· tony f chan hong kong university of science and technology hong kong [email protected] louis chen...

Asia PacificMathematics NewsletterOctober 2012 Volume 2 Number 4

www.asiapacific-mathnews.com

Featuring

Anthony J Guttmann(page 28)

Ashoke Sen(page 24)

C S Seshadri(page 17)

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

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

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

Kenji FukayaDepartment of MathematicsKyoto [email protected]

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

Gerard Jennhwa ChangDepartment of MathematicsNational Taiwan [email protected]

Michio JimboRikkyo University [email protected]

Dohan KimDepartment of MathematicsSeoul National UniversitySouth [email protected]

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

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]

Derek HoltonUniversity of Otago, New Zealand, &University of Melbourne, Australia605/228 The AvenueParkville, VIC [email protected]

Chang-Ock LeeDepartment of Mathematical SciencesKAIST, Daejeon 305-701, South [email protected]

Yu Kiang LeongDepartment of Mathematics National University of Singapore 10 Lower Kent Ridge Rd Singapore [email protected]

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

Charles SempleDepartment of Mathematics and Statistics University of Canterbury New Zealand [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]

Advisory Board

Editorial Board

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

Shun-Jen ChengInstitute of MathematicsAcademia Sinica6F, Astronomy-Mathematics BuildingNo. 1, Sec. 4, Roosevelt RoadTaipei 10617, [email protected]

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

October 2012

Asia PacificMathematics Newsletter

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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.

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

Volume 2 Number 4

Electronic – ISSN 2010-3492

Editor-in-Chief

Phua Kok Khoo

Editor

S C Lim

Production

Tan Rok TingKwong Lai FunZhang JiHe Yue

Artist

C C Ng

Editorial

Self-avoiding Walks and Polygons — An Overview ................................................................................ 1

Distributive Lattices and Coherence in Homological Algebra ..................................................11

C S Seshadri — A Glimpse of His Mathematical Personality .......................................................17

A Game Based on Knot Theory ...................................................................................................................................22

Interview with Ashoke Sen .............................................................................................................................................24

Interview with Tony Guttmann...................................................................................................................................28

A Brief Account on the Relationship between SMF and VMS ....................................................35

Why Mathematics Papers Indians Publish Have So Little Impact ..........................................37

“Top 50” National Rankings in Mathematics ................................................................................................38

Mathematical Sciences Institute Medals for Distinguished Service ...................................39

China's First “Joint Laboratory of Applied Mathematics” ................................................................42

Conference in Honour of Haruzo Hida on His 60th Birthday......................................................43

Pan Asian Number Theory Conference 2012 ...............................................................................................45

The 5th IWONT 2012 ..............................................................................................................................................................47

Book Reviews .................................................................................................................................................................................48

News in Asia Pacific Region ............................................................................................................................................52

Conferences in Asia Pacific Region .........................................................................................................................66

Mathematical Societies in Asia Pacific Region ...........................................................................................77

Editorial

Asia Pacific Mathematics Newsletter welcomes contributions on the following items:

• 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 mathematics community

In this issue, we are fortunate to carry Professor Chandan Singh Dalawat’s interview with Professor Ashoke Sen, winner of the Fundamental Physics

Prize (page 24). The award, which came with a prize money of three million US dollars, was instituted by Russian billionaire entrepreneur Yuri Borisovich Milner.

Professor Peter Hall continues his series of interviews with prominent Australian mathematicians. For this issue, he interviewed Professor Tony Guttmann, who also contributed an interesting article “Self-avoiding Walks and Polygons — An Overview”, which gives a succinct overview on the subject (page 1).

In the article “Distributive Lattice and Coherence in Homological Algebra”, Professor Marco Grandis describes the coherence in homological algebra using basic theories of abelian groups and lattices (page 11).

Professor Vikraman Balaji provides us with a glimpse into the life of Professor C S Seshadri while focusing mainly on his mathematical contributions (page 17).

Professor Ayaka Shimizu in her interesting short article “A Game Based on Knot Theory” describes how the game Region Select was created and its potential (page 22). This is another good example of how pure mathematics such as knot theory can be used to create interesting games for both young and old.

Another interesting article by Professor Lê Dung Tráng discloses the history of the relationship between the French and Vietnamese mathematical societies (page 35).

I would like to thank Professor Derek Holton for his contribution to the “Problem Corner” since the first issue of this newsletter. Due to health reasons, he had to discontinue this interesting column. I would like to wish Professor Holton good health. Currently I am negotiating with one potential contributor to take over the “Problem Corner”. It is my hope that this column will resume in the Volume 3 Number 1 issue (January 2013).

APMN has completed two years of publication but there are still many areas we need to improve. We appeal to readers to send us their suggestions and comments as this feedback will help us to progressively raise the quality and contents of this publication. And more importantly, contributions from readers will ensure the continued success of this newsletter.

Swee Cheng LimEditor

1

Self-Avoiding Walks andPolygons — An Overview

Anthony J Guttmann

Abstract. We give a rather personal review of the prob-lem of self-avoiding walks and polygons. After definingthe problem, and outlining what is known rigorously,and what is merely conjectured, we highlight the majoroutstanding problems in the field. We then give severalapplications in which the author has been involved.These include a study of surface adsorption of poly-mers, counting possible paths in a telecommunicationnetwork and the modelling of biological experimentson polymers, in which a polymer is pulled from a wall.The purpose of the review is to show that the problemis not only of intrinsic mathematical interest, but alsohas many interesting and useful applications.

1. Introduction

The problem of self-avoiding walks is one ofdeceptive simplicity of definition, hiding malevo-lent difficulty of solution. The problem was intro-duced by two theoretical chemists, Orr [31] andFlory [13], as a model of a polymer in dilute solu-tion. It soon became an interesting combinatorialmodel to mathematicians, and a canonical modelof phase transitions, of interest to mathematicalphysicists. It is also a simple model of a non-Markovian process. Attempts to count the num-ber of SAW have led to the development of newalgorithms, with widespread applicability, whilemany more applications were discovered. Theseinclude application to the design of telephonenetworks, the folding and knotting of biologicalmolecules, and a variety of chemical phenom-ena. Attempts at a solution have driven severalmathematical advances, including developmentsin stochastic differential equations and probabilitytheory.

Nearly 70 years after the model was proposed,we have a huge amount of numerical information,a substantial amount of exact information — thatis to say, results that are universally believed, butremain unproved — and a very small body ofrigorous results. In contrast, some other canonicalmodels of phase transitions, such as the Isingmodel, the Potts model and percolation have ei-ther been solved (the Ising model) or much hasbeen rigorously proved. In this short article Iwill outline the development of the subject, givesome applications, and show that we appear tobe on the verge of some major breakthroughs,which will result in proofs of much of the exact,

Fig. 1. A self-avoiding walk on the square lattice

Fig. 2. A typical two-dimensional SAW of 225 steps on thesquare lattice [courtesy of Nathan Clisby]

but unproved, information that currently exists.Unfortunately all the exact and conjectural infor-mation we have applies only to the model on atwo-dimensional lattice. In the case of three di-mensions, we only have numerical results. Exceptwhere otherwise stated, this article will discussthe two-dimensional situation.

2. What is Known and What is Not

2.1. Self-avoiding walks

A self-avoiding walk (SAW) of length n on aperiodic graph or lattice L is a sequence of distinctvertices w0, w1, . . . , wn in L such that each vertexis a nearest neighbour of its predecessor. In Fig. 1a short SAW on the square lattice is shown, whilein Fig. 2 a rather long walk of 225 steps is shown(generated by a Monte Carlo algorithm [8, 9]).

2.1.1. How many self-avoiding walks are there?Two obvious questions one might ask are (i)how many SAWs are there of length n, (typicallydefined up to translations) denoted cn, and (ii)how big is a typical n-step SAW? Indeed, how

Self-Avoiding Walks andPolygons — An Overview

Anthony J Guttmann

October 2012, Volume 2 No 4 1

Asia Pacific Mathematics Newsletter

2

might we measure size? A third important, butless obvious question, asks “what is the scalinglimit of SAWs?”

Frequently one rather considers the associatedgenerating function

C(x) =∑n≥0

cnxn .

To see the difficulty of this problem, the readeris invited to try and calculate the first few termscn on Z2. We take c0 to be 1, then c1 = 4 as aone step walk can be in any of 4 directions. Thenc2 = 12, c3 = 36 and c4 = 100. It is at the stageof 4-step SAWs that the self-avoiding constraintfirst manifests itself, and the problem becomesincreasingly difficult thereafter.

As we prove below, cn grows exponentially.Accordingly, an enormous amount of effort hasbeen expended over the last 50 years in develop-ing efficient methods for counting SAW. For thesquare lattice, Jensen [20] has extended the knownseries to 79 step walks, for which he finds c79 =

10194710293557466193787900071923676. Methodsfor calculating these astonishing numbers arequite complicated (see [14, Chap. 7]), but thebest current algorithm still involves a countingproblem of exponential complexity, of about 1.3n

(while a direct counting algorithm would havecomplexity 2.64n).

One of the few properties one can readilyprove, by virtue of the obvious sub-multiplicativeinequality cn+m ≤ cncm, is that the number cn growsexponentially. From this inequality it follows that

µ := limn→∞

c1/nn = inf

nc1/n

n

exists [29], and further that cn ≥ µn.However even the value of this “growth con-

stant” µ is difficult to calculate exactly. Only in2010 was µ for one two-dimensional lattice, no-tably the honeycomb lattice, actually proved by

Duminil-Copin and Smirnov [10] to be√

2 +√

2(see Sec. 3). For other lattices in two dimensions,and all lattices in higher dimensions, we onlyhave numerical estimates. For example, for thesquare lattice the best current estimate is µ =2.638158530323±2×10−12, a result I obtained basedon extensive series of Jensen [20].

In fact it is believed that, for dimensionalityd > 1 and d 4,

cn ∼ const.× µnng .

The critical exponent g is believed to depend onthe dimension, but not on the details of the lat-tice. In particular, it is predicted to be a rationalnumber, namely 11/32, in two dimensions. Inthree dimensions, the best estimate we have isg = 0.156957± 0.000009 given by Clisby [9]. Thereis no reason to believe that this number is rational.

Despite these accurate estimates, we still can-not even prove the existence of this exponent ford < 5, let alone establish its value rigorously. Ford > 4 the higher dimensionality means that theself-avoiding restriction is less confining than inlower dimensions, and indeed has no effect on thedominant asymptotic behaviour, with the resultthat the SAW behaves as a random walk. Moreprecisely, Hara and Slade [18, 17] have provedthat g = 0 in this case, and that the scalinglimit is Brownian motion. In four dimensions theabove expression for cn must be modified byan additional multiplicative factor ( log n)1/4, withg = 0. The appropriately rescaled walk is alsoexpected to have Brownian motion as its scalinglimit. These assertions for the four-dimensionalcase are believed to be true, but no proof exists.Bounds established 50 years ago by Hammersleyand Welsh [16] have hardly been improved upon.They proved that, for SAW in dimensionalityd ≥ 2,

µn ≤ cn ≤ µneκ√

n .

The lower bound follows immediately from sub-additivity, while the upper bound depends onan unfolding of the walk. The number of possibleunfoldings can be bounded by the number of par-titions of the integer n, which has the exponentialbehaviour given above. Note that the existenceof a critical exponent implies behaviour µneκ log n,which is rather far from the upper bound. Ayear later, Kesten [23] slightly improved the upperbound to

cn ≤ µneκn2/(d+2) log n .

2.l.2. How large is a typical self-avoiding walk?

Another important measure of SAW is the averagesize of a SAW of length n, taken uniformly atrandom. The most common measure is the mean-square end-to-end distance, which is believed tobehave as

En(|wn|2) ∼ const. n2ν ,

(for lattices in dimensions other than 4), where νis another critical exponent. Again, its existencehas not been proved for d < 5, but it is acceptedthat for two-dimensional lattices ν = 3/4. Inthree dimensions the best numerical estimate isν = 0.587597 ± 0.000007 [7]. In four dimensions itis believed that ν = 1/2, and again one expects amultiplicative factor ( log n)1/4. Finally, for d > 4 ithas been proved [18] that ν = 1/2. Rigorous resultsabout En(|wn|2) are almost non-existent. It wouldseem intuitively obvious that

cn ≤ En(|wn|2) ≤ Cn2−ε ,

but only this year, in an important calculation, hasthe upper bound been proved by Duminil-Copinand Hammond [11] for two-dimensional SAW.

October 2012, Volume 2 No 42


3

Fig. 3. All seven 8-sided polygons on the square lattice

2.2. Self-avoiding polygons

If the end-point of a SAW is adjacent to the origin,an additional step joining the end-point to theorigin will produce a self-avoiding circuit. If weignore knowledge of the origin, and distinguishcircuits only by their shape, we refer to self-avoiding polygons (SAP). On the square lattice, thefirst nonzero embedding of a SAP is the unitsquare, of perimeter 4 and area 1. There are two6-sided polygons of area 2, and seven 8-sidedpolygons, shown in Fig. 3, one of which has area4, and six of which have area 3.

Clearly, SAPs are a subset of SAWs. Theyare a particularly interesting subset for at leasttwo reasons. Because the conjectured exponentsfor SAPs (discussed below) are integers or half-integers (which is not the case for SAWs), it ishoped that this means the underlying solution forthe SAP case is simpler. Secondly, by including asecond parameter, that of area, SAPs can be usedto model a range of biological phenomena, suchas cell inflation and collapse [12].

Denote by pm the number of SAPs of perimeterm, by an the number of SAPs of area n, and by pm,nthe number of SAPs of perimeter m and area n. Wecan define two single variable generating func-tions, for perimeter and areaa respectively, and atwo-variable generating function, as follows:

P(x) =∑

m

pmxm

A(q) =∑

n

anqn

P(x, q) =∑m,n

pm,nxmqn .

Hammersley [15] proved that the numberof SAPs, like SAWs, grows exponentially; moreprecisely

µ = limm→∞

p1/2m2m .

While it is far from obvious, Hammersley alsoproved that the growth constants µ that arise inthe polygon case and the walk case are identical.

aClearly the area of a polygon is a concept peculiar to the two-dimensional case.

While unproved, a much stronger result is widelybelieved to hold, namely that

pm ∼ const.× µmmα−3 (1)

where α is a critical exponent.b The exponent α isrelated to the exponent ν defined above throughthe hyper-scaling relation dν = 2−α. This equationhas not been proved, but follows from physicalarguments, and of course the assumption thatthe exponents exist. It therefore follows from theresult for ν quoted above that in three dimensionsα = 0.237209 ± 0.000021.

For polygons there is a second growth con-stant, and exponent, associated with the area gen-erating function. By concatenation arguments itcan be readily proved that

λ = limn→∞

a1/nn

exists. It is also generally accepted, but notproved, that

an ∼ const. × λnnτ .

Unfortunately we only have numerical estimatesof λ and τ [14]. However for two-dimensionallattices τ is believed to be −1, corresponding to alogarithmic singularity of the generating function.That is to say,

A(q) ∼ const.× log(1 − λq),

so that an ∼ const × λn/n.Of great interest is the two-variable generating

function P(x, y). From this, we can define the freeenergy

κ(q) = limm→∞

1m

log

∑

n

pm,nqn

.

It has been proved [12] that the free energyexists, is finite, log-convex and continuous for0 < q < 1. For q > 1 it is infinite. The radius ofconvergence of P(x, q), which we denote xc(q), isrelated to the free energy by xc(q) = e−κ(q). This iszero for fixed q > 1. A plot of xc(q) in the x−q planeis shown (qualitatively) below. For 0 < q < 1, theline xc(q) is believed to be a line of logarithmicsingularities of the generating function P(x, q).The line q = 1, for 0 < x < xc(1) is believed tobe a line of finite essential singularities [12]. At thepoint (xc, 1) we have more complicated behaviour,and this point is called a tricritical point.

bNote that p2m+1 = 0 for SAP on Zd, as only polygons witheven perimeter can exist on those lattices. For such latticesthe above asymptotic form is of course only expected to holdfor even values of m. For so called close-packed lattices, suchas the triangular or face-centred cubic lattices, polygons of allperimeters greater than two are embeddable, so Eq. (1) standsas stated.



4

Around the point (xc, 1) we expect tricriticalbehaviour, so that

P(sing)(x, q)

∼ (1 − q)θF((xc − x)(1 − q)−φ

)as (x, q)→ (xc, 1−) .

Here the superscript (sing) means the singularpart. There is an additional, additive part that isregular in the neighbourhood of (xc, 1).

For self-avoiding polygons, in a series of pa-pers, Richard and co-authors [33, 34, 32] haveprovided abundant evidence (but no proof ) forthe surprisingly strong conjecture that

F(s) = − 12π

log Ai(π

xc(4A0)

23 s)+ C(q) .

Here Ai(x) is the Airy function, and C(q) is a func-tion, independent of x, that arises as a constantof integration. The exponents are believed to beφ = 2/3 and θ = 1. Here A0 is a constant knownonly numerically.

Finally, a veritable treasure trove of rigorousresults would be unlocked if we could prove that,in the large size limit, more precisely the scalinglimit, that two-dimensional random SAWs aredescribed by one of the SLE processes (Schramm–Loewner Evolution), which, in the past 20 years,have been proved to describe the limit of severaldiscrete models in combinatorics and statisticalphysics. Indeed, Lawler, Schramm and Wernerproved that, if the scaling limit of SAWs existsand is conformally invariant, then this limit has tobe SLE8/3. This has been checked via simulationsby Kennedy [22]. This would in particular implythe conjectured values of the exponents g and νin the two-dimensional case. We explain this inmore detail in the conclusion.

In the next section we give the proof due toDuminil-Copin and Smirnov of the exact growthconstant for the honeycomb lattice. In the follow-ing section we give three examples of applicationsof SAWs to other areas of science, and in theconclusion we give more detail of recent devel-opments that we hope point the way to futurebreakthroughs.

