance of middle and senior schoolgirls and boys in science subjects in classes 8 and 9. They found that as the children moved from middle to senior school, girls tended to outperform boys in science and maths, but were less likely to pursue those subjects for higher studies. According to the Department of Science and Technology, in 2005, only 37 percent of PhDs in science were held by women. And a 2004 report by the Indian National Science Academy concluded from the little data it could gather that the percentage of women occupying faculty positions in most research institu-tions and prestigious universities was less than 15 percent. Why are so many women slipping out of science along the way?

The scientific establishments inability to attract enough women and keep them in the workforce is a large enough problem for it to feature in interactions between nations governments. Women in science has been identified as a priority area for engagement between the US and India in July 2014, the two countries organised an exchange on Evidence-Based Techniques to Advance Gender Equality in Science, Technology, Engineering, and Mathematics. And at the huge Indo-US Technology Summit in Noida, a workshop has been organised to promote women in science.

Throwing Like A Girl, Experimenting Like A Boy

Heres a question. Why is it important to have women in science at all?

The range of scientific research can only be as varied as the interests of its researchers, what heats of the curiosity of the individual scientist and in turn the establishment she/he becomes part of. The highly



respected experimental physicist Athene Donald began her career around 40 years ago as one of eight women in a class of 100 at Cambridge. When she began her research into soft matter physics and its application to living organisms, her peers laughed at her and told her that it was not physics, but today the work she kick-started might lead to a cure for Alzheimers. Prima-tologist Alison Jolly among the first generation of women primatologists in the 1960s like Jane Goodall is said to have changed evolutionary biology forever. Through her work in the forests of Madagascar, she shattered the faith held until then that males are dominant in all primate species. She was also able to prove that social ties and environment, rather than ecological factors, led to the evolution of higher intel-ligence among primates.

The continued underrepresentation of women, Dalits and minorities in sciences is not only a social justice problem. It leads to a homogeneous, stagnant approach to problem solving, when science itself says, groups of diverse problem-solvers can beat groups of high-ability problem solvers.

Some months ago, the poster-covered stairway of the Bangalore bookshop Blossom featured a small flyer asking for volunteers for a National Centre for Biological Sciences (NCBS) study in the human throwing motion. The study asked unselfconsciously and specifically for men. And why would the flyer be self-conscious when this until very recently has been the norm for science?

The gendered language of science and technology (where mechanical or electrical parts are assigned genders for example, a bolt is male while a nut is female) is often a reflection of cultural gender stereo-types. Biology once saw female eggs as passive agents and sperm as active ones. Right up to the 1990s, even. Johns Hopkins researcher Emily Martins study was the first to do major damage to the warrior sperm and damsel-in-distress egg trope. A developmental biolo-gist who came around early to Martins theory said, If you dont have an interpretation of fertilisation that allows you to look at the egg as active, you wont look for the molecules that can prove it. You simply wont find activities that you dont visualise.

Or you could ask Sarah S Richardson why science needs diversity. Richardsons 2013 book Sex Itself: The Search for Male and Female in the Human Genome shows that the X and Y are not sex chromosomes after all. But once they were so named, around 30 years after they were discovered, it put blinkers on the way researchers approached chromosomes, bringing

cultural gender stereotypes into the way scientists looked at the science of sex. And in some cases, it resulted in some rather poor science for instance, all the decades in which people wrongly believed that the XYY chromosome syndrome made men dangerous, violent and criminally inclined.

We are only just beginning to understand the impact of gender bias in research in areas such as womens health. Until very recently, there was little medical research into women and cardiac disease because it was assumed that women did not have heart attacks. But the medical establishment has now admitted that the signs we think are the classic symptoms of a heart attack (the pain in the left arm, etc.) are all signs men have. Women experience heart attacks very differently and are often under-diagnosed, misdiagnosed and likely to die. Similarly, one-third of all osteoporotic fractures are said to occur in men. Since the disease continues to be seen as the problem of post-menopausal women, men are very rarely tested for it.

Why do we have so little information on cardiac disease in women? Because science, medicine, drug trials most often use male subjects, whether rodent or human, even to test drugs that are not gender-specific. Hormone fluctuations in women and potential harm to foetuses during trials privileging womens child-bearing ability over contributions to trials have been seen as good reason to exclude women from studies in biology and medicine.

Because a male subject, in the minds of a male scientific establishment, is the neutral and the normal. It is an argument that is increasingly being seen as a flawed one, calling into question the very evidence basis of medicine. What this means is that in some cases, the medical treatment that women get, including drug dosage, may be far from right.

The US National Institutes of Health (NIH) on May 2014 announced that it would roll out policies begin-ning in October that would require applicants for funding to report their plans for the balance of male and female cells and animals in preclinical studies. Amidst increasing recognition that men experience hormone fluctuations too, the NIH pointed out in its announcement that [t]ypically, reasons for male focus in animal-model selection centre on concerns about confounding contributions from the oestrous cycle. But for most applications, female mice tested throughout their hormone cycles display no more variability than males do, as confirmed in a meta-analysis. But this skew has led to what is known as the drug-dose gap, where insufficient tests mean that women are receiving



the wrong doses of medicine, and while it may drive up the cost of studies, it does not make financial sense in the long term in 2005, it emerged that a male bias in drug efficacy and side-effect research led to the withdrawal of 8 out of 10 prescription drugs from the US market, because they affected womens health. Taking sex differences into account can have a wide-spread impact on science, and the instinct to control for variation needs to be examined.