Mh,

Rh,

Mh,

Lh,

h

a

p

Fig. 4. A trapezoid T on the honeycomb lattice

3. The Honeycomb Lattice

As mentioned above, a breakthrough wasachieved in 2010, when Duminil-Copin andSmirnov [10] proved that the growth constant

on the honeycomb lattice is µ =√

2 +√

2, aspredicted by Nienhuis [30], using compellingphysical arguments from conformal field theory,30 years previously. The argument is, in hindsight,so simple, and the result so important, that wesketch it here.

We consider SAWs that start from a point alocated on the left side of a trapezoid T of width and height h, as shown in Fig. 4. For p a mid-edge of T , let F( p) be the generating function ofSAW w that end at p, weighted by the number ofvertices v(w) and the number of turns T(w) (a leftturn counts +1, a right turn −1):

F( p) ≡ F( p; x,α) :=∑

w:ap

xv(w)eiαT(w) .

For instance, the walk of Fig. 4 visits 17 vertices,makes 10 left turns and 7 right turns, so that itscontribution to F( p) is x17e3iα. Then, if v is anyvertex of T and p1, p2, p3 are the three mid-edgesadjacent to it, the following local identity holds:

( p1−v)F( p1)+( p2−v)F( p2)+( p3−v)F( p3) = 0 , (2)

provided x = xc := 1/√

2 +√

2, which is thereciprocal of the conjectured growth constant, andα = −5π/24. (We consider that the honeycomblattice is embedded in the complex plane C, sothat pi − v is a complex number). This identityis easily proved by grouping as pairs or tripletsthe SAWs that contribute to its left-hand side,as depicted in Fig. 5. One then checks that thecontribution of each group is zero.

If we now sum (2) over all vertices v of T , thendue to the terms ( pi − v), all terms F( p) such thatp is not a mid-edge of the border disappear. After



5

vp1 = 0

= 0

p3

p2

+

++

Fig. 5. A very local proof of the local identity (2)

a few more reductions based on symmetries, oneis left with(

cos3π8

)Lh,(xc) +

1√

2Mh,(xc) + Rh,(xc) = 1 ,

where Lh,(x) (resp. Rh,(x), Mh,(x)) is the generat-ing function of SAWs w that end on the left side(resp. right side, top or bottom) of T , weightedby the number of vertices v(w).

By letting h and then tend to infinity,Duminil-Copin and Smirnov derived from thisidentity that the generating function of SAWsdiverges at xc, but converges when x < xc. Thismeans that its radius of convergence is xc, so that

the growth constant is 1/xc =

√2 +√

2.Unfortunately these ideas do not generalise

to SAW on the square or triangular lattices, forwhich we only have accurate numerical estimatesfor the growth constant µ.

4. Applications

One reason that SAWs and SAPs are so exten-sively studied, apart from their intrinsic mathe-matical interest, is that they model many prob-lems that arise in other fields. The first suchexample we will consider extends the proof givenabove to the situation where the SAW can in-teract with a surface. The second example con-siders SAWs crossing a square, with applicationto telecommunication networks, and the third ex-ample models some recent biological experimentswhere strands of DNA (a polymer) are pulledfrom a wall with optical tweezers.

4.1. Walks attached to a surface

The interaction of polymers with a surface isscientifically and industrially an important phe-nomenon. A common example is the adherence ofpaint to a surface, clearly an industrial process ofconsiderable significance. To model such phenom-ena requires the inclusion of an interaction termbetween the polymer and the surface. To achievethis, we add a weight y to vertices in the surface,as shown in Fig. 6. In physics terms, y = e−ε/kBT

where ε is the energy associated with a surfacevertex, T is the absolute temperature and kB isBoltzmann’s constant. It is known that the growth

where p, q, r are the three mid-edges adjacent to an arbitrary v ∈ V (Ω).In Section 2.1 we outlined the proof by Duminil-Copin and Smirnov [30] that the growth constant

of the self-avoiding walk is equal to x−1c = (2 cos(π/8)) =

2 +

√2. Recall that the proof involved

a special domain ST,L (see Figure 2.3) and generating functions of SAW ending on the differentsides of this domain.

Here we generalise their construction to include a boundary weight. As shown in Figure 4.2,we will identify the surface with the β boundary of ST,L.

α β

+

−

a2L

T

Figure 4.2: Finite patch S3,1 of the hexagonal lattice with a boundary. Contours, possibly closed,of the O(n) model run from mid-edge to mid-edge acquiring a weight x for each step, and a weighty for each contact (shown as a black disc) with the right hand side boundary. The SAW componentof a loop configuration starts on the central mid-edge of the left boundary (shown as a).

Let us define the following generating functions:

AT,L(x, y) :=

γ⊂ST,La→α\a

x(γ)yν(γ)nc(γ),

BT,L(x, y) :=

γ⊂ST,La→β

x(γ)yν(γ)nc(γ),

ET,L(x, y) :=

γ⊂ST,L

a→+∪−

x(γ)yν(γ)nc(γ),

where the sums are over all configurations for which the SAW component runs from a to the α, βor +, − boundaries respectively. Furthermore define the special generating function

CT,L(x, y) :=

γ⊂ST,La→a

x(γ)yν(γ)nc(γ)

which sums over configurations comprising only closed loops inside ST,L; that is, configurationswhose self-avoiding walk component is the empty walk a → a.

122

Fig. 6. Trapezoidal domain ST,L with vertices on the right-handside wall, shown in bold, carrying a weight y

constant µ = 1/xc for such walks is the same as forthe bulk case.

Let c+n (i) be the number of half-plane walks ofn-steps, with i monomers in the surface, and de-fine the partition function (or generating function)as

C+n ( y) =n∑

i=0

c+n (i)yi .

If y is large, the polymer adsorbs onto the surface,while if y is small, the walk is repelled by thesurface.

Proposition 1. For y > 0,

µ( y) := limn→∞

C+n ( y)1/n

exists and is finite. It is a log-convex, non-decreasingfunction of log y, and therefore continuous and almosteverywhere differentiable.

For 0 < y ≤ 1,

µ( y) = µ(1) ≡ µ .

Moreover, for any y > 0,

µ( y) ≥ max( µ,√

y) .

This behaviour implies the existence of a critical valueyc, with 1 ≤ yc ≤ µ2, which delineates the transitionfrom the desorbed phase to the adsorbed phase:

µ( y)= µ if y ≤ yc ,> µ if y > yc .

In 1995 Batchelor and Yung [1] extended Nien-huis’s [30] work to the adsorption problem justdescribed, and making similar assumptions toNienhuis conjectured the value of the criticalsurface fugacity for the honeycomb lattice SAWmodel, to be yc = 1+

√2. In 2012 this was proved

by Beaton, Bousquet-Melou, de Gier, Duminil-Copin and Guttmann [3], and here we will sketchtheir proof.

Take the same trapezoid as above, now calledST,L, and add weights to the vertices on the β



6

boundary, as shown in bold in the figure above:Then we find the corresponding identity betweengenerating functions, with y∗ = 1 +

√2, to be

1 = cos(

3π8

)AT,L(xc, y) + cos

(π

4

)ET,L(xc, y)

+y∗ − y

y(y∗ − 1)BT,L(xc, y)

where y is conjugate to the number of visits tothe β boundary. The generating functions AT,L,BT,L and ET,L are two-variable generalisations ofthose defined in the previous section. To provethe conjecture we need to show that yc = y∗.

It is safe to take L → ∞ so that the trapezoidbecomes a strip. The identity then becomes

1 = cos(

3π8

)AT(xc, y) + cos

(π

4

)ET(xc, y)

+y∗ − y

y( y∗ − 1)BT(xc, y) .

It is then straightforward to prove that

(i) ET(xc, y) = 0 for 0 ≤ y < y∗,(ii) yc ≥ y∗,

(iii) limT→∞ AT(xc, y) = A(xc, y) = A(xc) is constantfor 0 ≤ y < y∗.

If we now write

cos (3π/8)A(xc, y) = 1 − δ

then the above identity reduces to

B(xc, y) = limT→∞

BT(xc, y) =δy( y∗ − 1)

y∗ − y

and in particular

B(xc, 1) = δ.

Proposition 1. If δ = 0 then yc = y∗.

The proof uses a decomposition of A walks ina strip of width T into B walks in that same strip,and gives rise to an inequality. In particular, fory < yc = limT→∞ yT,

0 ≤ αxc +1

BT(xc, 1)y∗ − y

y( y∗ − 1).

If BT(xc, 1) tends to 0, this forces y∗ ≥ yc, other-wise the right-hand side would become arbitrarilylarge in modulus and negative as T → ∞ fory∗ < y < yc.

Together with y∗ ≤ yc, this establishes yc = y∗ =1+√

2 and completes the proof of the proposition.The proof that δ = 0 is complicated, and unlike

most other proofs we have given is almost totallyprobabilistic. It is unrealistic to give any details,but in essence one first uses renewal theory toshow that δ−1 is the expected height of an irre-ducible bridge, which is a SAW that crosses thestrip from left to right, and cannot be expressed

as the concatenation of two or more smaller suchbridges. Next one shows that, for irreduciblebridges, E[width] < ∞ implies that E[height] <∞. Finally one shows that the assumption thatE[height] < ∞ leads to a contradiction, from whichthe desired result that δ = 0 readily follows.

4.2. Walks crossing a square

Some years ago I was asked by a telecommu-nications engineer to help him with the follow-ing problem: His company had a square grid ofnodes, connected by wires, and phone-calls couldbe routed from the bottom left-hand corner to thetop right-hand corner of the grid. He wished toknow how many such routes there were, as thisdetermined the carrying capacity of the network.

After some discussion we agreed that this wassimply the question “how many distinct SAWs arethere on a square grid of side-length L originatingat (0, 0) and ending at (L, L)?” The problem asstated was first considered by Knuth [27] in 1976,who gave a Monte Carlo estimate for the numberof paths for L = 10, a result we now know exactly.The problem was generalised by Whittington andthe author [38] to include a weight x associatedwith each step of the walk. This gives rise to acanonical model of a phase transition. For x < 1/µthe average length of a SAW grows as L, whilefor x > 1/µ it grows as L2. Here µ is the growthconstant of unconstrained SAWs on the squarelattice, defined above. For x = 1/µ numericalevidence, but no proof, was given that the averagewalk length grows as L4/3. Let cn(L) denote thenumber of walks of length n. Clearly cn(L) = 0for n < 2L. We denote the generating functionby CL(x) :=

∑n cn(L)xn. The answer to the original

question is∑

n cn(L).Subsequently, Madras [28] proved a number of

relevant results. In fact, most of Madras’s resultswere proved for the more general d-dimensionalhypercubic lattice, but here we will quote them inthe more restricted two-dimensional setting.

Theorem 2. The following limits,

µ1(x) := limL→∞

CL(x)1/L and µ2(x) := limL→∞

CL(x)1/L2,

are well-defined in R ∪ +∞.More precisely,

(i) µ1(x) is finite for 0 < x ≤ 1/µ, and is infinite forx > 1/µ. Moreover, 0 < µ1(x) < 1 for 0 < x < 1/µand µ1(1/µ) = 1.

(ii) µ2(x) is finite for all x > 0. Moreover, µ2(x) = 1for 0 < x ≤ 1/µ and µ2(x) > 1 for x > 1/µ.

In [38] the existence of the limit µ2(x) wasproved, and in addition upper and lower boundson µ2(x) were established.



7

The average length of a (weighted) walk isdefined to be

〈n(x, L)〉 :=∑

n

ncn(L)xn/∑

n

cn(L)xn . (3)

We define Θ(x) as follows: Let a(x) and b(x) betwo functions of some variable x. We write thata(x) = Θ(b(x)) as x→ x0 if there exist two positiveconstants κ1 and κ2 such that, for x sufficientlyclose to x0,

κ1 b(x) ≤ a(x) ≤ κ2 b(x) .

Theorem 3. For 0 < x < 1/µ, we have that 〈n(x, L)〉 =Θ(L) as L→ ∞, while for x > 1/µ, we have 〈n(x, L)〉 =Θ(L2).

In [38] it was proved that 〈n(1, L)〉 = Θ(L2).The situation at x = 1/µ is unknown. In [5] wegave compelling numerical evidence that in fact〈n(1/µ, L)〉 = Θ(L1/ν) , where ν = 3/4, in accordancewith an intuitive suggestion of Madras in [28].

Theorem 4. For x > 0, define f1(x) = log µ1(x) andf2(x) = log µ2(x).(i) The function f1 is a strictly increasing, negative-

valued convex function of log x for 0 < x < 1/µ.(ii) The function f2 is a strictly increasing, convex

function of log x for x > 1/µ, and satisfies 0 <f2(x) ≤ log µ + log x.

Some, but not all of the above results were pre-viously proved in [38], but these three theoremselegantly capture all that is rigorously known. In[5] an extensive numerical study was described,including exact enumerations up to squares ofside 19. For the largest square there are exactly1 523 344 971 704 879 993 080 742 810 319 229 690899 454 255 323 294 555 776 029 866 737 355 060592 877 569 255 844 distinct paths! The numberof such paths, as we have seen, grows as λL2

. In[5] it was also proved that 1.628 < λ < 1.782 andestimated that λ = 1.744550 ± 0.000005.

4.3. Pulling a polymer from a wall

During the past decade, force has been used as athermodynamic variable to understand molecularinteractions and their role in the structure of bio-molecules [35, 21, 37]. By exerting a force inthe picoNewton range, one aims to experimen-tally study and characterise the elastic, mechan-ical, structural and functional properties of bio-molecules [6].

In [24] SAWs were used to model the situationin which a polymer is attached to a surface andpulled from that surface by an applied force.The situation is shown in Fig. 7. Interactions areintroduced between neighbouring monomers onthe lattice that are not adjacent along the chain.The pulling force is modelled by introducing anenergy proportional to the x-component of the

Fig. 7. An interacting self-avoiding walk on the square latticewith one end attached to a surface and subject to a pullingforce at the other end. Each step of the walk connecting a pair ofmonomers is indicated by a thick solid line while interactions be-tween non-bonded nearest neighbour monomers are indicatedby jagged lines

end-to-end distance. One end of the polymer isattached to an impenetrable surface while thepolymer is being pulled from the other end witha force acting along the x-axis.

Boltzmann weights ω = exp(− ε/kBT) and u =exp(− F/kBT) conjugate to the nearest neighbourinteractions and force, respectively, were intro-duced, where ε is the interaction energy, kB isBoltzmann’s constant, T the temperature and Fthe applied force. For simplicity, we set ε = −1and kB = 1. The relevant finite-length partitionfunctions are

ZN(F, T) =∑

all walks

ωmux =∑m,x

C(N, m, x)ωmux , (4)

where C(N, m, x) is the number of interactingSAWs of length N having m nearest neighbourcontacts and whose end-points are a distancex = xN − x0 apart. The partition functions of theconstant force ensemble, ZN(F, T), and constantdistance ensemble, ZN(x, T) =

∑m C(N, m, x)ωm, are

related by ZN(F, T) =∑

x ZN(x, T)ux. The free ener-gies are evaluated from the partition functions

G(x)=−T log ZN(x, T) and G(F)=−T log ZN(F, T) .(5)

Here 〈x〉 = ∂G(F)∂F and 〈F〉 = ∂G(x)

∂x are the controlparameters of the constant force and constantdistance ensembles, respectively.

All possible conformations of the SAW wereenumerated. The challenge facing exact enumer-ations is to increase the chain length. Using di-rect counting algorithms the time required toenumerate all the configurations increases as µN,where µ is the connective constant of the lattice( µ ≈ 2.638 on the square lattice). So even witha rapid increase in computing power only a fewmore terms can be obtained each decade. In [24]the number of interacting SAWs was calculatedusing transfer matrix techniques [19]. Combinedwith parallel processing these algorithms allowedthe enumerations to be extended to chain lengthsup to 55 steps, roughly doubling the previouslyavailable enumerations.



8

0.0 0.5 1.0 1.50.0

0.4

0.8

1.2

T

F

0.0 0.5 1.00

10

20

N=25

0.0 0.5 1.00

20

40

60

N=35

0.0 0.5 1.00

40

80

120

N=45

0.0 0.5 1.00

100

200

N=55

TT

χχ

b

a

Fig. 8. (a) The force-temperature phase diagram for flexiblechains. (b) The fluctuations χ in the number of contacts vs. tem-perature at fixed force F = 1.0 for various values of the chainlength N

In Fig. 8(a) we show the force-temperaturephase diagram for flexible chains. At low temper-ature and force the polymer chain is in the col-lapsed state and as the temperature is increased(at fixed force) the polymer chain undergoes aphase transition to an extended state. The tran-sition temperature as plotted in Fig. 8(a) wasfound (in the thermodynamic limit N → ∞) bystudying the reduced free energy per monomer.The most notable feature of the phase-diagramis the re-entrant behaviour — that is to say, theinitial increase of force with temperature, prior toa decrease.

The positive slope dFc/dT at T = 0 confirmsthe existence of re-entrance in the F − T phase-diagram. The authors pointed out that the valueof the transition temperature obtained in the ther-modynamic limit and the one obtained from thefluctuations in non-bonded nearest neighbours(which can be calculated exactly for finite N = 55)gives almost the same value (within error barsof ±0.01). The fluctuations are defined as χ =〈m2〉 − 〈m〉2, with the k’th moment given by

〈mk〉 =∑m,x

mkC(N, m, x)ωmux/∑

m,x

C(N, m, x)ωmux .

In the panels of Fig. 8(b) the emergence of twopeaks in the fluctuation curves with increasing N

SELF-AVOIDING WALKS 13

a

aδ

bbδ

Ω

Figure 9. Discretisation of domain Ω.