Back to Bangalore and ball throwing. The NCBS scientist behind the study, Madhusudhan Venkadesan, responded as unselfconsciously as his flyer to my enquiry about the throwing study: The current study in my lab is focused on understanding how humans achieve throwing accuracy at the same time as speed. [] Those who throw often in early childhood develop an arm morphology that aids in throwing at very high speeds. There is then a strong possibility that social and cultural factors that sometimes preclude girl children from outdoor play could in turn affect the throwing ability in women. This conjecture is plausible, but not yet scientifically proven. Nevertheless, because it is important for our study to control for such variation in morphology, we are looking primarily for men. The goal of our study is not to differentiate between motor function in men versus women, but simply to find consistently fast throwers, particularly those who have been throwing since early childhood.

The assumption is that among all the humans who learn to throw balls as children, the small subgroup of gifted, consistently fast throwers are most likely male and that the human throwing motion is equal to the male throwing motion. Even if, to borrow the scientists phrase, it is not scientifically proven.

Who Knows Where the Men Are? We Are Going to Mars

Anusha Mujumdar is a 27-year-old aerospace engineer from Bangalore. She is one of only 35 women across the globe this year who have been awarded the Zonta International Amelia Earhart fellowship for research into aerospace, science and engineering. Mujumdar is a part of the European Space Agencys Mars Sample Return Mission, which will retrieve soil samples so scientists can study them to determine, among other things, whether there really is life on Mars. And she is a third-year PhD student at Exeter in the UK, working in the Department of Applied Mathematics on verifica-tion and validation of spacecraft controllers. Her friends teasingly refer to her as a rocket scientist.

Around two and a half weeks ago, Mujumdar got married and moved to her in-laws home in a Bangalore suburb when I visited her, I could still see the mehendi on her hands and her feet. Mujumdar grew up on the Indian Institute of Science campus. She says she was never very good at science and math, but in the 8th and 9th standard, I had good science teachers and that was what motivated me to go into science, when I was around 13 or 14. At some point she was struck by the discovery that she could find patterns in any system that can be expressed mathematically. That really excites me, she says. The coolest thing I have done so far is work on the special controllers for the Airbus launch vehicle Ariane 5ME. I used some of my fellowship money to go to Airbus [an aircraft manu-facturer] in Bremen, Germany, to work on it. The Ariane 5ME launches multiple satellites at a time, and to do that it has to stay in orbit for really long. One side of it faces the sun, so it has to keep rotating the special controllers keep it evenly heated, preventing damage from thermal stress. And I worked on that.

Most female PhD students in India learn to answer grotesque questions about marriage in informal situa-tions at work and during formal, career-changing, life-changing interviews. Mujumdar had to deal with enough of them, but I throw in one of my own: Why did she choose to get married before she finished her PhD? It felt like the right time, she tells me. But for now, she still has a year of her PhD left to complete, and her sights are set firmly on her career in December, she will be back at Exeter to make sure spacecraft stay in the sky.

Marriage and families remain recurrent motifs in the daily drama of women in the scientific establish-ment, in their leaving of the scientific establishment. In the last decade and a half, the Indian government

Aerospace engineer Anusha Mujumdar. [Photo courtesy University of Exeter]



has made several efforts to encourage more girls and women to take up (and stay in) science. In 2003, the Council of the Indian Academy of Sciences constituted a committee on women in science, and later set up the Women in Science (WiS) panel, now chaired by particle physicist Rohini Godbole, the author of important work in the hadronic structure of high-energy photons. The WiS panels main initiatives included publishing books to inspire more women to take up science, and a report [an Indian Academy of Sciences and National Institute of Advanced Studies (IAS-NIAS) study in 2010, titled Trained scientific women power: How much are we losing and why?] which was not appreciated as much as I think it should have been I havent known any other study of that variety. The panel also holds lectures and workshops on careers in science, and in February, the panel intends to organise its first conference with international collaborators.

In October 2004 came the Indian National Science Academys Science Career for Indian Women one of the first reports to attempt to examine why Indian women were dropping out of science. In 2008, a report by the Task Force on women in science set up by the Department of Science and Technology looked into the subject with greater depth, having conducted meetings with scientists across India and having sought informa-tion from a range of institutions. Both reports identified family pressure to get married, or have children, or care for dependent relatives as a significant reason for women failing to continue in science despite being qualified to do so.

In 2010, the IAS-NIAS study examined the reasons for women with PhDs in science dropping out of their fields after doing a PhD. It surveyed 568 women scien-tists and 226 men scientists with PhDs in Science, Engineering or Medicine. Women were classified in three groups: women in research (WIR), women not in research (WNR) and women not working (WNW). Although the majority of women in all three groups were married, 14 percent of WIR between 30 and 70 the highest in all groups answered that they had never married. The corresponding figure for men in research (MIR) was 2.5 percent. When it came to children, 74.4 percent of WIR had children, a lower proportion than women in the other groups, including MIR 86.3 percent of whom had children.