Schramm and Werner [25] is that this random curve converges to SLE8/3 from a to b in the domain Ω. These twoconjectures must be considered the principal open problems in the field. If they could be proved, the existenceand value of the critical exponents, as predicted by conformal field theory for two-dimensional walks would beproved.

5.2. Schramm Löwner Evolution

For an approachable discussion of SLEκ, see Chapter 15 of [14]. Here we give a very minimal outline. Let Hdenote the upper half-plane. Consider a path γ starting at the boundary and finishing at an internal vertex.Then H\γ is the complement of this path, and is a slit upper half-plane. It follows from the Riemann MappingTheorem that it can be conformally mapped to the upper half-plane. Löwner [26] discovered that by specifyingthe map so that it approaches the identity at infinity, the conformal map so described (actually a family of maps,appropriate to each point on the curve) satisfies a simple differential equation, called the Löwner equation. Themapping can alternatively be defined by a real function. This observation led Schramm to apply the Löwnerequation to a conformally invariant measure for planar curves. That is to say, the Löwner equation generatesa set of conformal maps, driven by a continuous real-valued function. Scramm’s profound insight was to useBrownian motion Bt as the driving function3. So let Bt, t ≥ 0 be standard Brownian motion on R and let κ bea real parameter. Then SLEκ is the family of conformal maps gt : t ≥ 0 defined by the Löwner equation

∂

∂tgt(z) =

2

gt(z)−√κBt

, g0(z) = z.

This is actually called chordal SLEκ as it describes paths growing from the boundary and ending on the boundary.If κ ≤ 4 then the path is almost surely a simple curve, in the upper half plane. Larger values of κ lead to morecomplicated behaviour.

Hopefully this rather vague description will convey the flavour of this exciting and powerful development instudying not just two-dimensional SAWs, but a variety of other processes, such as percolation, the randomcluster model, and the Ising model. We refer the reader to [4] for greater detail of both SLE and these appli-cations. Despite these remarkable advances, we still have no real idea how to obtain comparable results for the3-dimensional model4.

3It is the only process compatible with both conformal invariance and the so-called domain Markov property.4This is also true of other classical models, such as the Ising model, the Potts model and percolation.

Fig. 9. Discretisation of domain Ω

at fixed force F = 1.0 are shown. The twin-peaksreflect the fact that in the re-entrant region as oneincreases T (with F fixed) the polymer chain un-dergoes two phase transitions. The importance ofpowerful enumeration data is highlighted by theobservation that the twin-peaks are not apparentfor small values of N. Many more details andcomparison with experiments are given in [24] —our purpose here is just to show the applicabilityof SAWs to this problem.

5. Conclusion

5.1. The scaling limit

One topic we have failed to adequately addressis the question of the scaling limit of SAW. Anintuitive grasp of this concept can perhaps begained by looking at the first two figures in thisarticle. In the first figure, the effect of the latticeis clear. In the second figure, there is no obviouslattice, and indeed no way to tell that this isnot a continuous curve. We formalise this notionas follows: Consider a smooth (enough) closeddomain Ω, with an underlying square grid, withgrid spacing δ as shown in Fig. 9. Denote by Ωδthat portion of the grid contained in Ω. Take twodistinct points on the boundary of Ω labelled aand b. Now take the nearest lattice vertex to a,and label it aδ, and similarly bδ is the label of thenearest lattice vertex to point b. Consider the setof SAWs ω(Ωδ) on the finite domain Ωδ from aδto bδ. Recall that δ > 0 sets the scale of the grid.Now let |ω| be the length of a walk ωδ ∈ ω(Ωδ),and denote the weight of the walk by x|ω|. Thereason for this is that the walks are of differentlengths, making the uniform measure not partic-ularly natural. (There is also a normalising factor,which for simplicity we ignore.)

As we let δ → 0 we expect the behaviour ofthe walk to depend on the value of x. For x < xcit is possible to prove that ωδ goes to a straight



9

line as δ → 0. (Strictly speaking it converges indistribution to a straight line, with fluctuationsO(√δ).) For x > xc it is expected that ωδ becomes

(again, in distribution) space-filling as δ→ 0. Butat x = xc it is conjectured that ωδ becomes (indistribution) a random continuous curve, and isconformally invariant. This describes the scalinglimit. If this conjecture is correct, a second, pivotal,conjecture by Lawler, Schramm and Werner [25] isthat this random curve converges to SLE8/3 from ato b in the domain Ω. These two conjectures mustbe considered the principal open problems in thefield. If they could be proved, the existence andvalue of the critical exponents, as predicted byconformal field theory for two-dimensional walkswould be proved.

5.2. Schramm–Lowner Evolution

For an approachable discussion of SLEκ, see Chap-ter 15 of [14]. Here we give a very minimal out-line. Let H denote the upper half-plane. Considera path γ starting at the boundary and finishing atan internal vertex. Then H\γ is the complement ofthis path, and is a slit upper half-plane. It followsfrom the Riemann Mapping Theorem that it canbe conformally mapped to the upper half-plane.Lowner [26] discovered that by specifying themap so that it approaches the identity at infinity,the conformal map so described (actually a familyof maps, appropriate to each point on the curve)satisfies a simple differential equation, called theLowner equation. The mapping can alternativelybe defined by a real function. This observationled Schramm to apply the Lowner equation to aconformally invariant measure for planar curves.That is to say, the Lowner equation generates aset of conformal maps, driven by a continuousreal-valued function. Scramm’s profound insightwas to use Brownian motion Bt as the drivingfunction.c So let Bt, t ≥ 0 be standard Brownianmotion on R and let κ be a real parameter. ThenSLEκ is the family of conformal maps gt : t ≥ 0defined by the Lowner equation

∂

∂tgt(z) =

2gt(z) −

√κBt

, g0(z) = z .

This is actually called chordal SLEκ as it describespaths growing from the boundary and endingon the boundary. If κ ≤ 4 then the path isalmost surely a simple curve, in the upper halfplane. Larger values of κ lead to more complicatedbehaviour.

Hopefully this rather vague description willconvey the flavour of this exciting and pow-erful development in studying not just two-dimensional SAWs, but a variety of other pro-cesses, such as percolation, the random cluster

cIt is the only process compatible with both conformal invari-ance and the so-called domain Markov property.

model, and the Ising model. We refer the readerto [4] for greater detail of both SLE and these ap-plications. Despite these remarkable advances, westill have no real idea how to obtain comparableresults for the 3-dimensional model.d

In this article I have only scratched the surfaceof this topic. More details on the mathemati-cal aspects can be found in [29] and the recentreviews [2, 4]. More information on numericalaspects and some applications, particularly to theSAP subset can be found in the monograph [14].Another approach to this problem that has notbeen discussed is to simplify the problem so thatit can be solved (see [14, Chap. 3]). Unfortunatelymost such simplifications involve rendering themodel Markovian, which removes a significantfeature.

References

[1] M. T. Batchelor and C. M. Yung, Exact results forthe adsorption of a flexible self-avoiding polymerchain in two dimensions, Phys. Rev. Lett. 74 (1995)2026–2029.

[2] R. Bauerschmidt, H. Duminil-Copin, J. Goodmanand G. Slade, Lectures on self-avoiding walks,arXiv:1206.2092, Clay Mathematics Institute Sum-mer School, Buzios (2010).

[3] N. R. Beaton, M. Bousquet-Melou, H. Duminil-Copin, J. de Gier and A. J. Guttmann, The criticalfugacity for surface adsorption for SAW on thehoneycomb lattice is 1 +

√2, arXiv:1109.0358v3

(2012).[4] V. Beffara, Schramm–Lowner Evolution and other

conformally invariant objects, Clay MathematicsInstitute Summer School, Buzios (2010).

[5] M. Bousquet-Melou, A. J. Guttmann and I. Jensen,Self-avoiding walks crossing a square, J. Phys A:Math. Gen. 34 (2005) 9159–9181.

[6] C. Y. Bustamante, Y. R. Chemla, N. R. Forde andD. Izhaky, Mechanical processes in biochemistry,Annu. Rev. Biochem. 73 (2004) 705–748.

[7] N. Clisby, Accurate estimate of the critical expo-nent ν for self-avoiding walks via a fast imple-mentation of the pivot algorithm, arXiv:1002.0494,Phys. Rev. Lett. 104 (2010) 055702.

[8] N. Clisby, Efficient implementation of the pivotalgorithm for self-avoiding walks, arXiv:1005.1444,J. Stat. Phys. 140 (2010) 349–392.

[9] N. Clisby, Private communication. Publication inpreparation.

[10] H. Duminil-Copin and S. Smirnov, The connec-tive constant of SAW on the honeycomb lattice is√

2 +√

2, Ann. Math. 175 (2012) 1653–1665.[11] H. Duminil-Copin and A. Hammond, Self-

avoiding walk is sub-ballistic, arXiv1205:0401v1.[12] M. E. Fisher, A. J. Guttmann and S. G. Whittington,

Two-dimensional lattice vesicles and polygons, J.Phys A: Math. Gen. 24 (1991) 3095–3106.

[13] P. J. Flory, The configuration of real polymerchains, J. Chem. Phys. 17 (1949) 303–310.

[14] A. J. Guttmann (ed.) Polygons, Polyominoes andPolycubes, Lecture Notes in Physics 775 (Springer,The Netherlands, 2009).

dThis is also true of other classical models, such as the Isingmodel, the Potts model and percolation.



10

[15] J. M. Hammersley, The number of polygons on alattice, Proc. Camb. Phil. Soc. 57 (1961) 516–523.

[16] J. M. Hammersley and D. J. A. Welsh, Furtherresults on the rate of convergence to the connectiveconstant of the hypercubical lattice, Quart. J. Math.Oxford (2) 13 (1962) 108–110.

[17] T. Hara and G. Slade, The lace expansion for selfavoiding walk in five or more dimensions, ReviewsMath. Phys. 4 (1992) 235–327.

[18] T. Hara and G. Slade, Self avoiding walk in five ormore dimensions I. The critical behaviour, Comm.Math. Phys. 147 (1992) 101–136.

[19] I. Jensen, Enumeration of self-avoiding walks onthe square lattice, J. Phys. A 37 (2004) 5503–5524.

[20] I. Jensen, Private communication. Publication inpreparation.

[21] M. S. Z. Kellermayer, S. B. Smith, H. L. Granzierand C. Bustamante, Folding-unfolding transitionsin single Titin molecules characterized with lasertweezers, Science 276 (1997) 1112–1116.

[22] T. Kennedy, Conformal invariance and stochasticLoewner evolution predictions for the 2D self-avoiding walk — Monte Carlo tests, J. Stat. Phys.114 (2004) 51–78.

[23] H. Kesten, On the number of self-avoiding walks,J. Math. Phys. 4 (1963) 960–969.

[24] S. Kumar, I. Jensen, J. L. Jacobsen and A. J.Guttmann, Role of conformational entropy inforce-induced bio-polymer unfolding, Phys. Rev.Lett. 98 (2007) 128101.

[25] G. F. Lawler, O. Schramm and W. Werner, On thescaling limit of planar self-avoiding walk, Proc.Symposia Pure Math. 72 (2004) 339–364.

[26] K. Lowner, Untersuchungen uber schlichte kon-forme Abbildungen des Einheitskreises, I. Math.Ann. 89 (1923) 103–121.

[27] D. E. Knuth, Science 194 (1976) 1235–1242.

[28] N. Madras, J. Phys. A: Math. Gen. 28 (1995)1535–1547.

[29] N. Madras and G. Slade, The Self-avoidingWalk, Probability and its Applications (BirkhauserBoston Inc., Boston, MA, 1993).

[30] B. Nienhuis, Exact critical exponents of the O(n)model in two dimensions, Phys. Rev. Lett. 49 (1982)1062–1065.

[31] W. J. C. Orr, Statistical treatment of polymer so-lutions at infinite dilution, Trans. Faraday Soc. 43(1947) 12–27.

[32] C. Richard, Scaling behaviour of two-dimensionalpolygon models, J. Stat. Phys. 108 (2002) 459–493.

[33] C. Richard, A. J. Guttmann and I. Jensen, Scalingfunction and universal amplitude combinationsfor self-avoiding polygons, J. Phys. A: Math. Gen.34 (2001) L495–L501.

[34] C. Richard, I. Jensen and A. J. Guttmann, Scalingfunction for self-avoiding polygons revisited, J.Stat. Mech.: Th. Exp. (2004) P08007.

[35] M. Rief, M. Gautel, F. Oesterhelt, J. M. Fernandezand H. E. Gaub, Reversible unfolding of indi-vidual Titin immunoglobulin domains by AFM,Science 276 (1997) 1109–1112.

[36] I. Rouzina and V. A. Bloomfield, Force-inducedmelting of the DNA double helix 1. Thermo-dynamic analysis, Biophys. J. 80 (2001) 882–893;Force-induced melting of the DNA double helix 2.Effect of solution conditions, Biophys. J. 80 (2001)894–900.

[37] L. Tskhovrebova, J. Trinick, J. A. Sleep and R.M. Simmons, Elasticity and unfolding of singlemolecules of the giant muscle protein Titin, Nature387 (1997) 308–312.

[38] S. G. Whittington and A. J. Guttmann, J. Phys. A:Math. Gen. 23 (1990) 5601-5609.

AJG: Department of Mathematics and Statistics,The University of Melbourne,Victoria, 3010, AustraliaE-mail address: [email protected]

Anthony J GuttmannThe University of Melbourne, Australia [email protected]

Anthony J Guttmann did his PhD at the University of New South Wales, in Sydney, and went on to postdoctoral work at King’s College, London. He is currently a professor at The University of Melbourne, and also the Director of MASCOS.

Distributive Lattices and Coherence in Homological Algebra



1

Distributive Lattices and Coherence inHomological Algebra

Marco Grandis

Abstract. This article is about coherence in homologi-cal algebra, and only needs the elementary theory ofabelian groups and lattices. Its results are developedin a recent book to analyse spectral sequences — animportant tool of homological algebra with applicationsin many branches of mathematics.

0. Introduction

Spectral sequences, one of the main tools of homo-

logical algebra (see [12, 8, 11, 17, 19, 13]), find ap-

plications in many branches of mathematics, from

algebraic topology to algebraic geometry, differ-

ential geometry and partial differential equations,

thence to physics through the C-spectral sequence

of a PDE [18, 15] and control theory [9].

This expository article is about coherence in

homological algebra. The main applications, de-

veloped in a recent book [7], deal with spectral

sequences, but this exposition only needs the

elementary theory of abelian groups and lattices.

In fact, various parts of homological algebra

are based on “induction on subquotients” (i.e.

quotients of subgroups, or — equivalently —

subgroups of quotients). However, the coherence

of this procedure of induction leads to serious

problems, that are often overlooked.

Problems may already arise in the simplest

situation, canonical isomorphisms between subquo-

tients of the same object (induced by the identity

of the latter): first, such isomorphisms need not

be closed under composition; second, if we extend

them in this sense the result need not be uniquely

determined (as shown in Sec. 3). Yet, such isomor-

phisms are frequently used when working with

complicated systems, in particular those that give

rise to spectral sequences.

The solution to this coherence problem de-

pends on the distributivity of the lattices of

subgroups generated by the system that we

are studying. We prove in Sec. 6 the following

theorem:

Given a sublattice X of the (modular) lattice of

all subgroups of an abelian group A, let us consider

the subquotients M/N of A with M, N belonging

to X. Then the canonical isomorphisms among these

subquotients are closed under composition (and form

a coherent system) if and only if the lattice X is

distributive.

This is an elementary form of our “Coherence

theorem for homological algebra”. A more com-

plete form of the theorem, sketched in Sec. 8, can

be found in the book [7] (see also [4]–[6]).

These works prove that the following systems

are “distributive”, i.e. they generate distributive

lattices of subgroups and their coherence automati-

cally holds:

– bifiltered object,

– sequence of morphisms,

– filtered chain complex,

– double complex,

– Massey’s exact couple [12],

– Eilenberg’s exact system [2].

The same property of distributivity also per-

mits representations of these structures by means

of lattices of subsets; this yields a precise founda-

tion for the heuristic tool of Zeeman diagrams [20,

8], as universal models of spectral sequences.

On the other hand, the bifiltered chain complex

is not distributive, and we show in [7] a strong

form of inconsistency in this system, that can lead

to gross errors if the interaction of the two spectral

sequences of the complex is explored further than

it is normally done.

The symbol ⊂ always denotes weak inclusion

(of subsets, subgroups, etc.).

1. Subquotients and Regular Induction

For the sake of simplicity, we work in the cate-

gory Ab of abelian groups, but everything can be

extended to abelian categories and even further

(see Sec. 8).

A subquotient S = M/N of an abelian group

A is a quotient of a subgroup (M) of A, or

equivalently a subgroup of a quotient (A/N). It

Distributive Lattices and Coherence in Homological Algebra

Marco Grandis



2

is determined by two subgroups N ⊂ M of A,

via a commutative square that is bicartesian, i.e.

pullback and pushout:

M m

p

A

q

S n

A/N

(1)

The prime example, of course, is the homology

subquotient H = Ker ∂/Im ∂ of a differential group

(A, ∂); more complex examples come from the

terms of spectral sequences.

A homomorphism f : A → B is given. If M

and H are subgroups of A and B respectively,

and f (M) ⊂ H, we have a commutative diagram

with short exact rows, and two induced homo-

morphisms

M m

f ′

Ap

f

A/M

f ′′

H

h B

u B/H

(2)

More generally, given two subquotients M/N

of A and H/K of B, suppose that:

f (M) ⊂ H and f (N) ⊂ K. (3)

Then, we have a regularly induced homomor-

phism g : M/N → H/K. In fact, one can form the

diagram below, by applying (2) in two ways

M m

f ′

Aq

f

A/N

f ′′

H

h B

v B/K

(4)

Then we get a new commutative diagram, and

the homomorphism g, by factorisation of the rows

of the previous diagram through their images

Mq′

f ′

M/N m′

g

A/N

f ′′

H

v′ H/K

h′ B/K

(5)

Regular induction is (obviously) preserved by

composition. But it is too restricted a notion.