Of course women have to choose, says Anupama Surenjan, a third-year PhD student at IIT Chennai, with some heat. She tells me about a match that was arranged for her while she was studying for her MTech degree, where the boy did not want her to do a PhD. He

expected that she would relocate after marriage to an area near his workplace, and find an engineering job that would bring in money while causing the least disruption in his life. Surenjan chose her PhD.

Nandini Nagarajan, a 64-year-old retired geophys-icist, was once the only woman in her class at IIT Kharagpur. In 1977, the Oil and Natural Gas Corpora-tion (ONGC) wanted the Indian Institute of Geomag-netism to install a continuously running magnetometer in Port Blair in the Andaman and Nicobar islands. I was given the task. I did everything from scratch including passports to fly through Burma, permission letters from the Commissioner of the Andamans to buy a ticket to fly to the Andamans, instrument packing in 4 days. I set up the instrument in a wooden hut and left soon after, and we managed to give ONGC four months data. In 1988, she was the joint lead for a team to Ladakh again, it involved permissions, instrument testing and deployment. We camped outside Leh town for a month and bathed in streams. I brought a team of 3 vehicles and 4 colleagues back by the long route through Srinagar, long before daily flights, cell phones, or even telephones were around.

Geophysicist Nandini Nagarajan with colleagues on a field trip to Ladakh, 1988. [Photo courtesy Nandini Nagarajan]

Nagarajan believes that one of the main reasons women are forced to drop out of science is relocation, reloca-tion, relocation. Her husband, who works as a chemical engineer, had to move cities every two years for the first decade of their marriage. Well, the only solution to that, she says dryly, is divorce. Id have been far more senior without those interruptions. My contem-poraries who didnt have those problems went on to get promotions, and head groups and institutions.

The IAS-NIAS study points out that a significantly lower proportion of men have reported breaks in career compared to women. While personal factors such as health, further studies and voluntary retirement have led to breaks for men, for women, domestic



responsibilities of childcare and care for elders have been the primary reason for the breaks in career, it says.

Interestingly, the report found that the spouses of 41 percent of WIR were scientists too. They all tend to pair off in the end, senior wildlife biologist Rauf Ali chuckled over the phone from Pondicherry about the ecology students he has had over the years. Swapna Neraballi, a 34-year-old wildlife scientist currently studying vegetation patterns in the Andaman Islands, agrees that it is common for scientists in her field to pair up. The couples I know tend to pick similar research interests and work locations so that they get to spend time with one another, she says of her former classmates and colleagues. But Neraballi is married to a photographer who travels often for work, like she does. My long-distance phone conversation with her takes place at 6 am on a weekday, before she heads out into the field with her assistants from Wandoor (South Andaman) to examine a plot of land in Alexandria for changes in vegetation, on which she has been collecting data for a month. The bottom line is, we spend a lot of time apart, she says.

Anusha Mujumdar grew up on the Indian Institute of Science campus, where her father works as a scientist, and she grew up surrounded by men and women in science. Many of the women, she knows, had to take up less demanding jobs than their husbands after marriage or stop working entirely (significantly, the IAS-NIAS report points out that the largest proportion of women with PhDs who had spouses who worked in the same field or organisations were not working, indicating that having a partner doing similar work did not necessarily mean they would be more supportive of a womans career in science). Mujumdar tells me she has been lucky so far about not having to make a choice between a career in science and having a family. But later in our conversation, she mentions that she is clear she wants to have children. And when I do that, I want to do it well she trails off. I want to be a good mother For a moment, I see her confidence waver and wished I had not asked the question. I had just contributed to the death by a thousand cuts on young women who are pushed to leave before they leave. In Lean In, Facebook COO Sheryl Sandberg wrote, From an early age, girls get the message that they will likely have to choose between succeeding at work and being a good wife and mother. By the time they are in college, women are already thinking about the trade-offs. In a survey of Princetons class of 2006, 62 percent of women said they anticipated work/family conflict, compared

with 33 percent of men and of the men who expected a conflict, 46 percent expected that their wives would step away from their career track. These expectations yield predictable results: among professional women who take time off for family, only 40 percent return to work full time. But women rarely make one big decision to leave the workforce. Instead, they make a lot of small decisions along the way.

Feeling At Home In the Lab

In 2004, Vineeta Bal of the National Institute of Immu-nology (NII), New Delhi, found that 85.7 percent of the papers from India in 38 high-impact journals in biological sciences had men as the corresponding/senior authors and only 14.3 percent had women, despite the higher representation of women in these fields.

For the science-loving woman who fights her own sense of dutifulness to the family (real or imagined), the establishment often raises new obstacle courses. Only these obstacles are ones that the female scientist cannot talk about without raising suspicions that she is too sensitive or feeling that it is her own fault.

In the IAS-NIAS study, the researchers did some-thing interesting. They asked both men and women in science what support they thought women scientists needed to stay in the game. The answers exhibited fascinating differences: While a majority of WIR and MIR have reported flexibility in timings as an important provision, a larger percentage of responses by MIR indicated the need for refresher courses, fellowships, awareness and sensitisation campaigns to retain women in Science. In contrast, women perceive provisions such as accommodation and transportation as provisions that would help them balance their career and family.