2. Canonical Isomorphisms

We now use the category RelAb of (additive)

relations, or (additive) correspondences, of abelian

groups (cf. Mac Lane [10]).

A relation a : A→ B is a subgroup of the direct

sum A ⊕ B. It can be viewed as a “partially de-

fined, multi-valued homomorphism”, that sends

an element x ∈ A to the subset y ∈ B | (x, y) ∈ a

of B. The composite ba, with b : B→ C, is

(x, z) ∈ A⊕C | ∃y ∈ B : (x, y) ∈ a, (y, z) ∈ b .

The converse relation of a : A → B is obtained

by reversing pairs, and written as a♯ : B→ A. This

involution is regular in the sense of von Neu-

mann, i.e. aa♯a = a, for all relations a. Therefore a

monorelation, i.e. a monomorphism in the category

RelAb, is characterised by the condition a♯a = 1,

and an epirelation by the condition aa♯ = 1.

The category Ab is embedded in RelAb, iden-

tifying a homomorphism with its graph. This

embedding preserves monomorphisms and epi-

morphisms (but we shall see that a monorelation

is more general than an injective homomorphism).

Isomorphisms are the same, in these categories.

Let us come back to the bicartesian square

making S into a subquotient M/N of the abelian

group A

M m

p

A

q

S n

s

A/N

(6)

This square determines one relation s = mp♯ =

q♯n : S → A, that sends the class [x] ∈ M/N to

all the elements of the lateral x + N in A. It is

actually a monorelation (since s♯s = id(S)) and all

monorelations with values in A are of this type,

up to isomorphism. The subquotients of the abelian

group A amount thus to the subobjects of A in

RelAb.

RelAb makes possible to consider a more gen-

eral notion of induction on subquotients, as de-

fined in [10]. Given a relation a : A → B and two

subquotients s : S → A, t : T → B, we say that a

induces from s to t the relation

t♯as : S→ T. (7)

In particular, if a is a homomorphism with

a regularly induced homomorphism S → T, the

latter coincides with t♯as.

If s, t are subquotients of the same object A, the

relation u = t♯s : S→ T induced by the identity of

A will be called the canonical relation from s to t;

and a canonical isomorphism if it is an isomorphism

(of RelAb or Ab, equivalently). The isomorphism

u need not be regularly induced.

Writing the subquotient s as H/K, and t as

H′/K′, it is easy to verify the following properties



3

of the canonical relation u = t♯s : H/K→ H′/K′:

(a) u is everywhere defined ⇔ H ⊂ H′ ∨K,

(a∗) u has total values ⇔ H′ ⊂ H ∨K′,

(b) u has a null annihilator ⇔ H ∧K′ ⊂ K,

(b∗) u is single-valued ⇔ H′ ∧K ⊂ K′,

(c) u is an isomorphism ⇔ (H ∨K′ = H′ ∨K,

H ∧K′ = H′ ∧K).

It follows that

(d) u is a regularly induced isomorphism ⇔ (K =

H ∧K′, H′ = H ∨K′),

which shows that a regularly induced isomor-

phism is the same as a second-type Noether

isomorphism

H/(H ∧K′)→ (H ∨K′)/K′. (8)

We write H/KΦH′/K′ the property expressed

in (c). It is obviously reflexive and symmetric, but

not transitive in general, as shown below.

It is easy to see that, if H/KΦH′/K′, there is a

commutative diagram of canonical isomorphisms

(between Φ-related subquotients of A)

(H ∨H′)/(K ∨K′)

H/K

u H′/K′

(H ∧H′)/(K ∧K′)

(9)

Note that the solid arrows are regularly in-

duced (Noether) isomorphisms; this is important,

because regular induction is always respected by

composition.

3. A Case of Incoherence

The following examples show some instances

of inconsistency of induction on subquotients: first,

canonical isomorphisms need not be closed under

composition; second, if we extend them in this

sense the result need not be uniquely determined.

As in Mac Lane’s book [10], our examples

of inconsistency are based on the lattice L(A) of

subgroups of A = Z⊕Z, and more particularly on

the (non-distributive) triple formed of the diagonal

∆ and two of its complements, the subgroups A1

and A2A1 = Z ⊕ 0, A2 = 0 ⊕ Z,

Ai ∨∆ = A, Ai ∧∆ = 0.(10)

We thus have the subquotients mi : Ai → A and

s = p♯ : A/∆→ A.

(a) The identity of A induces two canonical iso-

morphisms ui = pmi : Ai → A/∆ (regularly in-

duced Noether isomorphisms, by (10)), and a

canonical isomorphism u−12 : A/∆ → A2 (that is

not regularly induced).

Then, the composed isomorphism w = u−12 u1 :

A1 → A2 is not canonical. Indeed:

w : A1 → A/∆→ A2,

(x, 0) → [(x, 0)] = [(0,−x)] → (0,−x),(11)

while the canonical relation m♯2.m1 : A1 → A2 has

graph (0, 0).

(b) Using the subgroup ∆′ = (x,−x) | x ∈ Z

instead of the diagonal ∆, we get the opposite

composed isomorphism from A1 to A2

A1 → A/∆′ → A2,

(x, 0) → [(x, 0)] = [(0, x)] → (0, x).(12)

This shows that a composite A1 → A2 of

canonical isomorphisms between subquotients of

Z2 is not determined.

Now, a change of sign can be quite important,

in homological algebra and algebraic topology.

For instance, it is the case in the usual argument

proving that “even-dimensional spheres cannot

be combed”: if the sphere Sn has a non-null

vector field, then its antipodal map t : Sn → Sn is

homotopic to the identity, and the degree (−1)n+1

of t must be 1. The conclusion cannot be obtained

if we only know the induced homomorphism

t∗n : Hn(Sn)→ Hn(Sn) up to sign change.

4. Coherent Systems of Isomorphisms

Let X be a sublattice of the (modular) lattice L(A)

of subgroups of the abelian group A; we always

assume that X contains the least and greatest

elements of L(A). We are interested in the set X

of all the subquotients of A with numerator and

denominator in X, whose coherence is discussed

below.

Plainly, the set X can be identified with the set

X2 of decreasing pairs (numerator, denominator)

of X, where the relation (x, y)Φ (x′, y′) is expressed

by the following two equivalent conditions:

(a) x ∨ y′ = x′ ∨ y, x ∧ y′ = x′ ∧ y,

(b) x x′ ∨ y, x′ x ∨ y′, x ∧ y′ y, x′ ∧ y y′.

For a system Σ of subquotients of A (usually

of the previous form), we are interested in the

following equivalent properties

(i) whenever u : S → S′ and v : S′ → S′′ are

induced isomorphisms between elements of the

system, the composed isomorphism vu coincides

with the canonical relation S→ S′′,



4

(ii) the relation Φ is an equivalence relation among

the subquotients of Σ, and all diagrams of canon-

ical isomorphisms between them commute.

When this holds we say that Σ is a coherent

system of subquotients of A. We also express this

fact saying that the canonical isos among all S ∈

Σ are closed under composition, or form a coherent

system of isomorphisms. (Since Mac Lane’s paper

[11], a coherence theorem in category theory states

that, under suitable assumptions, all the diagrams

of a given type commute.)

When such a system has been fixed (e.g. using

the Coherence theorem below) we shall express

the (equivalence!) relation SΦ S′ of Σ by saying

that the subquotients S and S′ are canonically

isomorphic (within Σ). But expressing in this way

the relation Φ when transitivity does not hold is

misleading and should be carefully avoided.

We have seen that the whole system of sub-

quotients of Z2 is not coherent (Sec. 3); the same

holds for any abelian group A⊕A, where A is not

trivial.

Even when a set Σ = X is coherent, one should

not expect that all the induced homomorphisms

(or even less relations) be closed under com-

position. In fact, the composite of the canonical

homomorphisms

A/0→ A/A→ 0/0→ A/0

is null, while the canonical homomorphism

A/0 → A/0 is the identity (and all these subquo-

tients necessarily belong to X).

5. Lemma

Let X be a modular lattice. The following conditions

are equivalent:

(i) the lattice X is distributive,

(ii) the relation (x, y)Φ (x′, y′) defined above on the

set X2 of decreasing pairs of X is an equivalence

relation.

Proof. Let X be distributive, and assume that

(x, y)Φ (x′, y′)Φ (x′′, y′′). Then:

x = (x′ ∨ y) ∧ x = (x′′ ∨ y′ ∨ y) ∧ x

x′′ ∨ (y′ ∧ x) ∨ y = x′′ ∨ (y ∧ x′) ∨ y = x′′ ∨ y.

The other three inequalities of (x, y)Φ (x′′, y′′),

in form (b) of Sec. 4, are proved in a similar way.

Conversely, suppose that the relation Φ is tran-

sitive. Let M = m′, x, y, z, m′′ be a sublattice of X,

where the meet (resp. join) of any two elements

out of x, y, z is m′ (resp. m′′). Then we have

(x, m′)Φ (m′′, y)Φ (z, m′), whence (x, m′)Φ (z, m′)

and x = z.

In other words, the modular lattice X cannot

have a sublattice M as above, formed of five

distinct elements; by a well-known theorem ([1],

II.8, Theorem 13), X must be distributive.

6. Coherence Theorem of Homological

Algebra (Reduced Form)

Theorem. Let X be a sublattice of the lattice L(A) of

subgroups of the abelian group A. Then the following

conditions are equivalent:

(i) the lattice X is distributive,

(ii) the family X is coherent (i.e. the canonical iso-

morphisms among subquotients of A with numer-

ator and denominator belonging to X are closed

under composition).

Proof. If (ii) holds, the relation Φ is transitive in

X (or equivalently in X2) and X is distributive, by

the previous lemma.

Conversely, let us assume that X is distribu-

tive, and consider two canonical isomorphisms

between three subquotients

u : H/K→ H′/K′, v : H′/K′ → H′′/K′′. (13)

We must prove that the composite vu is the

canonical relation w : H/K → H′′/K′′. By Lemma

5, these three subquotients are Φ-equivalent.

Let us write

S1 = (H ∧H′)/(K ∧K′),

S2 = (H′ ∧H′′)/(K′ ∧K′′),

S0 = (H ∧H′ ∧H′′)/(K ∧K′ ∧K′′).

By Sec. 2, we can form the following com-

mutative diagram, where all subquotients are Φ-

equivalent, and the solid arrows are regularly in-

duced by id(A)

H/Ku H′/K′

v H′′/K′′

S1

S2

S0

(14)

But we can also form a second commutative

diagram with regularly induced solid arrows

H/Kw H′′/K′′

S1

(H ∧H′′)/(K ∧K′′)

S2

S0

(15)



5

Since the four solid arrows of the “boundary”

of these two diagrams coincide, the thesis follows:

vu = w.

7. Filtered Chain Complexes

Let us now consider one of the most usual struc-

tures giving rise to a spectral sequence, a filtered

chain complex A∗ of abelian groups, with (canoni-

cally) bounded filtration

A∗ = ((An), (∂n), (FpAn)). (16)

This is a chain complex of abelian groups

... An∂n−→ An−1 → ... → A1

∂1−→ A0

(∂n∂n+1 = 0),

where each component An has a filtration of

length n + 1, consistently with the differentials:

0 ⊂ F0An ⊂ ... FpAn ⊂ ... FnAn = An,

∂n+1(FpAn+1) ⊂ FpAn.(17)

On each component An the filtrations of An+1

and An−1 produce a second finite filtration (of

length 2n+3), by direct and inverse images along

the differentials (while the other components have

a trivial effect)

0 ⊂ ∂n+1(F0An+1) ⊂ ... ∂n+1(Fn+1An+1)

= Im ∂n+1 ⊂ Ker ∂n = ∂−1n (0) ⊂

∂−1n (F0An−1) ⊂ ... ∂−1

n (Fn−1An−1) = An.

(18)

By a well-known Birkhoff theorem on the free

modular lattice generated by two chains ([Bi],

III.7, Theorem 9), the two filtrations generate a

finite, distributive lattice of subgroups of An, that

can be represented as (a quotient of) a lattice

of subsets of the plane. (Notice the crucial role

played here by the condition ∂∂ = 0: without that,

the lattice generated by the data would not be

distributive.)

In particular, FpAn has a filtration of relative

cycles and relative boundaries, that is the “trace” of

the second filtration (18) (with n = p + q)

Zrpq(A∗) = FpAn ∧ ∂

−1(Fp−rAn−1),

Brpq(A∗) = FpAn ∧ ∂(Fp+rAn+1).

(19)

Now, the term Erpq, of the spectral sequence of

A∗ is usually defined as a subquotient of An (with

n = p + q), by one of the following “equivalent”

formulas:

Zrpq/(Z

r−1p−1,q+1 ∨Br−1

pq ), (20)

(Zrpq ∨ Fp−1An)/(Br−1

pq ∨ Fp−1An), (21)

that are linked by a canonical isomorphism,

regularly induced from the first to the second

subquotient.

The first expression is used, for instance, in

Hilton–Wylie [8, Section 10.3], and Spanier [17,

9.1]. The second is used in Mac Lane’s “Homol-

ogy” [10, XI.3]. Weibel [19] uses both, in Sec. 5.4

(with a different notation).

And indeed, no problem can here arise from

using different formulas linked by canonical iso-

morphisms, because of the distributivity of the

system. But this is no longer true in a non-

distributive system like the bifiltered chain com-

plex [7], if we let its spectral sequences (derived

from the two filtrations) interact.

8. The Full Coherence Theorem

We end by mentioning, without proof, a more

complete form of our coherence theorem.

The proof can be found in the book [7], with

various other equivalent conditions and many

applications to the theory of spectral sequences.

The required setting is an extension of abelian

categories. A p-exact category, i.e. an exact cate-

gory in the sense of Puppe and Mitchell [16, 14,

3], is a category with a zero object, where every

map factorises as a cokernel (of some morphism)

followed by a kernel. The setting is selfdual, and

the existence of cartesian products is not assumed.

A p-exact category E is said to be distributive

if all its lattices of subobjects are distributive. The

main example is the category I of sets and partial

bijections, where every small distributive p-exact

category can be exactly embedded.

A non-trivial abelian category cannot be dis-

tributive; but all p-exact categories, including the

abelian ones, have a distributive expansion to which

the theorem below applies.

Coherence theorem of homological algebra

For a p-exact category E, the following conditions are

equivalent:

(i) canonical isomorphisms between subquotients of

the same object are closed under composition,

(ii) induced isomorphisms between subquotients

(induced by arbitrary homomorphisms, or even

by relations) are preserved by composition,

(iii) E is distributive,

(iv) the category of relations RelE is orthodox (i.e.

its idempotent endomorphisms are closed under

composition).



6

References

[1] G. Birkhoff, Lattice Theory, Third edn. (Amer. Math.Soc. Coll. Publ., Providence 1973).

[2] S. Eilenberg, La suite spectrale, I: Constructiongenerale, Sem. Cartan 1950–1951, Exp. 8.

[3] P. J. Freyd and A. Scedrov, Categories, Allegories(North-Holland Publ. Co., Amsterdam, 1990).

[4] M. Grandis, On distributive homological algebra,I. RE-categories, Cahiers Top. Geom. Diff. 25 (1984)259–301.

[5] M. Grandis, On distributive homological algebra,II. Theories and models, Cahiers Top. Geom. Diff. 25(1984) 353–379.

[6] M. Grandis, On distributive homological algebra,III. Homological theories, Cahiers Top. Geom. Diff.26 (1985) 169–213.

[7] M. Grandis, Homological Algebra, the Interplay ofHomology with Distributive Lattices and OrthodoxSemigroups (World Scientific, Singapore, 2012).

[8] P. J. Hilton and S. Wylie, Homology Theory (Cam-bridge Univ. Press, Cambridge, 1962).

[9] E. A. Jonckheere, Algebraic and Differential Topologyof Robust Stability (Oxford Univ. Press, New York,1997).

[10] S. Mac Lane, Homology (Springer, Berlin, 1963).[11] S. Mac Lane, Natural associativity and commuta-

tivity, Rice Univ. Studies 49 (1963) 28–46.[12] W. S. Massey, Exact couples in algebraic topology,

Ann. Math. 56 (1952) 363–396.[13] J. McCleary, A User’s Guide to Spectral Sequences,

Second edn. (Cambridge Univ. Press, Cambridge,2001).

[14] B. Mitchell, Theory of Categories (Academic Press,New York, 1965).

[15] A. Prastaro, Geometry of PDEs and Mechanics(World Scientific, Singapore, 1996).

[16] D. Puppe, Korrespondenzen in abelschen kate-gorien, Math. Ann. 148 (1962) 1–30.

[17] E. H. Spanier, Algebraic Topology (McGraw-Hill,New York, 1966).

[18] A. M. Vinogradov, Cohomological Analysis of PartialDifferential Equations and Secondary Calculus (Amer.Math. Soc., Providence 2001).

[19] C. A. Weibel, An Introduction to Homological Algebra(Cambridge Univ. Press, Cambridge, 1994).

[20] E. C. Zeeman, On the filtered differential group,Ann. Math. 66 (1957) 557–585.

Marco Grandis University of Genova, Italy

Marco Grandis is Professor at the Department of Mathematics of the University of Genova. He works on Algebraic Topology, Homological Algebra and higher dimensional Category Theory. He is the author of a book on Directed Algebraic Topology, published at Cambridge University Press, and two books on Homological Algebra that are being published at World Scientific; the first of them develops the problems described here and their applications.