The researchers also pointed out that family and societal pressures cannot explain completely why women drop out of Science, cautioning against an overemphasis on womens family roles. It pointed out that other organisational factors and infrastructure in the workplace also had a significant impact on whether women stayed on.

Hostile or unsafe work environments are a deterrent to women pursuing science careers. Whether it is within an institution or out in the field, women are often reluctant to talk about the harassment they face because their concerns can often be dismissed by male colleagues.

Rajaram Nityananda, a senior physicist who has worked at several scientific research institutions across



the country in the course of his career, served as the Centre Director of the National Centre for Radio Astrophysics in Pune, and is currently at the Azim Premji University, Bangalore. He says he had to deal with a couple of cases of sexual harassment. In one instance, a complaint was lodged about the doctor of an institute who was reported to have made his female patients from the institute uncomfortable, by touching them unnecessarily. Once the case came up, more women began to speak up to the womens cell about their experiences with the doctor. In that particular instance, the doctors contract was terminated.

In another instance, a woman student doing a project with a senior academic accused him of inap-propriate behaviour. This person had developed a reputation for making his women students uncomfort-able, many years earlier. The institute did take some immediate formal action based on the investigation and report of its Womens Cell, and the student was given an alternative project and guide. However, it appears that this incident did not have any conse-quences for later decisions, which were examined purely based on the academic record. It appears that the prevailing attitude at the highest level was one of letting sleeping dogs lie.

Shobhana Narasimhan, a theoretical physicist at JNCASR in Bangalore, says that when men tend to go for drinks after work, they are also creating informal but very significant spaces to network and share valu-able information. How to apply for grants, which journals to approach, which institutions to apply to these are things that are otherwise hard to learn; no one teaches you these things. Women are typically excluded from these circles.

Nandini Rajamani Robin, a wildlife biologist with IndiaBioScience, the non-profit that organised the Wikithon on women scientists, also identifies networking as being a major hindrance to career progression for women. Appearing at conferences, which is one way to network, requires time and travel, and women with families arent always able to partici-pate in this. Another factor she points to is a sense of discomfort with self-promotion. Networking also involves consciously putting yourself out there and talking about your work, which is something women have to learn to be comfortable doing.

Listening to pioneering women scientists talk of their incredible achievements can be greatly invigor-ating but also disorienting. Some can believe that they controlled their lives and careers, but are hesitant when it comes to questions about gender. A common

tendency is to casually intersperse their sincere argu-ments that women just need to work hard instead of feeling like victims, with the stories of the shocking discrimination they faced.

Nandini Nagarajan was the first woman in her class, has four siblings who studied science (one of whom is Rajaram Nityananda), and her father was a mathema-tician. She sharply zeroes in on the relocations that disrupted her career, but when she talks about how she started in geophysics at IIT Kharagpur, she says, The admissions committee was gender-blind. Then, she says, The teachers sat me down and asked me to consider going back to the physics department because there was fieldwork involved in the geophysics depart-ment, which they said would be hard for a woman. They neither coddled nor tried to marginalise me. After me there was someone who did her fieldwork in Bastar! For six months! Those were the good days. But its important to note that I was not a unique case. Just isolated because women were rare in some fields then. In that era, every discipline probably had a lone woman.

A little later, Nagarajan points out that the Indian Institute of Chemical Technology, the institute next door to the National Geological Research Institute (NGRI), where she worked, got its first woman director in 60 years. The new director is in good company. Fabiola Gianotti, the first woman director-general of CERN in the 60-year existence of the particle physics lab was quoted as saying that she does not believe there is any intellectual discrimination against women in science. In the same profile where she was praised for her calm and ability to smile during stressful situations.

The feisty Anna Mani ragged Abha Sur, author of Dispersed Radiance, soon after meeting her, What is this hoopla about women and science? It must be getting difficult for women to do science these days. We had no such problems in our time. Sur wrote, Yet, as I asked Anna Mani about the social environment and the support of her peers, a deep-seated hurt and anger surfaced. He was an odious man, she said, refer-ring to a colleague who had done his best to make the women feel inept, both as scientists and as women. Any slight error the women made in handling instrumenta-tion or in setting up an experiment was immediately broadcast by some men as a sign of female incompe-tence. After she finished her PhD dissertation, Anna Mani was disqualified on a technicality and was never awarded her doctorate.



Silver Linings and Jasmine Strings

One significant, positive factor is that women in India do not have to go through negotiation for equal pay in their science careers, unlike their counterparts abroad. I once travelled to a conference in the US where I heard a group of scientists say Indians were so progressive because they paid men and women the same amount! says Narasimhan. In the US, she points out, scientists in research often have to negotiate pay with their institutions and this is where women tend to lose out, and are often paid less. In the UK and Europe, Mujumdar tells me, women postdocs are paid less than their male colleagues, even if they have more experience and are better qualified.