1

C S Seshadri — A Glimpse of HisMathematical Personality

V Balaji

C S Seshadri

Abstract. The aim of the article is to give a quick in-sight into the mathematical personality of C S Seshadriwho turned eighty this year. We take a small journeythrough the areas of research where he has madeoutstanding contributions.

1. Introduction

Conjeevaram Srirangachari Seshadri was born on

February 29, 1932, in Kanchipuram. He was the

eldest among eleven children of his parents, Sri

C Srirangachari (a well-known advocate in Chen-

gleput, a town 60 km South of Chennai) and

Srimati Chudamani. Seshadri’s entire schooling

was in Chengleput. He joined the Loyola College,

Chennai in 1948, and he graduated from there in

1953 with a BA (Hons) degree in mathematics.

During his years at college, Professor

S Narayanan and Fr C Racine played a decisive

role in Seshadri’s taking up mathematics as a

profession.

Seshadri joined the Tata Institute of Funda-

mental Research, Mumbai in 1953 as a student.

He received his PhD degree in 1958 from the Bom-

bay University for his thesis entitled “Generalised

multiplicative meromorphic functions on a com-

plex manifold”. His thesis adviser was Professor

K Chandrasekaran who shaped the mathematical

career of Seshadri as he did for many others.

Seshadri spent the years 1957–1960 in Paris,

where he came under the influence of many great

mathematicians of the French school, like Cheval-

ley, Cartan, Schwartz, Grothendieck and Serre.

He returned to the TIFR in 1960 and was a

member of the faculty of the School of Mathe-

matics until 1984, where he was responsible for

establishing an active school of algebraic geom-

etry. He moved to the Institute of Mathematical

Sciences, Chennai in 1984.

In 1989, Seshadri became the director of

the Chennai Mathematical Institute, then called

the SPIC Mathematical Institute, founded by

A C Muthiah.

Seshadri is a recipient of numerous distinc-

tions. He received the Bhatnagar Prize in 1972

and was elected a fellow of the Royal Society,

London in 1988. He has held distinguished po-

sitions in various centres of mathematics, all over

the world. In 2006, Seshadri was awarded the

TWAS Science Prize along with Jacob Palis for his

distinguished contributions to science.

In the past five years since he received the Na-

tional Professorship, Seshadri has been awarded

the H K Firodia Award for Excellence in Sci-

ence and Technology, Pune, 2008, the Rathindra

Puraskar from Shantiniketan’s Visva-Bharati Uni-

versity, Kolkata, 2008, the Padma Bhushan by the

President of India, 2009. More recently, he was

elected a Foreign Associate of the US National

Academy of Sciences, 2010.

On February 29, 2012, Seshadri turned eighty

and the Chennai Mathematical Institute and the

Institute of Mathematical Sciences together held

their first joint International Mathematics Confer-

ence in his honour.

Seshadri is also an accomplished exponent

of the Carnatic Music and even to this day he

continues to religiously do his musical sadhana.

C S Seshadri — A Glimpse of His Mathematical Personality

Vikraman Balaji

C S Seshadri — A Glimpse of His, Mathematical Personality,



2

Seshadri married Sundari in 1962, and they

have two sons, Narasimhan and Giridhar.

2. Seshadri’s Mathematical Work

Over the past fifty years, C S Seshadri has been

a towering figure in the mathematical horizon,

and his contributions have been central to the

development of moduli problems and geometric

invariant theory as well as representation theory

of algebraic groups. In 2012, his Collected Papers

was published in two volumes and runs to nearly

1700 pages. The subject matter in these volumes

is a true reflection of the diversity of his mathe-

matical contributions.

J P Serre in his famous paper “Faisceaux

algebriques coherents”, posed the following ques-

tion: “Is a finitely generated projective module

over the polynomial ring in several variables

free, or equivalently, is an algebraic vector bun-

dle over the n-dimensional affine space trivial?”

Seshadri’s ingenious solution of Serre’s problem

on projective modules in two variables was a

catalyst for much of the later developments in this

area. This work attracted much attention, culmi-

nating in the famous Quillen–Suslin theorem. This

paper ([1]) was written during Seshadri’s stay in

Paris in the late 1950’s where he came under the

influence of Chevalley and Serre. His early work

([3]) on the Picard varieties and related problems

has its roots in the Chevalley Seminar where

he contributed several important exposes ([2]).

Besides the ideas of Chevalley, the construction of

the Picard variety of a complete variety uses the

descent theory of Cartier for purely inseparable

coverings and those related to the existence of

a moduli for a rational map of a smooth curve

into a commutative group variety (in the sense

of Rosenlicht). This work was influential in the

later work of J P Murre on representability of

the Picard functors (Publications of IHES, 1964)

(see also A Grothendieck’s “Fondements de la

geometrie algebrique” for these developments).

Subsequently, he took up the problem of con-

structing “orbit spaces” when one is given a good

action of a group variety on an algebraic variety.

The orbit space X/G in general need not exist

as an algebraic variety even when G is a finite

group, unlike the complex analytic or differen-

tiable cases. Seshadri showed in [4] that if X is

a normal variety the obstruction to the existence

of an algebro-geometric orbit space comes from

a finite group action. This result (see also [11])

is a sort of precursor to the existence of X/G as

an algebraic space in the sense of M Artin (see

also the work of Janos Kollar, Annals of Math-

ematics, 1997). If moreover G happens to be an

abelian variety, Seshadri showed ([5]) that the

orbit space always existed as an algebraic variety.

An interesting point of this work is that it has a

criterion for a Weil divisor on the product of a

normal variety and a smooth variety to be locally

principal. This led to a stronger version known as

the Ramanujam–Samuel theorem which figures in

the Appendix to this paper by C P Ramanujam

([5]).

It was around this time in the early 1960s that

D Mumford had come up with his deep work on

geometric invariant theory and at much about the

same time Seshadri and Narasimhan began their

work on vector bundles which had its origins

in the paper of Weil written in 1938 entitled

“Generalisation des fonctions abeliennes”.

One of the important developments in alge-

braic geometry in the last few decades is that

of the deep study of moduli problems, starting

initially with that of curves, abelian varieties and

vector bundles on curves. Initial results on vector

bundles on curves were those of Grothendieck

on P1 and Atiyah on elliptic curves. The work

of Weil mentioned above contained many ideas

on the characterisation and classification of vector

bundles on compact Riemann surfaces and their

relationship with representations of the funda-

mental group of the Riemann surface. In 1962, in

his talk at the International Congress of Mathe-

maticians, David Mumford gave a sketch of his

“Geometric invariant theory”, or GIT as it is called

now. In this talk, Mumford outlined how GIT

could be used to solve moduli problems of curves,

abelian varieties and vector bundles. The notions

of stability and semistability were introduced in

this work of Mumford. He also sketched a proof

of the quasi-projectivity of the moduli space of

stable bundles of fixed rank and degree.

The theme in the work of Narasimhan and

Seshadri ([6, 7]) is the study of the space which

parametrises conjugacy classes of representations

of the fundamental groups of Riemann surfaces.

This can be seen as a non-abelian generalisation

of the classical Jacobian of a Riemann surface.

In the classical abelian case, the Abel–Jacobi map



3

identifies the space of representations H1(X, U(1))

with the Jacobian of the curve X. The Jacobian

can be seen geometrically as the moduli space of

holomorphic line bundles on X of degree 0. The

corresponding non-abelian analogy is the theme

in the papers of Narasimhan–Seshadri.

The basic object in the non-abelian theory

turned out to be that of a stable bundle obtained

in an altogether different context by D Mumford.

The paper of Narasimhan–Seshadri studies the

space M(n, d)s of isomorphism classes of stable

holomorphic vector bundles of rank n and degree d.

They prove that M(n, d)s can be identified as a

topological space with the space of irreducible

unitary representations of π1(X). The main theme

of this work can be described as establishing

a functorial correspondence between the cate-

gories of irreducible unitary representations of certain

Fuchsian groups and stable holomorphic bundles of

degree d.

The Narasimhan–Seshadri theorem has had

a profound impact on the subject. It has been

developed and generalised on many fronts. Just to

name a few, starting with the paper of Atiyah and

Bott, unexpected links with mathematical physics

were perceived, coming from the so-called Yang–

Mills equations, where they prove that irreducible

unitary representations realise the minimum, in

the Morse theoretic sense, of the Yang–Mills func-

tional. This led to a radically different differen-

tial geometric approach to these problems and

vast ramifications in mathematical physics and

4-manifold topology, leading for instance to the

deep work of Simon Donaldson.

In his papers of 1967 and 1968 ([8, 9]), Seshadri

then proceeded to compactify the moduli spaces

M(n, d)s by extending Mumford’s Geometric In-

variant Theory. The notion of a semi-stable bundle

is a slight generalisation of that of a stable bundle

and these under a special kind of equivalence

provide the points needed to compactify the mod-

uli space. The fundamental notions which had

its origins in these papers, such as that of “S-

equivalence” and the technique of proving that

a bundle is semi-stable if and only if it happens

to be GIT semi-stable in a suitable space, have

become the standard tools in most constructions

of compactifications found in the literature. In-

deed, to be able to generalise the moduli con-

structions to fields of arbitrary characteristics, it

was firstly essential that GIT be generalised to

arbitrary characteristics and secondly, to be able to

prove the properness of the moduli without using

the compactness of the underlying topological

space (what is now known as Langton’s valuative

criterion); this is achieved in [9].

In fact, David Mumford pointed out in his talk

during Seshadri’s sixtieth birthday celebrations

that Seshadri’s construction of the compactifica-

tion of the moduli of stable bundles with all

its conceptual complexity was a perfect repre-

sentative example and a forerunner of all later

GIT constructions of compactifications in a whole

range of moduli problems.

In the mid-1960s, towards generalising GIT

for fields of arbitrary characteristics, D Mumford

made his conjecture on the equivalence of geo-

metric reductivity and reductivity. Seshadri proved

this conjecture in 1968 for the case of GL(2) ([9]);

earlier T Oda had proven this for a field of

characteristic 2. Viewed from a geometric stand-

point, the projectivity of the moduli space of semi-

stable bundles thought of as a GIT quotient provides

strong evidence for the validity of Mumford con-

jecture for GL(n). Following this train of thought,

Seshadri wrote his paper ([11]) on Quotient spaces

in 1970 as an attempt to solve this conjecture

using algebro-geometric methods. The paper was

not quite successful in proving the Mumford con-

jecture, however it contained many fundamental

ideas such as for instance what is now known as

“Seshadri’s ampleness criterion” and the so-called

“Seshadri constant” which plays a key role in the

classification of algebraic varieties. The conjecture

which was finally settled by W Haboush in the

mid-1970s using crucially the work of Steinberg in

representation theory. But very recently, drawing

on results of Sean Keal from a paper in 1998,

Seshadri (in collaboration with P Sastry [17])

has given a more algebro-geometric proof of the

Mumford Conjecture which he had envisaged in

his paper ([11]) of 1970 on Quotient spaces.

Seshadri, inspired again by A Weil’s

“Generalisation des fonctions abeliennes”,

went on to define the notion of a parabolic bundle

as the natural analogue for studying the bundle

theoretic aspects of representation theory of more

general Fuchsian groups (see [10]). His paper

([13]) (written in collaboration with V B Mehta)

which interprets unitary representation of

Fuchsian groups as parabolic semi-stable bundles,

has had profound applications in the synthesis of



4

mathematical physics and topology. In a sense,

this work of Seshadri gave a final shape to the

theme that had been envisaged in Weil’s paper.

Very recently, in a joint work ([19]), Balaji and

Seshadri interpret homomorphisms of Fuchsian

groups into maximal compact subgroups of

semisimple algebraic groups in terms of torsors

under Bruhat–Tits groups schemes which need

not be semisimple. This is in striking contrast with

the earlier results on parabolic vector bundles.

One of the difficult problems in the study of

vector bundles on curves is that of classification of

bundles on singular curves. Seshadri constructed

a natural compactification of semistable vector

bundles on irreducible nodal curves by adding

torsion-free sheaves under a suitable equivalence.

The key property of this construction was that

it had good specialisation properties ([14]). This

problem was not trivial even when the bundles

were of rank 1 and this was studied in great

depth by Oda and Seshadri (see [18] and [12]).

Subsequently, in collaboration with D S Nagaraj

([15, 16]), Seshadri has made significant progress

in the general problem of compactifications with

“normal crossing singularities”, generalising the

work of Gieseker who had done it earlier for the

rank 2 case. The problem of constructing projec-

tive moduli spaces of sheaves on nodal curves

has many applications especially towards solving

several topological questions on M(n, d).

Seshadri’s contributions to the field of rep-

resentation theory and standard monomials has

been dealt with in detail by an article by Seshadri

himself in the second volume of his recently

published collected papers.

We now turn to give a very brief account of

his work on standard monomial theory much of

which in its later developments was a collab-

oration with V Lakshmibai and C Musili. The

modern standard monomial theory was initiated

by C S Seshadri in the early 1970’s which was

a vast generalisation of the classical theory of

Hodge for the Grassmannians. The broad aim

of this theory was the construction of bases for

the space of sections of line bundles on Schubert

varieties which reflects the intrinsic geometry of

the Schubert variety and the intricate combina-

torics of the Weyl group. The theory has led to

very fundamental developments in the fields of

Representation theory, Geometry and Combina-

torics. Following a series of basic papers written

in collaboration with V Lakshmibai and being

guided by careful analysis and a study of Schu-

bert varieties for exceptional groups, Lakshmibai

and Seshadri formulated the LS conjectures. The

key point of the conjectures was that it gave

an indexing of the SMT bases which implied a

remarkable character formula now termed the

LS character formula. There was a second aspect

to these conjectures which constructed bases for

the usual Demazure modules associated to the

Schubert varieties. P Littelmann proved these con-

jectures by bringing in fresh inputs and new ideas

from the theory of Quantum groups.

3. Seshadri’s Contribution to Mathematics

Education

The Chennai Mathematical Institute in its present

form was founded in 1998 but its roots go back to

1989 when Seshadri founded a new institute, then

called the School of Mathematics, SPIC Science

Foundation. The Chennai Mathematical Institute

(CMI) is a unique institution in India which at-

tempts to integrate undergraduate education with

research; it grew out of Seshadri’s vision that

higher learning can be only in an atmosphere of

active research amidst the presence of masters in

the subject. It was a brave venture in the face

of extraordinary opposition and skepticism even

from his very close friends and well-wishers. It

was his dream to build a centre of learning which

can compare itself with the great centres such as

the Ecole Normale in Paris, the Oxford and Cam-

bridge Universities in England and the Harvard

University in the US. It opens up opportunities for

the gifted students in India to learn in this unique

academic atmosphere and also gives possibilities

for the active researchers to participate in this

experiment which one believes will leave an ev-

erlasting influence on the development of mathe-

matics in India. It would not be an exaggeration

to say that the Chennai Mathematical Institute is

now rated as one of the best schools in the world

for undergraduate studies in mathematics. This

is indeed a first step in its stride and much still

needs to be done to fulfill Seshadri’s dream.

References

[1] C. S. Seshadri, Triviality of vector bundles over theaffine space K, Proc. Mat. Aca. Sci., USA 44 (1958)456–458.



5

[2] C. S. Seshadri, Many exposes in the ChevalleySeminar, Seminaire Chevalley, 3 Aunce (1958–1959).

[3] C. S. Seshadri, Variete de Picard d’une Varietecomplete, Annali di Mat. Italy IV LVII (1962)117–142.

[4] C. S. Seshadri, Some results on the quotient spaceby an algebraic group of automorphism, Math.Annalen 149 (1963) 286–301.

[5] C. S. Seshadri, Quotient space by an Abelianvariety, Math. Annalen 152 (1963) 185–194.

[6] M. S. Narasimhan and C. S. Seshadri, Holo-morphic vector bundles on a compact Riemannsurface, Math. Ann. 155 (1964) 69–80.

[7] M. S. Narasimhan and C. S. Seshadri, Stable bun-dles and unitary bundles on a compact Riemannsurface, Annals of Math. 82 (1965) 540–567.

[8] C. S. Seshadri, Space of unitary vector bundles ona compact Riemann surface, Annals of Math. 85

(1967) 303–335.[9] C. S. Seshadri, Mumford’s conjecture for GL(2) and

applications, Proc. Intern. Colloquium on AlgebraicGeometry, Bombay (1968) 347–371.

[10] C. S. Seshadri, Moduli of π-vector bundles overan algebraic curve, Proc. C.I.M.E. Session, Varenna(1969).

[11] C. S. Seshadri, Quotient spaces module reductivealgebraic groups, Ann. Math. 95(3) (1972) 511–556.

[12] T. Oda and C. S. Seshadri, Compactifications ofthe generalised Jacobian variety, Transactions of theA.M.S. 253 (1979) 190.

[13] V. B. Mehta and C. S. Seshadri, Moduli of vectorbundles on curves with parabolic structures, Math.Ann. 228 (1980) 205–239.

[14] C. S. Seshadri, Vector bundles on curves, Lecturesat the Ecole Normale Superieure (1980) — Aster-isque, 96.

[15] D. S. Nagaraj and C. S. Seshadri, Degenerationsof the moduli spaces of vector bundles on curvesI, Proc. Indian Acad. Sci. (Math. Sci.) 107 (1997)101–137.

[16] D. S. Nagaraj and C. S. Seshadri, Degenerations ofthe moduli spaces of vector bundles on curves II(Generalized Gieseker moduli spaces), Proc. IndianAcad. Sci. (Math. Sci.) 109(2) (1999) 165–201.

[17] P. Sastry and C. S. Seshadri, Geometric reductivity— A quotient space approach to appear in JournalRamanujan Mathematical Society (2011).

[18] C. D’Souza, Compactication of generalised Jaco-bians, Proc. Indian Acad. Sci. Sect. A Math. Sci.88(5) (1979) 419–457.

[19] V. Balaji and C. S. Seshadri, Moduli of parahoricG-torsors on a compact Riemann surface, preprint(2011).

Vikraman BalajiChennai Mathematical Institute, India

[email protected]

Vikraman Balaji is currently a Professor at the Chennai Mathematical Institute. He works in Algebraic Geometry and Representation Theory. He did his doctoral work under Professor Seshadri’s guidance.



A Game Based on Knot TheoryAyaka Shimizu

1

A Game Based on Knot TheoryAyaka Shimizu

1. Background — Region Crossing

Change

A puzzle game — Region Selecta — was pro-

duced by Akio Kawauchi, Kengo Kishimoto and

the author at Osaka City University Advanced

Mathematical Institute (OCAMI). In December

2011, an Android application “Region Select” was

released, and now the number of installations is

more than 5,000. (We have a plan for an iPhone

version, too.) You can also play Region Select at

OCAMI’s website [5]. Young and old alike play

Region Select all over the world. This game is

based on knot theory.

In this report, I will explain how Region Select

was created, and what Region Select might do in

the future.

In autumn of 2010, Kengo Kishimoto, who was

a researcher at OCAMI (and now a lecturer at Os-

aka Institute of Technology), asked the following

question in a seminar at Osaka City University:

Is a region crossing change on knot diagrams an

unknotting operation?

A region crossing change is a local move on

knot and link diagrams defined by Kishimoto.

We explain Kishimoto’s question in detail. A knot

is an embedding of a circle in the 3-sphere. A

knot diagram is a projection on the 2-sphere S2

of a knot with over/under information such as

D and D′ in Fig. 1. Note that a knot diagram

with n crossings divides S2 into n + 2 parts. We

call the parts regions. A region crossing change on

a region R of a knot diagram D is defined to

be a crossing change at all the crossings on the

boundary of R. Kishimoto’s question is whether

we can obtain a diagram for the trivial knot

from any knot diagram by a finite sequence of

region crossing changes. To answer Kishimoto’s

question, the author, who was a graduate student

at Osaka City University, proved the following

theorem ([4]):

aRegion Select is patent pending for the game mechanics andprogram by Osaka City University.

mm

D D'

R region crossing

change on R

Fig. 1. Region crossing change

D D

rccc c

Fig. 2.

Theorem. We can change any crossing of any knot

diagram by a finite number of region crossing changes.

(See Fig. 2.) It is well-known that we can obtain a

diagram of the trivial knot from any knot diagram

by crossing changes. Therefore, the answer to

Kishimoto’s question is “Yes”. Recently, Chen and

Gao generalised this result to links ([3, 2]).

2. Creation of the Game

From Kishimoto’s question, we produced the

game as follows: First, we create a knot projection

with lamps, namely, a knot projection with lamps

on the crossings. The lamps can be turned on or

off. A region crossing change on a region of a

knot projection with lamps will turn on/off of

the lamps on the boundary of the region. From

the above theorem, we have the following:

We can turn on/off any lamp of any knot

projection by a finite number

of region crossing changes.

Then, the goal of the game Region Select is to light

up all the lamps of a given knot projection with

lamps by a sequence of region crossing changes

chosen by clicking on regions on a display (see

Fig. 3).

D

Drcc

c

c

D

Drcc

c

c

D D'R region crossing

change on R



2

Fig. 3. Region Select

Later, Kawauchi, Kishimoto and the author

created the dual version of Region Select, and

Ahara and Suzuki showed the Region Select with

n-colour lamps instead of on/off lamps is also

well-defined ([1]). We hope more related games

will appear all over the world.

3. Future Development

Since Region Select does not need words or nu-

merical equations, we can imagine many kinds

of applications of Region Select. For example, we

expect Region Select will be used in primary edu-

cation. We hope children enjoy this game and ap-

preciate its graphics. Their ability to think ahead

will be straightened by playing the game. Now

we need to design the game for children as shown

in Fig. 4 or [6]. We also expect to use Region Select

for training cognitive functions to recognise shape

during rehabilitation. Since this game is based

on pure mathematics, we expect and believe that

Region Select has limitless possibilities.

Fig. 4. Region Select for children

References

[1] K. Ahara and M. Suzuki, An integral region choiceproblem on knot projection, arXiv: 1201.4539.

[2] Z. Cheng, When is region crossing change an un-knotting operation? arXiv: 1201.1735.

[3] Z. Cheng and H. Gao, On region crossing changeand incidence matrix, to appear in Science ChinaMathematics.

[4] A. Shimizu, Region crossing change is an unknot-ting operation, arXiv:1011.6304.

[5] Region Select: http://www.sci.osaka-cu.ac.jp/math/OCAMI/news/gamehp/etop/gametop.html

[6] Region Select for children:http://www.sci.osaka-cu.ac.jp/math/OCAMI/news/gamehp/c3game/game3/top.html

Ayaka ShimizuHiroshima University, Japan

Ayaka Shimizu is a mathematician at Hiroshima University where she is a Research Assistant Professor. She is also a researcher member at Osaka City University Advanced Mathematical Institute (OCAMI). She graduated Ochanomizu University in 2007, and received MS (Master of Science) and DS (Doctor of Science) from Osaka City University in 2009 and 2011, respectively. She was a JSPS Research Fellow from 2010 to 2012. She works on knot theory, in particular on knot diagrams.

Translated by author from Sugaku Tushin, Vol. 17, No. 1, May 2012



Ashoke Sen was born in Calcutta and studied physics at the Presidency College of the city, at the Indian Institute of Technology in Kanpur,

and did his doctorate at Stony Brook. He has been with the Harish-Chandra Research Institute for the last seventeen years. His main area of work is String Theory, which has deep connections with mathematics.

Ashoke Sen is a Fellow of the Royal Society in London, and he has won many prizes and awards, such as the Infosys Prize in the Mathematical Sciences for the year 2009. Recently, he was among the first recipients of the Fundamental Physics Prize “for opening the path to the realisation that all string theories are different limits of the same underlying theory”. This richly endowed prize has been set up by the Russian billionaire Yuri Milner for rewarding scientific breakthroughs. Ashoke Sen was the only recipient from Asia of this inaugural prize; the others being Nima Arkani-Hamed, Alan Guth, Alexei Kitaev, Maxim Kontsevich, Andrei Linde, Juan Maldacena, Nathan Seiberg and Edward Witten.

Chandan Singh Dalawat recently had an interview with Ashoke Sen at Harish-Chandra Research Institue.

Chandan Singh Dalawat: Congratulations on receiving the Fundamental Physics Prize. It must

be very gratifying to see so many years’ hard work so richly rewarded. You went to school in Calcutta, then to Presidency College (founded by the British colonial authorities) for your undergraduate studies and to the Indian Institute of Technology in Kanpur for your master’s degree. What role have these institutions played in your formation, and when did you first realise that you could become a physicist?

Ashoke Sen: Of course the institutions had a major role in my formation but it is hard to quantify it. For example, if instead of these institutions I had attended some completely different sets of institutions, would I be very different? I do not know.

I wanted to be a scientist since my childhood, but had no idea of what science meant. This desire remained with me, and as I went to college and then to IIT I slowly learned what science means.

CSD: What are your impressions of the state of science education in India at the school level and at the university level? Do you feel that there is some room for improvement in the number of institutions and in the quality of teaching?

AS: Since I am not involved in school and university level science education, it is hard for me to comment on this. There is always room for improvement in any system, but to really identify what they are one needs to be involved in the system which I have not been.

CSD: I was quite disappointed a few years ago by the quality of the standard mathematics textbooks in our high schools. Have you seen the science textbooks in use in our high schools and colleges, and what do you think of them?AS: I have seen some textbooks. All I can say is that they are better than what we studied in school.

CSD: The Indian government has recently created a number of new science institutes devoted to teaching and research. I’m told that they are finding it difficult to hire the right people. Were you involved in their creation, and are you somehow involved in their functioning? How does one explain their

Interview with Ashoke Sen

C S Dalawat

September 19, 2012, Harish-Chandra Research Institute, India

Ashoke Sen



inability to find the right candidates, and what are the prospects of these institutes?

AS: No I was not involved in any way in their crea-tion or functioning. It is not surprising that they are finding it hard to hire people. If one suddenly creates a large number of institutes like this, the demand for good people suddenly goes up, and there are simply not enough people available to fill these positions. But the situation will probably improve over the next 10–15 years as larger number of trained people become available.

CSD: Some Western universities have put many of their courses online for free, while others make them available for a fee. Do you think these online courses might help improve the quality of science education in our universities, and should we do something similar to make up for the scarcity of good teachers?

AS: Yes one should certainly try to make use of these as much as possible. These cannot replace classroom teaching completely, but one may be able to work out an effective system by combining these online courses with classroom teaching.

CSD: Let us turn to the quality of scientific research in India. Do you think that we have largely achieved our potential, or do we still have some way to go?

AS: There is certainly a long way to go. It is hard for me to comment on all areas of research, but I feel quite posi-tive about my area of research i.e. string theory. India now has a large number of excellent people working in various institutions, and I see a very bright future.

CSD: There are many attempts at quantifying or measuring the scientific achievements of individual scientists. A crude measure is the number of publica-tions. These “metrics” seem to influence decisions about hiring, promotions, awards, grants, and other fellowships. In your experience, do these metrics reflect quality, or has their influence been largely negative?

AS: One certainly has to be careful about using these metrics. But I certainly see a positive point: by providing us with some quantitative measure, however defective it may be, it prevents people from blatantly misusing their power to promote incompetent people, and more importantly, from preventing competent people for rising up. Now if somebody is pushing for someone with few publications or citations, at least a third person

can ask for a justification. In genuine cases it should be possible to provide such justification. Similarly if someone with large number of highly cited papers is being denied a grant/award, at least the granting authority can be asked to provide a justification for their action. Again in genuine cases it should be possible to provide such justification.

CSD: You have travelled all around the world, and you have seen how science is organised and managed in other countries. Do you think that they have something to learn from the way science is run in India? Or, perhaps, do we have something to learn from them?

AS: In theoretical physics the needs are few, and as long as we have a computer and an internet connection, and some money to travel to conferences and invite visitors, we can do our work. So the research is largely unaffected by how the administration functions, and in this sense I think there is not much difference between how the groups function abroad and in India. In experimental sciences things are certainly more complex, but I am not competent to comment on that.

CSD: We both work at the Harish-Chandra Institute which is devoted to research and where teaching takes place only at the graduate level. Such research institutes are almost the only places in the country which run decent graduate programmes in mathematics and theoretical physics. Do you think it is possible to revivify the graduate programmes in the various universities in the country?

AS: There are some excellent people in the universities who have produced excellent students. Their number may be few, but their existence certainly shows that it should be possible to make the universities vibrant centres of research by providing them with sufficient resources, and simplifying the bureaucracy. This in turn will attract bright people to join universities.

CSD: Every week we get emails soliciting papers for journals such as Fuzzy Sets, Rough Sets and Multivalued Operations and Applications (I haven’t made that up). How do you explain the proliferation of such journals, and do you think they pose a threat to genuine scientific research?

AS: I just delete these mails, and I presume many of my colleagues do so too. So as far as I can see, the problem they pose is the time that one wastes in deleting these mails.



CSD: At least in mathematics, it is very important to have access to old papers. The European Digital Mathematics Library has taken the initiative of digitising old journals and to make them freely available online. However, old issues of many other journals are accessible online only to those who can afford to pay a hefty fee. Do you think that fundamental research, completely devoid of military or commercial interests, should be shared freely and widely?

AS: Yes I certainly think so.

CSD: The Cambridge mathematician Tim Gowers has recently called on the scientific community to boycott the journal publisher Elsevier for its policies regarding pricing and access. Our own library has to make very tough decisions about which journals to prune from the list of subscriptions. There was massive support for the boycott, even among some Elsevier editors. Do you think that the responsibility for making their work more widely available lies with the scientists?

AS: For papers written after early 1990’s I never consult the journal but instead look at the arXiv. So to me the cost and availability of the new journals seem irrelevant for one’s research. As long as we can work out a scheme for accessing the pre 1990’s journals, we can get rid of the problem we are facing with Elsevier and any other expensive journals of that kind. (In any case I have not published in an Elsevier journal for many years, probably for about last 15 years.)

CSD: You use a lot of mathematics in your work, and the level of mathematics being used in string theory is far higher than in any previous physical theory. In return, string theory has been inspiring some purely mathematical insights, especially in algebraic geometry. The fact that physicists can predict some mathematical results with uncanny accuracy perhaps points to some underlying mathematical principles which have not yet been enunciated. Instead of asking a direct question, I would like to hear your view of the relationship between mathematics and string theory (and its generalisations).

AS: I do not really have any great insight into this. The inability to produce the kind of energy that is required to verify string theory by direct experiments compels us to look for other ways to convince ourselves that string theory is on the right track. One of these ways

is to test the internal consistency of the theory in all possible ways; if the theory passes all such consistency tests then it bolsters our confidence in the theory. It is fortunate that such consistency tests often leads to non-trivial mathematical identities which are often unknown even to the mathematicians.

CSD: In mathematics there are some vast research programmes such as the conjectural theory of motives or the Langlands Programme. Although very sophisticated mathematics is required for their proper formulation, their aims and achievements can still be illustrated through concrete examples. What are some of the fundamental problems of theoretical physics and how would you illustrate them?

AS: The fundamental goal of string theory is quite clear, it is to find a single theory that explains the origin of all matter and the forces between them. If we ignore the force of gravity, then this can be achieved by quantum field theory. But once we try to include the effect of gravity, the techniques of quantum field theory seem to break down. String theory on the other hand naturally incorporates gravity, and there is strong indication that it can also incorporate all the other forces and the kind of matter we see in nature.

CSD: Has it sometimes happened to you that you needed some mathematical result for your work but didn’t know whether it is true or not, whether it had been proved or not; you look around, and it turns out that precisely that result has been proved by someone many years ago?

AS: It has happened occasionally and in such cases I seek Surya Ramana’s help in finding the mathematical result. But more interesting cases are those in which even after looking around I found that the result was not known to the mathematicians. I shall give two examples. The first one concerns my work on duality in mid 90’s — the work that was cited in the prize. I found that the existence of certain symmetries in quantum field theories and string theories leads to a precise conjecture about the cohomology of an infinite class of non-compact manifolds. I verified this for some examples, but for the rest of the manifolds the cohomology was unknown at that time. Later a large part of this conjecture was proved by Grame Segal and Alex Selby. As far as I know the complete proof is still not available.

The second example is much more recent. Based on the study of black holes I arrived at the conjecture that certain infinite subset of Fourier expansion



coefficients of a class of Siegel modular forms must be positive. I verified this explicitly for a finite subset of Fourier coefficients and also in certain asymptotic limits, but otherwise had no proof. Very recently this has been proved for a small (but infinite) subset of these coefficients. This was the result of collaboration between a mathematician (Kathrin Bringmann) and a physicist (Sameer Murthy). But again a large part of this conjecture still remains unproven.

CSD: Some people hold the view that the boundaries between physics and chemistry and biology are somewhat artificial, whereas there is a sharp boundary between mathematics and the natural sciences. This is not to say that they don’t influence each other, but the aims and the preoccupations are different: proof, beauty and relevance in mathematics, correspondence with reality and utility in the sciences. What is your view?

AS: I certainly agree that in physics, experimental test always takes precedence over beauty. However mathematical consistency is a must for all physical laws.

It is universally accepted that the fundamental laws of physics must be written in the language of mathematics, and must be logically consistent to the same extent that a mathematician will demand a system of axioms to be internally consistent. A physicist may be more easily satisfied than a mathematician about such internal consistency, but eventually if some mathematician takes the effort to prove that a system

of axioms is internally inconsistent, then the physicist has no option but to abandon that system — even if that system of axioms may describe correctly the results of available experiments — and look for alternative set of axioms which may describe the laws of nature. From this viewpoint I do not think that the boundary between mathematics and physics is that sharp.

CSD: Are there some mathematical results or theories which you particularly admire, even though they might not have been directly useful to you in your work?

AS: Given my limited knowledge of higher mathematics it is difficult for me to answer this question.

Since this is not the answer you will get from all string theorists, I should perhaps try to explain my position. String theory has a wide spectrum of people, from those who use very little higher mathematics and lots of physical intuition to those who are highly mathematical (and of course there are few who span the whole range). One of the greatest strengths of the subject is that people over the entire spectrum can make nontrivial contribution to the growth of the subject, and in fact one needs contribution from the whole spectrum for the overall growth of the subject. In this spectrum I am somewhere in the middle. I am willing to learn new mathematics if it is needed for my research (particularly if I have more mathematically oriented collaborators who can help) but I do not really have a global picture of mathematics as a subject.

Chandan Singh DalawatHarish-Chandra Research Institute, [email protected]

Chandan Singh Dalawat was born in a small village in the foothills of the Aravallis, and now lives on the banks of the Ganges. He is interested in Number Theory and its history, and enjoys teaching the subject.



Introduction: Anthony John Guttmann was born in Melbourne on April 8, 1945, the son of Hungarian immigrants. He studied electrical engineering at the University of Melbourne, before switching to science during his second year. He did his PhD at the Univer-sity of New South Wales, in Sydney, and went on to postdoctoral work at King’s College, London. This training set him on course for a distinguished career in mathematical physics, throughout which a common thread has been his research on the mathematics of critical phenomena.

Early in his career many of Tony’s contributions had a strong numerical flavour; he developed ingen-ious methods for approximating infinite series that converge extremely slowly. In more recent times he has worked on problems that are more typical of the Australian mathematical physics community — for example, research on the Ising model, and more generally on processes defined on lattices and other geometric structures. In 2002, in recognition of his many research achievements, he was elected to the Australian Academy of Science.