This is something other women scientists experi-ence when they leave India. Shakti Lamba is a 32-year-old evolutionary biologist and anthropologist at the University of Exeter. Her research is looking for insights into human behaviour, including some recent fasci-nating work on self-deception. In particular, I study how people solve cooperative dilemmas. I work with the Pahari Korwa, a small-scale, forager-horticulturist society in Chhattisgarh and with the Khasi of Megha-laya. The coolest thing about my work is that I get to work in places Id never have gone to otherwise. In Chhattisgarh, I work with people who are hunter-gatherers, they use bows and arrows, they live without electricity and running water just experiencing life like that was amazing. Lots of adventures, falling sick,

getting stuck out in the middle of the forest, all sorts of stuff. That was more of a cultural shock, I think, than coming to the UK! She reiterates the gender pay gap problem in the UK. There are differences between what men and women are paid in academia, and women are paid significantly less, on average. This arises because there is negotiation of pay within a range, and women for whatever reason are less likely to be given, or to negotiate, higher salaries.

The other positive factor comes via Mujumdar. She says she feels more comfortable expressing her identity as a female scientist in India than she does in the UK. When I asked her if she had seen the photo-graphs of the women scientists at ISRO hugging each other over Mangalyaans success, she exclaimed, Thats so cool! On a Facebook page dedicated to space science that she visits, she saw a discussion on the photograph. While some commented on how progressive India seemed, having women scientists working in a space mission, others remarked that the women seemed comfortable with their femininity. In the photograph, the women are dressed as if for a special occasion, in silk sarees, one even with a long cluster of jasmine trailing down her back. The biggest difference I see working in Europe and in India, is that women in science can still be themselves to a large degree. In India, it didnt matter how I dressed, but in Europe, women in science tend to dress more severely in shirts and trousers, and they model themselves on their male colleagues. I like to be flexible in the way that I

Evolutionary biologist and anthropologist Shakti Lamba in Chattisgarh. [Photo by Shakti Lamba, Creative Commons]



dress sometimes its trousers, or a kurta, or a dress but dressing more feminine means that perhaps I am instantly stereotyped.

Geophysicist Nandini Nagarajan, extreme right, with fellow earth scientists at NGRI, Hyderabad, 1992. [Photo courtesy Nandini Nagarajan]

Nandini Nagarajan sent me two emails with pictures of herself; the second mail includes the line, This is how women in earth science look? The mail has a scanned photograph of five women, Nagarajan and her colleagues at the NGRI, taken over two decades ago. Four of them are wearing saris. Nagarajan stands far right in a cotton sari bordered in red, with her hair down and a bright red bindi on her forehead. I sent you that one because it reminded me of the Mangalyaan scientists picture. You can wear a silk sari and wear flowers in your hair and still be a scientist at ISRO.

Matt Taylor, a Rosetta scientist (part of a team that landed a space probe on a comet) with the European Space Agency, made a televised appearance wearing a shirt with sexy, barely-clad women firing guns, his tattoo sleeves on display. As one astronomer wrote of the huge #Shirtstorm that followed: I dont think Taylor is a raging misogynist or anything like that; I think he was just clueless about how his words might sound and his shirt might be interpreted. We all live in an atmos-phere steeped in sexism, and we hardly notice it; a fish doesnt notice the water in which it swims. Not noticing is rarely an option for women.

Future Shockproof

The moment of falling in love with science comes at different stages for different people. Shakti Lamba says, I was always interested in science at school but I was equally interested in other things. There was a point towards the end of my undergraduate degree in Zoology when I realised I wanted to do this as a career. I saw some interesting talks that grabbed my attention.

I saw a talk years ago by a visiting student from IISc (I was a student at Delhi University at the time, at Hindu college) who gave a talk about cooperation in animal societies bees, termites, wasps live in these big hives and nests and help each other in various ways that captured my attention.

For more women to have that career-shaping moment in India, we need to make some very big steps. For students in rural India, the chance encounter with charismatic science such as the one Shakti Lamba had continues to be very low. Scientific institutions need efficient redressal for sexual harassment (according to the Vishaka guidelines), and managements that are aware of the sexist water in which the fish are swimming would make women scientists welcome in the work-place.

And when it comes to levelling with the old boys club, theres plenty to be done. You have to ask, how do women feel in the workplace? Are they able to participate in scientific discussions in the way that their male colleagues do? says Nityananda. Narasimhan says, One reason why women dont rise is that theyre hesitant to ask for things for more lab space, for better tools, fixed working hours, lesser teaching loads, and more pay. Ive been thinking a lot about what to do for working women scientists, and weve [the DST and COACh] been having these workshops where women are explicitly taught [the things that men are able to pick up while networking]. Two months ago, she organised a workshop for women in Bangalore, and last month, she was at one in Italy, with many more such workshops in the pipeline.

As in other realms, there is the danger that issues of women in science will be seen as a womens issue, Narasimhan points out. The DSTs Task Force report mentions in its introduction a conference that it once organized for a large number of participants on women in science. There were only a handful of men in the audience, and they slipped away after the inaugural lecture. Gender sensitisation workshops should take place, but getting men to attend means making them mandatory, and theres enormous resistance to that, says Narasimhan. A PhD student who asked not to be named told me about how her otherwise supportive supervisor did not agree that women were not repre-sented enough in their field. And then he said women made bad leaders, as they tended to panic under pres-sure. I said, if thats true, might it be because the pres-sure on them is so much higher women have so much more to prove, and so much more to lose? But I dont think he saw my point. And it is unlikely he



would, unless he was forced by the workplace to examine his attitudes.