However, Tony’s contributions to mathematics go well beyond his own research. He has served as the Director of MASCOS (originally the Australian Research Council Centre of Excellence for Math-ematics and Statistics of Complex Systems) since its inception in 2003. MASCOS’ initial funding from the

Interview with Tony Guttmann

Peter Hall

July 20, 2012, University of Melbourne

Tony Guttmann

Australian Research Countil (ARC), about $11 million for five years, was later extended for a second term. In addition to providing substantial leadership and support for excellent research in the mathematical sciences, MASCOS stands out as the only ARC-funded mathematics centre in Australia since Neil Trudinger’s Centre for Mathematical Analysis, which operated from 1982 to 1990.

Tony’s interest in mathematics is as broad as it is deep. He has made many contributions to school and university syllabuses, and to issues of equity and access.

For almost 30 years he has run a high-level, state-wide school mathematics competition in Victoria, often with the support of private industry. The competition has been successful in many ways, primarily by recog-nising and encouraging mathematical talent.

Peter Hall: Thanks very much, Tony, for agreeing to this interview. If I may I’d like to start not just with your own early life, but with that of your parents. I believe your origins in Australia, like those of number of other Australian mathematicians, owe much to the turmoil in Europe 80 or so years ago.

Anthony Guttmann: Yes, my parents both were Hungarian and Jewish. My father, as a youth, had some particularly unpleasant experiences in World War I which made him apprehensive of German militarism. Thus, with a premonition of difficulties to come, and despite being rather risk averse, he persuaded my mother, whom he had married in 1937, to leave Hungary for Australia. This they did, more or less on the last boat before the outbreak of World War II in 1939. They were bound for Sydney, to a future entirely unknown, but someone on the boat knew someone in Melbourne, and persuaded my parents to disembark there.

PH: Can you tell us a little about your mother and father, and their lives in Australia?

AG: My father was an architect, but had to retrain in Australia as his qualifications weren’t recognised here. My mother came from a family of four girls, and her



parents did not value education highly, particularly for girls. She was interested in languages, literature and the arts. In Hungary she had worked as a secretary for her uncle, who was at that time Hungary’s leading sculptor, Telcs Ede. She spoke excellent German as well as Hungarian and English, and in Melbourne got a job as a secretary with the Dutch Embassy during the war, and quickly learned Dutch. My parents were too uncertain of the future to risk having children until 1945, when I was born. My mother was 35, and that was considered quite elderly for a first child, and so I remained an only child.

As recent migrants from eastern Europe to Australia my parents came under suspicion during the war. For example, my father had arrived with a Leica camera, but was forced to dispose of it here; he had to sell it to the Royal Australian Air Force. And he was forbidden to operate his car.

PH: What was your own schooling like, and were you ostracised as a refugee?

AG: No, I don’t recall any prejudice on account of my origins. However, my primary schooling was unre-markable, except that at age six I contracted mumps, which caused permanent nerve deafness in my left ear. I spent six months in Sydney, undergoing a useless course of treatment.

Back in Melbourne I then spent four years at Camberwell Central School, where I recall an excel-lent French teacher, but little else. The last four years of my schooling were spent at Wesley College. This was not a particularly happy period of my life. Wesley viewed itself as an outpost of an imagined Empire, and attempted to imbue, by osmosis and the cane, values that didn’t resonate with me.

However, I liked the science education, and at home set up laboratories for electronics, another for chemistry, a photographic darkroom and a budgerigar aviary. These activities were rather more interesting to me than school. To my current regret I had virtually no interest in sports at that time. I had a brilliant chemistry teacher, Alan Gess, and solid, rather than inspiring, mathematics teachers.

Overall, my education in science was more inspiring than that in mathematics. You might describe me as very “hands-on” as a child. I left school more practically than theoretically minded. This was to determine the directions I took in my early years at university.

When I left school I was rather confused as to what course of study to take at University. I entered Melbourne University in early 1961 at age 16, and,

unsurprisingly given my experience at school, enrolled in Electrical Engineering. I loved the freedom of university life, the parties, the fact that most of my friends had cars, and of course there was no querying one’s age in pubs in those days. As a result I came very close to failing my first year. This gave me quite a shock. In second year I started taking my studies more seriously, and realised by mid-year that I liked physics and mathematics more than the engineering subjects.

PH: So, in your second year we see your math-ematical side, and perhaps even an instinct for abstraction, emerge, despite your experience with mathematics at school.

AG: There was little about my experiences at school that could have inspired me to become a mathemati-cian. While studying engineering at university I began to develop an interest in mathematics, but even then it was not deep. But by second year I realised that I was enjoying the mathematics side of my work much more than the experimental side. I was quite adept at experimental work, but not intellectually attracted to it.

In those halcyon days academics controlled the university administration, so I spoke to the person in charge of second year physics, Ken Hines, about my desire to switch to Science. He said that I could switch from engineering mathematics to science mathematics, and make up whatever I’d missed, just by reading the textbooks. Likewise the all-important physics practical work — I could wander into the labs and make up the missed practical work. All this suited me very well.

In third year as an undergraduate I probably learned most of my mathematics from the physics depart-ment. I learned about differential equations and, to an extent, group theory by studying quantum mechanics, and complex variable theory and integral transforms through diffraction physics.

PH: So, even though you turned to mathematics at university, it was very much in the context of physics.

AG: Yes, I received a lot of inspiration from John Cowley, who was a brilliant, newly appointed Professor of Physics and built a world class group in diffraction physics. I became interested in the theoretical side. I did my honours project trying to adapt the theory of electron diffraction to neutron diffraction, including an abortive attempt at an experiment at Sydney’s Lucas Heights reactor, for which I had to get security clearance. This confirmed to me the advantages of a



theoretician’s life over an experimentalist’s, even though I was probably more inclined to the latter.

PH: I imagine that your postgraduate work followed a theoretical course, too.

AG: In early 1965 I commenced an MSc in physics at the University of Melbourne, with my project being to calculate X-ray dispersion corrections — so my thesis topic was distinctly theoretical. I finished this project early, and Norm Frankel got me involved in a calcula-tion of the properties of Bose–Einstein condensates. This was a massive computational project. I was trained to run the university’s mainframe computer, and would spend weekends in the machine room running programs for 24–48 hours, with my friends bringing me food from the Genevieve Restaurant. In those days, large scale computing meant boxes of punched cards for input, and storing data on massive tape drives. The area now occupied by the campus post office held the computer at that time.

I shared the prize for the best Masters thesis with Andrew Prentice, and this gave Ken Hines, who’d taken a risk with me, particular pleasure. I was pleased to have justified his faith.

PH: Well done! I believe that in 1964 the university purchased an IBM 7044 machine, and retired CSIRAC II, then the oldest working electronic computer in the world. But we digress. You did your PhD in Sydney, in mathematics; how did you make that transition?

AG:I had heard excellent things of John Blatt, Professor of Applied Mathematics at The University of New South Wales (UNSW), and as my girlfriend, now my wife, lived in Sydney, I applied for (and was accepted as) a PhD student there. This was at the beginning of 1967. Almost immediately there was a Mathematical Physics Summer School at the Australian National University (ANU), with a cast of experts possibly never since matched in Australia. They included C N (Frank) Yang, Freeman Dyson, Bram Pais, Dmitry Shirkov, Joel

Lebowitz, John Blatt, Stuart Butler and others. The lectures were mostly at too high a level for me, in my first month of a graduate program, but were inspiring nonetheless. At the end of that year I married Susette, a recent Arts/Social Work graduate.

However, John Blatt was mostly absent, frequently travelling in the US. (He felt he’d been robbed of the Nobel Prize for the discovery of superconductivity.) As a result I did my PhD at UNSW under the joint supervision of Barry Ninham and Colin Thompson. I submitted my thesis in 1969.

PH: At that point, I think, you left Australia to work in London.

AG: Yes, I was offered a postdoctoral position at King’s College, London. Susette and I travelled by ship, as I’d won a travelling scholarship to cover those expenses. The Suez Canal was closed, so we went via South Africa, and were able to leave the ship in Durban and drive to Cape Town and reboard. That was the highlight of the trip. The King’s College group was a very active one, and I formed life-long friendships with a number of my colleagues there.

PH: You came back to Australia after your postdoc, to the University of Newcastle — established only while you were doing your MSc.

AG: In 1971 we returned to Australia. I’d applied at the ANU, to work in Barry Ninham’s department, and also at the University of Newcastle. Newcastle offered me a job first, and we thought that after London there was not much difference between Newcastle and Canberra, so I accepted a lectureship at Newcastle. It was a wonderful time, with typically three or four new appointments each year for a few years, so we were a young, naive but enthusiastic group. Everything seemed possible then.

Newcastle had the first (and probably last) Faculty of Mathematics in Australia. The Foundation Dean was Reyn Keats, a former Rat of Tobruk [the name given to Allied soldiers who held Tobruk, in Libya, against the Afrika Corps in 1941]. He did an outstanding job building the Faculty, and in particular he decided to initiate a postgraduate Diploma in Computer Science. Based on the fact that I knew how to program in Fortran, I was put in charge of this diploma, and asked to lecture in the foundation courses. I had never studied computer science, but read the relevant textbooks, and was at least a week and sometimes two weeks ahead of the students. I wrote a book, Programming and Algorithms, based on one of the courses I’d taught!

Newcastle was meritocratic, and it was possible to

Peter Hall and Anthony Guttmann



AG: It began in 2002 when Jan Thomas and I wrote a successful proposal to the Victorian Government for a mathematical sciences institute. Thus the Australian Mathematical Sciences Institute (AMSI) was born. I was the first Director. Melbourne University was very supportive and provided premises and other facilities. A year later I participated in a bid for an ARC funded Centre of Excellence. This was successful, and thus MASCOS, the ARC Centre of Excellence for Math-ematics and Statistics of Complex Systems, was born. I became, and still am, the Director of MASCOS, so I had to resign from the Directorship of AMSI, though MASCOS and AMSI have continued to cooperate on various activities, to our joint benefit.

PH: Your efforts have been remarkable — Australia has had so little by way of research institute activi-ties in the mathematical sciences, and you have been behind the two most recent successful ones. Do you have in mind any model for the type of research institute that might suit Australia best?

AG: I think there are two conventional models, both working successfully abroad. The first is for an institute that runs programs, typically weeks or months long, in which both young and experienced visitors participate. The second type focuses more on younger people, for example students or postdocs, and there the period of residency may be (but is not necessarily) relatively long. The first type is more common, and includes, for example, Berkeley’s Mathematical Sciences Research Institute (MSRI), Oberwolfach, and the Isaac Newton Institute.

I think the most appropriate type for Australia is probably a mixture of these two. I’ve recently spent periods at both MSRI and the Mittag-Leffler Institute in Stockholm, which focuses on the training of young mathematicians, especially students. It runs both long and short programs. Canada arguably has the greatest variety of mathematics research institutes, at least in terms of the ways in which they operate, and we could learn a great deal from the Canadian experience.

My preference is for an institute that is a reasonable distance from major institutions, such as universities. I’d favour a stand-alone facility, away from a major metropolitan centre. If it is attached to a university, the local people tend to go home in the evenings and much of the life of the institute is drained away.

PH: Perhaps you could give us your view of the state of mathematics in Australia.

AG: Australia, like most English speaking countries,

advance quickly. I became a Senior Lecturer after a year, and Associate Professor a couple of years later. A few years after that I was Professor and Dean.

PH: Those were heady times, and must have contrasted with your experience at King’s College. However, the administrative load must have been considerable.

AG: Yes, the University of Newcastle was unconstrained by tradition, unlike King’s. Keats always tried to appoint the very best people he could. However, the distribu-tion of students’ preparation was much broader than at Melbourne.

After about a year of being Dean, and still in my 30s, I decided I really didn’t care for the amount of administration that the job entailed. I took a six month sabbatical at Melbourne University, and was offered a Readership at the end of that time. I accepted this (which did not go down well at Newcastle) and was appointed to a Personal Chair a year later. Colin Thompson had started the Statistical Mechanics Group, and I was fortunate enough to be there at a time when the opportunity was available to build the group into a large and highly successful one.

PH: This must have been quite a contrast to your time at Newcastle.

AG: In my 15 years at Newcastle I’d had one PhD student and one postdoctoral colleague, but at Melbourne the opportunities were much better, and I had a steady stream of very good to outstanding students, as well as very many first-class postdoctoral colleagues. Only one student failed to complete — he’d done more than enough for a thesis, but was seduced by Google before he finished writing up, and never bothered to do so, to my regret. I’ve also been able to help out with some exceptional school students, and undergraduates.

At the University of Newcastle I met Nick Wormald, whom I think you know from your school days in Sydney. He is a strikingly strong discrete mathemati-cian, and, was one of the mathematicians I persuaded to move to Melbourne. These days he is at the University of Waterloo, where he has a Canada Research Chair, although I'm particularly pleased to see that he will return shortly to Australia, to a position at Monash University.

PH: Perhaps we can turn now to your work devel-oping and leading research institutes in Australia. It has been highly successful, and particularly influential.



has a good rather than a great history of mathematics education at the school level. Given our comparative wealth, I feel we should all be doing a great deal better. There have been enough credible reports into the mathematical sciences in Australia that I don’t need to repeat the outcomes and recommendations here.

Primary and secondary school teachers here tend to be undertrained in the mathematical sciences, with some notable exceptions, and so are unable to provide as rich an education as they can in other areas. As a result, too many school children are indifferent or hostile to mathematics. There is a strong case for making school teaching a better paid profession, with more highly trained teachers, as is the case in some European countries.

Our universities are also doing as good a job as is possible in current circumstances, but are significantly under-resourced. This is due to a combination of increasing government imposition of rules and regulations, and a tendency by Vice Chancellors and Councils to run universities as corporations, so that the administration and support side is generally bloated, and the academic side — which is the heart of the university — is comparatively starved. Australia will never have a university, or mathematics department, in the top 25 until Vice Chancellors realise that they need to spend money on world class academics, rather than on yet another Deputy/Associate/Assistant Vice Chancellor, and the associated entourage.

It is still a source of considerable regret that Australia has no research institute of the type we’ve discussed. While I am delighted at the sporting success produced by various state and federal Institutes of Sport, it should be a source of national shame that we have no corresponding institute for the mathematical sciences. It is telling that the Australian Olympic team bound for London is larger than the Chinese one, yet China has several mathematics institutes; we have none.

PH: We haven’t yet spent much time discussing your own research. Let’s turn to that topic now.

AG: My PhD topic was a blend of combinatorics and numerical analysis. At that time mathematical models of phase transitions were something of a mystery. The Onsager solution of the two-dimensional Ising model free-energy was a singular exception. This was before the days of the renormalisation group, before the Yang–Baxter equation and concepts of integrability were utilised, before the theory of universality, and before Monte Carlo was a useful technique.

The idea at the time — and still a powerful technique

— is that to determine the asymptotic behaviour of some property of, say, the Ising model, one expanded it in a power series expansion. My thesis topic was to develop numerical techniques to determine the asymp-totics, and, to a lesser extent, to compute the terms more efficiently. As an indication of how far we have come, the susceptibility of the two-dimensional Ising model was then, and remains, a seminal problem. At the time of my PhD studies we had some 20 terms in the series, and we could predict the dominant asymptotic behaviour. We currently have 10,000 terms, and have about 100 terms in the asymptotic expansion, including subtle powers of logarithms.

During my time as a postdoc at King’s College I developed, with my colleague Geoff Joyce, the best method at the time for analysing power series expansions, called the method of differential approximants. Some 40 years later it is still the best method. Again with Joyce, and a Canadian visitor Donald Betts, we developed a generalised law of corresponding states, a modern version of van der Waal’s work, and a complement to the then burgeoning ideas of scaling and the renormalisation group.

Two years after I left King’s in late 1971, Ian Enting arrived at King’s from Monash, and together with Tom de Neef developed a powerful method for generating series expansions, called the Finite Lattice Method. It is still an incredibly powerful method, and Ian and I formed a partnership using his series expansion techniques and my analysis techniques to reshape what was considered possible in that area. Melbourne University is still the world centre of these ideas, due to further developments by Ian Enting, Iwan Jensen, and very recently Nathan Clisby.

Later, after joining Melbourne University, Ian Enting and I realised that we could use numerical techniques to explain why some lattice statistical problems were solvable, and others were not. This was a totally different, semi-numerical approach, which didn’t give a solution, but gave a strong hint of the presence or absence of solvability, which in favourable circumstances could be refined into a formal proof — as first demonstrated by my PhD student, Andrew Rechnitzer. It was quite different from the powerful analytic work than being done by Rodney Baxter and his colleagues at the ANU, and the connection with integrability remains obscure. I am still studying lattice models, but now from a more algebraic viewpoint, and using techniques from number theory, and more modern ideas like discrete holomorphicity to derive solutions, or sometimes proofs of conjectures.



After a sabbatical in Oxford in 1992, and visits to the University of Bordeaux both then and again in 1996, my interests changed to include a lot more algebraic combinatorics. As these interests grew, I was asked to edit a special issue of Annals of Combinatorics highlighting the connections between statistical mechanics and algebraic combinatorics. I was subsequently asked to organise the annual Formal Power Series and Algebraic Combinatorics Conference in Melbourne — I think the only time that that conference has been in the southern hemisphere.

PH: Against this background, perhaps we could take a look at how your areas of research have changed during your career.

AG: Mathematical physics and mathematics have definitely grown closer. Mathematical physicists really need a broad armoury of techniques these days, across many areas of mathematics and probability. Mathematicians have brought into the mainstream the outlandish ideas usually first developed by physicists. The theory of generalised functions is an early example with which I became familiar. In physics, areas like conformal field theory make predictions that are eventually made rigorous by mathematicians. Traditional concepts of mathematics, like analyticity, have been extended to the discrete case. The resulting concept of discrete holomorphicity is responsible for several important recent advances. Similar ideas, plus applications of stochastic ODEs leading to Schramm–Loewner Evolution and probability theory, have led to advances recognised by the award of several recent Fields Medals.