Scientific institutions around the world are learning to put their money where their mouth is. Meera Pillai, who works on gender issues, points out that there is a growing recognition around the world of the need to include female subjects in scientific studies, which is changing granting policies and reporting requirements. In 2010, the Canadian Institute of Health Research introduced mandatory questions on sex and gender in grant applications, and the proportion of applicants responding positively to considering issues of sex and gender increased by 22 percent in a single year. Granting agencies like the Bill and Melinda Gates Foundation, WHO, and the European Commission require gender sensitivity. And several journals, Pillai adds, including many of the most respected ones such as Nature and Lancet, now have editorial policies that require reporting of sex or gender specific issues in scientific research.

While Indian women scientists work and battle for policies that will bring more women on board in the future, the past is not without its inspirations. India-BioScience will continue their yearlong Wikipedia edit-a-thon to raise the profile of Indian women in science.

And Godbole, who appears to have made raising awareness about women in science her mission, will keep on at it. Why do I make it a point to talk about issues faced by women in science? I realise that not everyone notices the things that we face as women scientists, and it may seem new to some, so I make the effort to bring it up when I can. You just have to keep on talking about it. You have to bring it to peoples notice. Maybe if I keep saying it, it will register for people. Like Lewis Carroll says in Alice in Wonderland, I have said it thrice: What I tell you three times is true. Twenty years from now, I hope we will not be talking about women scientists. Except as scientists who happen to be women.

This article was originally published on Yahoo! Originals India on November 19, 2014

Deepika SarmaGrist Media, [email protected]

Deepika Sarma is a journalist based in Bangalore, India. She is Assistant Editor at Grist Media, an independent media organisation that produces Originals (Yahoo India's long-form journalism section) and the feminist web magazine The Ladies Finger.

Interview with Wen-Ching (Winnie) LiSujatha Ramdorai

Wen-Ching (Winnie) Li is a Distinguished Professor of Mathematics at Pennsylvania State University in USA. She was also the Director of the National Centre for Theoretical Sciences in Taiwan 20092014. Recently, Professor Sujatha Ramdorai had a chance to interview her.

Sujatha Ramdorai: Let us start by hearing from you about your early years in Taiwan and how you got interested in mathematics.

Winnie Li: Math has been my favourite subject since my childhood. Unlike other subjects, I did not have to memorise much once I understood the content. Winning math competitions in school gave me more encouragement and confidence. So I chose mathematics when I entered the college although I did not know at the time that the mathematics I was fond of was not the real mathematics I later encountered in college. Growing up in a mid-sized city in Taiwan, I did not learn calculus at high school, and nor did I have any sense of what mathematics was really about. I just mastered a bunch of small skills.

SR: You along with Fan Chung and Sun-Yung Alice Chang, are recognised as women mathematicians internationally, and are all contemporaries. Can you talk to us about this?

WL: My class was special in that the top students from the best girls high schools (at that time high schools were mostly segregated) all chose to go to the mathe-matics department of the National Taiwan University. For instance, Alice was from Taipei, Fan from Kaoh-siung, and myself from Tainan. My class was also unusual in that one third (ten) of the students were female. The girls got along very well. We discussed the homework problems, and we had our own fun activi-ties, including celebrating each others 20th birthday. In Chinese custom, turning 20 was a big event, as it signals entering adulthood.

SR: It was uncommon to hear of women scientists from Asia around that time, in the last century.

WL: Indeed, when I was growing up, the most famous female Chinese scientist was the physicist Chien-Shiung Wu, a professor at Columbia University, who was famous for doing the experiment to prove the theory that the conservation of parity is violated in the so-called weak nuclear reactions, proposed by two Chinese physicists, Chen-Ning Yang and Tsung-Dao Lee, for which they received the Nobel Prize in 1957.

SR: Please tell us about your years in France and the United States.

WL: I came to US in 1971 as a graduate student at UC Berkeley, supervised by A P Ogg. In 1974, I received my PhD and went to Harvard as the first female Benjamin Pierce Assistant Professor in Mathematics, a position I held for three and half years. The Harvard years were most crucial in my career. It was an eye-opening experience for me. All I did at Berkeley was writing a thesis, not much beyond that. Harvard was a very stimulating place; I learned a lot by attending classes and seminar talks, in particular from Tate and Serre. I also extended my research from classical modular forms to modular forms over function fields to automorphic forms in adelic setting. Many exciting developments in automorphic representations were happening at fast pace: Langlands proved his theory of base change, Arthur established the trace formula, DeligneSerre attached Galois representations to



weight one cusp forms, etc. I was fortunate to start learning this fascinating subject at Harvard together with the students of Tate then, and later at the Corvallis summer school and IAS. While I no longer work on representation theory, the knowledge acquired in my early life led me to view things from a better perspective when I became interested in noncongruence forms ten years ago.

I have consulted at AT&T for four weeks in the summer for twenty years, thanks to the invitation by Ron Graham. During these years, I collaborated with people at the Bell Labs and AT&T Research on various topics, including number theory, coding theory, graph theory, block designs, and communication networks. My research interests have broadened, and I began to appreciate applied mathematics more and more. It was also fun to apply number theory to other areas. To this date I retain keen interests in interactions between number theory and combinatorics. For instance, I used results from character sum estimates to construct Ramanujan graphs, and from studying eigenvalues of certain Ramanujan graphs I realised that the Kloost-erman sum conjecture over function fields should hold despite that it fails over the field of rational numbers. Also I extended my research from Ramanujan graphs to its higher dimensional analogue, Ramanujan complexes, which played an important role in my work with recent PhD students, where we succeeded in defining first zeta functions for higher-dimensional complexes with closed form and nice properties, extending the Ihara zeta functions for graphs.

I only spent one academic year, 19851986, visiting France. That was immediately after giving birth to my elder daughter. As a new mother I had difficulties to use my time wisely and efficiently. I was constantly in a dilemma. When I was taking care of my daughter, I felt bad since I should be spending time proving theorems. On the other hand, when I was attending a seminar, I felt guilty as I was not taking care of my daughter. This kind of struggle lasted for nearly one year until I learned how to switch my mind quickly: when I was at work I concentrated on math, when I returned home I spent quality time with my child.

Professionally the sabbatical year in France was also challenging. I spent the fall semester learning French conversations in order to teach a course at Universit de Paris Sud, in French, in the spring semester. That was a course on calculus and differential equations, which was taught once per week for three hours to a special group of students in physics, who would not study mathematics between two classes. I lectured for

half of the class time, and the remaining class time was devoted to problem solving, through which they were supposed to learn what they were responsible for and presumably to remember that until the next class one week later. That was the main challenge. At the end of the semester, the group mentor, a physics professor, called a deliberation in his office to gather all the teachers of that group of students, and asked student representatives to comment on each ones performance. This was an oral teaching evaluation made in public. I was really worried because, unlike other teachers, I barely spoke the language to manage to teach, let alone to please the students. The mentor certainly was aware of that, and I presumed that he was expecting criticisms. Surprisingly, when it was my turn, both students had no comments. The mentor asked them again, and they said it was OK and proceeded to the next person. I still remember the face of the mentor, fully taken by surprise, who cast an unbelievable look at me. It was an unforgettable experience in my life. It gave me a lot of confidence in myself. I also won a lot of respect from quite a few friends for my courage to take on the chal-lenge and to succeed in it.

SR: You now spend a lot of time in Taiwan again as the Director of the National Centre for Theoretical Sciences (NCTS). How would you compare your experiences abroad with coming back to Asia at a time when the whole world is keenly looking eastwards?

WL: I returned to Taiwan in 2009 to become the Director of the NCTS, except the year 20112012 when I went back to Penn State for one year. The centre has two divisions, mathematics and theoretical physics. I was pleased to see that the theoretical research in Taiwan has matured a lot since the founding of the centre in 1998. People are publishing in international leading journals and there are excellent young theorists. In the past five years I worked hard to broaden peoples horizon and increase the centres international visibility by inviting the very top mathematicians, including J-P Serre, D Zagier, G Huisken, F-H Lin, M Bhargava, etc., to give short courses in our centre. We also organised high quality conferences on a wide variety of topics, four of which were jointly supported by the National Science Foundation in the US. By now our centre has hosted numerous dignitaries and visitors, who all had very high opinion of the progress the centre has made. I am confident that NCTS has built an international reputation. That said, compared to elsewhere in Asia, for instance, Singapore, Hong Kong, China, and Korea,



the progress in Taiwan pales. Even under the currently less favourable job market situation in America and Europe, the much less competitive salary in Taiwan makes it extremely difficult to attract talents to work in Taiwan for a long term, despite the very pleasing cultural environment in Taiwan. The Taiwanese govern-ment needs to make a substantial improvement in this regard.

SR: How are the scientific relations between China and Taiwan? Any remarks about this for the future?

WL: Generally speaking, the students in China are more motivated, while students in Taiwan are much less driven. The Chinese government has invested a bigger proportion of its budget in science than the Taiwanese government. The progress in Taiwan is hindered by its own democratic system, which made the government very inefficient, especially in recent years. In my view Taiwan is rapidly losing its edge and I am very sorry to see this happen. The scientific interactions between China and Taiwan are improving on one hand; on the other hand, some top talents in Taiwan are now working abroad, attracted by the much higher salaries in China, Korea, and South East Asia. It is sad for Taiwan.

SR: Do you see any changes in Taiwan from your years as a student, vis--vis students coming to research, especially women students?

WL: The difference is day and night. When I was a student, there was little research going on among the faculty, whereas now the faculty in better universities are under pressure to publish in good journals, and they have been doing well in this regard. In some universities, a PhD student has to meet some publica-tion criterion before receiving the degree, certainly much more demanding than a Penn State PhD. The best students educated in Taiwan still study abroad. There are good young female mathematicians from Taiwan working in the US, for instance Melissa Liu, an associate professor at Columbia. There are also assistant professors and post-doctoral fellows at top universities. In Taiwan there are also female mathematicians, but no one is as outstanding.

SR: Tell us a little about your work and what you enjoy most as a researcher.

WL: I have mentioned some of my research interests

above. In pure math, I worked on the theory of new forms and studied the arithmetic of new forms. Then I moved to representation theory, in particular, in joint papers with Gerardin, I established local Langlands correspondence between representations of rank two groups by showing how the invariants determined the representations in each case, instead of the trace formula approach where the corresponding representa-tions are first identified and then the agreement of the invariants are shown. Using idele class characters, I obtained character sum estimates, which in turn are used to construct Ramanujan graphs and good sequences with low correlations. Jointly with Chai, we proved the Kloosterman sum conjecture over function fields. I proved high-dimensional analogue of the AlonBoppana theorem and gave explicit constructions of Ramanujan complexes. Together with my ex-PhD students, we extended Iharas zeta functions for graphs to zeta functions for higher-dimensional complexes, obtained a closed form expression, and showed that the Ramanujan complexes are characterised by their zeta functions satisfying the Riemann Hypothesis. In the past decade, working jointly with Long and Liu, we rejuvernised the study of the arithmetic of noncongru-ence modular forms. In applied math, I worked on spectral graph theory and coding theory.

As a researcher, I enjoy most working with students and young postdocs and see them making good progress.

SR: It is important that Asian countries network amongst themselves in international research. What are your views on this.

WL: As the role of Asian countries becomes more important in global economy, the scientific research in these countries also progresses at a rapid pace. The developed countries are certainly keenly eying their prospective students from Asia. While the research in Asia is still shaping up, it is essential that the Asian countries network amongst themselves to support and help each other. Hopefully in the near future, a critical mass will be formed, and Asian countries will lead in some areas of the scientific research. Our best talents will choose to remain in Asia or return to Asia to contribute to his/her home country.

SR: Congratulations on your recent birthday confer-ence, it is very satisfying to see the world take note of your contributions. How do you feel about this?

WL: As I said at the banquet, this conference was the



highlight of my career. I was very humbled by the list of speakers, and I was glad to be an excuse to call for such a high level conference.

SR: Do you have any stories or experiences you might like to share with younger students, especially women students?

WL: This is my advice to female students. To be a mathematician is a very tough profession. Mathematics is still a mens world. To succeed in mens world, a female has to be better and stronger than their male

counterpart in order to get the same respect and treat-ment. Also a woman has more responsibility when she has a family. There is no need to seek equality with man in this aspect. It is part of the nature that a child will ask more for mommy when in need. It only shows the status of mommy in a childs mind although this will undoubtedly increase a womans work load. I view this as a sweet load. It is an opportunity to build a strong bond with a child. It is a good feeling to be able to help someone. Personally I find bringing up my two daugh-ters are the most rewarding thing I have done in my life. It certainly makes my life more complete.

R Sujatha University of British Columbia, [email protected]

Sujatha Ramdorai is currently holding a Canada Research Chair at University of British Columbia. She was a Professor of Mathematics at Tata Institute of Fundamental Research (TIFR), Bombay, India. Her research interests are in the areas of Iwasawa theory and the categories of motives. She served as a Member of the National Knowledge Commission of India from 2007 to 2009.



An Interview with Tai-Ping LiuY K Leong

The following is a reprint of an interview with Professor Tai-Ping Liu of the Institute of Mathematics, Academia Sinica, Taiwan, which was conducted on 2 December 2010 at the Institute for Mathematical Sciences (IMS) of the National University of Singapore during his visit for the IMS programme on Hyperbolic Conservation Laws and Kinetic Equations: Theory, Computation and Applications (November 1December19, 2010).

We would like to thank the Institute for Mathemat-ical Sciences, NUS for permission to reprint the interview. From the introduction to the interview published in Issue 22, June 2013 of the IMS newsletter Imprints:

Tai-Ping Liu had his undergraduate education in the National Taiwan University at a time when its department of mathematics was in its formative stages. From there he went to Oregon State University for his MS degree and then to University of Michigan for his PhD. Immediately after that, he joined the University of Maryland, where from 19731988, he established for himself a niche in research on hyperbolic conserva-tion laws and shock wave theory. He then spent 2 years at the Courant Institute for Mathematical Sciences of New York University before moving to Stanford University in 1990. From a distinguished career in applied mathematics, he returned to Taiwan in 2000 as

a Distinguished Research Fellow at the Institute of Mathematics, Academia Sinica. Initially maintaining links with Stanford University, he soon took up a full-time position at Academia Sinica and retired from Stanford as emeritus professor.

Since his return to Taiwan in 2000, Liu has focused his research interests on the study of microscopic phenomena; in particular, on the Boltzmann equation in the kinetic theory of gases. He was instrumental in forming a research group at the Institute of Mathematics to work on the quantitative aspects of the Boltzmann equation in a direction (via Greens function) different from the approach of the well-established French School. He began organising learning seminars on the Boltzmann equation for researchers, graduate students and postdocs. He and his co-workers started research communications with a group of physicists in Kyoto University led by Yoshio Sone and began the quantita-tive study of the Boltzmann equation.

Lius research output consists of more than 130 single-author and joint papers. Among his import

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