To be more specific, one problem that spans both algebraic combinatorics and statistical mechanics that I’ve been involved with all my professional life is studying the properties of self-avoiding walks on a lattice. Let cn denote the number of SAW on a lattice (periodic graph) equivalent up to translation. Some 60 years ago, John Hammersley proved, by simple concatenation arguments, that exists, and is greater than zero. A few years later he refined this to establish that . Numerical studies, and comparison with exactly solvable models, leads us to believe that , where it is known that μ depends on the choice of lattice, and it is believed that the exponent g depends only on the dimensionality of the lattice. For two- and three-dimensional lattices, to this day we do not even have a proof of the existence of the exponent g; though it is universally believed that g = 11/32 for two-dimensional lattices, and a somewhat smaller value, estimated to

several decimal places but not believed to be rational, for three-dimensional lattices.

The value of μ was conjectured for precisely one lattice, the hexagonal lattice, 40 years ago by B Nienhuis. It was not until 2010 that S Smirnov and H Duminil-Copin proved this conjecture, using ideas from discrete holomorphicity, notably the identification of a so-called parafermionic operator. For SAW originating in a surface, there is a second exponential growth constant associated with the number of steps of the walk that lie in the surface. Above a certain critical value of attraction, a macroscopic fraction of the steps of the walk lie in the surface. Following Nienhuis, M Batchelor and C Yung conjectured the exact value, again in the case of the honeycomb lattice in 1995. This was finally proved by my colleagues and I in 2012. You will be pleased to hear that one aspect of the proof relied heavily on probabilistic arguments.

As for critical exponents, if one could prove that the scaling limit of SAW was describable by SLE8/3 ; for which abundant evidence exists, but no proof, then not only would the existence of the exponent g be proved, but so would its value. A lot of effort is going into attempts to achieve this proof.

Changes in technology include the development of algebraic packages like Maple, Mathematica and Matlab, as well as more specialised systems. These free us from some of the drudgery of routine calculations — and at least in my case lowers the error rate significantly. Using computers to provide proofs, through certification of identities, is now commonplace. Also, increases in computer speed and reduction in memory costs permit calculations of formerly inconceivable scope to be made.

PH: How have your own students done? You have had more than ten, which in mathematical physics in Australia is large. Some of them have been remarkably young, like Yao-ban Chan, who was a postdoc with me for several years.

AG: I have had twelve PhD students for whom I was the primary supervisor. Six of these have gone on to academic careers. Eva Swierczak, Andrew Rogers and Will James are working in the finance industry, Debbie Bennett-Wood became a school teacher and is now raising horses, John Dethridge works for Google, and Andrew Conway started in academia, then built up his own software company in Silicon Valley, and now pursues private and family interests. Of the six currently pursuing academic careers, Albert Nymeyer is at UNSW, Andrew Rechnitzer is at the University of British Columbia, Yao-ban Chan is at the University of



Vienna, Nick Beaton is at Université Paris 13, Henry Wong moved to psychology at Melbourne University, and Markus Vöge was until recently at the Swiss Federal Laboratories near Zurich. Two of these, first Andrew Conway and then Yao-ban Chan, were the youngest PhD students in the history of the University of Melbourne.

PH: You’ve had an outstanding and varied career. Against this experience, do you have any advice for young men and women starting out in mathematics today?

AG: My generation has been extraordinarily fortunate. We have largely escaped wars — though I was drafted during the Vietnam war, but was medically rejected — and an academic life was very rewarding. Now there are ever-increasing burdens placed on academics. It is not enough to be an excellent researcher and a decent educator. One needs to be an educator loved by students, a successful earner of research grants, a supervisor of numerous graduate students, to be heavily involved in administration, to be chair of numerous committees, to respond to numerous on-line training courses, to fill out regular bizarre questionnaires, use incredibly expensive user-hostile software to perform what should be trivial tasks, and respond to reporting requirements of an invasive and time consuming nature. As a result it is increasingly difficult to find sufficient stretches of uninterrupted time that is needed to undertake high quality research.

On the other hand, there are far more opportunities for mathematics graduates these days. Indeed, I can think of few professions where having a mathematics degree would not be a great advantage, by virtue of both the obvious skills one possesses, and also for the analytic way of thinking with which a mathematical sciences degree equips one. I should also mention that it’s not just mathematics that has changed. To be a virtuoso violinist it used to be sufficient to play like an angel. Now it seems necessary, especially if you are female, to look like one as well.

PH: Discussing your academic descendants reminds me that we have not yet considered your family.

AG: I have two children, Jacki, who is an Arts Adminis-trator with Melbourne Museums and has two children of her own, who are a delight to my wife and me. My son Laurence is a school teacher, initially trained as an English as a Second Language teacher, but who subsequently did a Masters degree in mathematics education, and is increasingly teaching mathematics. Both my children did their final year’s of schooling at Wesley College, which has greatly changed for the better since my day — not least by becoming co-educational — and both attended Melbourne University for their undergraduate and graduate programs. My wife has worked as a Social Worker or Manager for much of our life together.

PH: Do you have any parting comments?

AG: Well, in my mid-30s my first PhD student, Albert Nymeyer, got me interested in running, and I have been running ever since, for example in marathons and triathlons. I could wax lyrical about the benefits of running — it was enormously helpful to me when I was appointed Head of Department in my early-mid 30s, with no training or experience; it helped me cope with stress.

I have also found running extremely useful when doing mathematics. Whenever I get stuck on a problem, I try to go for a run. I usually come up with a new angle or direction to tackle the problem. It doesn’t always work of course, but it is an alternative to a dead end. Running also provides a pleasant and beneficial way to stay in close touch with younger colleagues, and colleagues from different disciplines, not to mention one’s children and grandchildren.

PH: Thanks very much, Tony. This has been a particularly enjoyable experience, not least since our careers have much in common, meeting even in technical terms in the area of percolation. I wish you the very best for the future.

Peter HallUniversity of Melbourne, Australia

Peter Hall was born in Sydney, Australia, and received his BSc degree from the University of Sydney in 1974. His MSc and DPhil degrees are from the Australian National University and the University of Oxford, both in 1976. He taught at the University of Melbourne before taking, in 1978, a position at the Australian National University. In November 2006 he moved back to the University of Melbourne. His research interests range across several topics in statistics and probability theory.



A Brief Account On the Relationship between SMF and VMS

Lê Dung Tráng

The history of the link between the French Mathematical Society (SMF) and the Vietnam Mathematical Society (VMS) goes back to

the time Professor Lê Van Thiêm studied at the Ecole Normale Supérieure in Paris.

It was during the Second World War. He passed his thesis in Göttingen a few days before it fell in the hands of the American Army.

During many years the northern part of Vietnam was isolated from the World.

Laurent Schwartz, Professor at Ecole Polytechnique, a Fields medalist (considered to be a Nobel Prize in mathematics), founded the organisation “Comités France–Vietnam” in 1966 and, then, joined the Tribune of Bertrand Russell for crimes against humanity of the American War in Vietnam. But, only in 1967 did a mathematician, Alexander Grothendieck, also a Fields medalist, visit Vietnam for the first time. Laurent Schwartz visited Vietnam in 1968. However, it was more as member of the Russell’s Tribune than as a mathemati-cian. In 1969 Laurent Schwartz arranged that Nguyen Dinh Tri, a professor in the Polytechnique school in engineering of Hanoi, could visit Japan from Vietnam to attend a Mathematical meeting. Professor André Martineau, a former student of Laurent Schwartz, who unfortunately passed away in 1972, came in 1970. Professor Bui Trong Lieu, a Vietnamese mathematician living in France, visited Vietnam in 1970. He organ-ised my visit in 1972. So until then, nearly no one in mathematics visited Vietnam. One of the main reason is that Vietnam was continuously at war between 1945 and 1975.

In spite of the danger of the war a man stood at the side of Professor Lê Van Thiêm to develop Mathematics. Minister Ta Quang Buu studied in France before the Second World War. He told me that he was supposed to study at the Sorbonne, but in order to make things difficult to the French masters he decided to pass a free Licence, studying some mathematics, physics, literature, English. By this way he understood the value of science and the meaning of mathematics. At some point he was private secretary of President Ho Chi Minh, then vice-Minister of Defence. In 1954, he signed the Geneva Peace Agreement after Dien Bien Phu. When I met him, he was Minister of Higher Education. In the Vietnamese government he was the one who immediately understood the potential of mathematics in Vietnam.

Minister Ta Quang Buu knew who Grothendieck was. In those days no politician in the World would know who a mathematician like Grothendieck would be. It is rather surprising that Ta Quang Buu knew of him and of his mathematics. He organised the travel of Grothendieck, although the bombings were fierce and the universities had to hold their classes in the moun-tains north of Hanoi. A young female mathematician, Ms Hoang Xuân Sinh, answered a problem conjectured by Grothendieck during his course and a few years later passed her thesis under his supervision. Later in October 1974, Ta Quang Buu helped me organise a school with Bernard Malgrange, Alain Chenciner and Frédéric Pham. For the occasion he wrote a long article on the theory of Catastrophes in the Party newspaper Nhân Dân. He welcomed the visits of Yvette Amice who was once President of the SMF, Jean-Louis Verdier, another President of the SMF, Pierre Cartier, who later

L Schwartz, his wife, and Ta Quang Buu in North Vietnam, 1968

Grothendieck (middle) and Hoang Tuy (far right) at the evacuated University of Hanoi 1967



First row, left to right: Hoang Tuy, Ta Quang Buu, Pham Van Dong on a visit to the Institute of Mathematics in 1978

visited Vietnam several times, Dacunha-Castelle, who introduced Probability and Statistics in Vietnam. In relation with Japan he also organised the visit of Kyoji Saito who was in those days one of my best Japanese friend.

Nowadays all this seems an easy achievement. Young people have to understand that until the end of the 80’s, Vietnam was one of the poorest countries in the World. When I came in 1972, there were less than 30 mathematicians in Mathematics in North Vietnam. The most distinguished then were Professor Lê Van Thiêm, Professor Hoang Tuy and Professor Phan Dinh Diêu. The mathematical institute was a small room in the State Science Committee in Hanoi. The seminars happened in one of the universities of Hanoi. Obtaining a visa was a continuous battle with the authorities. Arriving to Hanoi by plane or by train was difficult. I do not remember if Malgrange, Chenciner or Pham went through Bangkok or Vientiane. I personally came by train in 1972 through Siberia and China. The following years I travelled by propeller plane through Moscow or Berlin. It was taking 37 hours.

Anything which looks now obvious or easy was then extremely difficult. To arrange the timing between the visas, the arrival of the mathematicians, the reserving of a hotel room, the disponibility of an audience, the room for the lectures, the transportation, the sightseeing, all these were endless source of difficulties. I remember that it was hidden to Grothendieck that, after his visit (he lectured around 70 hours in three weeks in the mountains) the mathematics library lost more than a hundred books in a flood.

Well, memories still flow in my head and I could endlessly speak about these earlier years. I have just chosen to tell them to-day so that younger generations do not forget all the efforts that were put in developing mathematics in Vietnam and remember the names of Lê Van Thiêm and Ta Quang Buu.

To end my talk, let me give you a vivid memory that I have of this early times.

It was during my first visit in 1972. In those days Tran Quynh was the Head of the Science State Committee. He was not really a scientist, but he was a practical man and wanted good reasons to develop these relations with the outside World. I had a private meeting with him for half an hour. Then he asked me abruptly: “Tráng, what do you want to do in Vietnam?” I did not know what to answer, because I did not think of any diplomatic answer, as I should have done politely. I had to show that I did not hesitate. I remembered that my whole brain was concentrating to give a proper answer. Then, I answered: “I wish that Vietnam in 25 years can have someone receiving the Fields Medal, the award that mathematicians consider as their Nobel Prize.” I am very sorry I made a mistake of 13 years.

Lê Dung TrángAix-Marseilles University, France

Lê Dung Tráng is presently Emeritus Professor at University of Provence in Marseille, France. He holds the position of editor for the International Journal of Mathematics and Acta Mathematica Vietnamica. Professor Lê is an elected fellow of the Academy of Sciences for Developing Countries (TWAS) since 1993.

Professor Lê, former Head of the Mathematics section at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, was the Directeur de Recherches of the French National Research Council (CNRS) from 1994 to 1999; Professor at the University of Paris 7 from 1975 to 1999; Maître de Conférences at Ecole Polytechnique; visiting Professor at Northeastern University, Boston, USA; Research fellow at Harvard University; and a visiting Professor at Kyoto University, Japan. Professor Lê was also the Mathematics editor of the ‘Hermann Editions’ in Paris until 2005 and the Editor of the Journal of Algebraic Geometry until 1993. He received the d’Aumale Prize from the French Academy in 1990. He authored more than 100 research papers, edited three conference proceedings and published four lecture notes.



Indian mathematicians have fallen behind in the race to break new ground in the subject, the comparison having been made in the “National

Year of Mathematics”. An article on “top 50 national rankings in mathematics”, published in Current Science, has found a gap not only between the work of mathematicians in India and those elsewhere, but also between the number of papers Indian mathematicians publish and the number of times those papers are cited or impact the work of other authors (see page 36 of this issue).

“With 2012 being the national year of maths, it will be meaningful to assess where India stands in the national rankings using data from the ‘Essential Science Indicators’ database from Thomson Reuters, covering the period January 1, 2001 to October 31, 2011,” says the article, going on to place India at 14th position among 50 countries in terms of “rankings by papers”, at 22nd in terms of citations, and at 29th in terms of an impact factor called exergy.

“The exergy is an indicator combining both quality and quantity aspects and in this India fares badly. Even when we consider the quality factor only, our ranking in terms of the number of citations is very poor,” said the article’s author Gangan Prathap, director of National Institute of Science, Communication and Information Resources. “We need more quality faculty, we need more schools of maths, and we need to re-orient our education to ensure that students don’t shy away from basic sciences and maths.”

Several academicians said they were not surprised by the “not-so-encouraging” picture. “Most Indian mathematicians tend to do derivative work, that is they work in an area where the main body of work already exists,” said a senior academician. “The problems start right at the level of schooling where there is a huge dearth of teachers who can create an interest in the subject.”

Avnita Bir, principal of R N Podar School in Santacruz, Mumbai, described the difference between what is taught at school in India and what is taught elsewhere. “The Standard X syllabus of the CBSE focuses on long calculations and doesn’t give students much scope to think while solving a problem. It’s more of a test of speed and how many questions one can solve within a given time limit,” she said. “In contrast, an

Why Mathematics Papers Indians Publish Have So Little Impact

international maths curriculum... focuses on problems where students are required to apply their mind while using the concepts and formulas they have learned. It’s a test of ability and not speed.”

There is a difference in the approach, too, she said. “In the international syllabus, the teaching approach is quite basic, without making the curriculum seem rigorous. There is, on the other hand, a lot of rigour in the Indian curriculum.”

Professor R Balasubramanian, director of the National Board for Higher Mathematics, said the problem is not with the syllabus. “The maths curriculum in India is as good as that in any other country. The problem is that we don’t have enough competent people to teach the subject across all levels — from schools to the higher education sector,” said Balasubramanian, who is also director of the Institute of Mathematical Sciences, Chennai.

Professor Vijay Singh, national coordinator of Science Olympiads from the Homi Bhabha Centre for Science Education, said Indian scientists are in the “backwaters” of maths and “they unfortunately tend to get cited only if their work is exceptional”.

Indians students, too, have fared poorly in inter-national competitions such as PISA, the Programme for International Student Assessment that evaluates 15-year-olds, and the International Mathematical Olympiad. According to data from the HBCSE, teams representing India have won only two gold medals from 2002 to 2011 at the Olympiad.

“We don’t have enough good trainers for the Math-ematical Olympiad. It needs a lot of volunteers to train the students and not many are willing to come forth,” said the HBCSE’s Professor B J Venkatachala.

The 3 dimensions:

• 14th among 50 countries in terms of papers published (5,766); top ranker US has 74,874 papers

• 22nd in terms of citations for these papers (11,794); US has 366,539

• 29th in terms of exergy (24,124), a measure of the impact of these papers; US score is 1,794,359

Courtesy: Mihika BasuThe Indian Express

June 4, 2012



With 2012 being the National Year of Mathematics, it will be meaningful to assess where India stands in the national rankings using data from the Essential Science Indicators SM database (http://esi.webofknowledge.com/home.cgi) from Thomson Reuters, covering the period January 1, 2001 – October 31, 2011. We start with an initial list of the top 50 countries ranked according to citations. Table 1 shows the rankings according to what we call the zeroth-, first- and second-order indicators of performance, namely the number of papers, citations and exergy. In this case, predictably, USA tops all rank-ings. Note that in Table 1, the number of articles, P and citations, C received are for the time window January 1, 2001– October 31, 2011. The impact i is then computed as C/P. While P and C are quantity measures (output and outcome respectively), i is inherently a quality

“Top 50” National Rankings in Mathematics*measure. One can think of P as being equal to i0P, and C as being equal to i1P. Thus P and C can be thought of as zeroth-order and first-order performance indicators. In continuing this as a series of the parameter spaces, the product iC (also i2P) is an energy-like term (called exergy X), which can be thought of as the second-order performance indicator, and is a scalar measure of the scientific activity during the window concerned that takes into account both quality and quantity. We see from Table 1 that research in USA during this period is far ahead of the other countries. In exergy terms, USA is now nearly four times as active as France and five times more active than China.

Gangan PrathapNational Institute of Science

Communication and Information Resources,New Delhi 110 012, Indiae-mail: [email protected]

* Reproduced from Current Science Vol.102 No.10, May 2012



Mathematical Sciences Institute Medals for Distinguished Service

As part of the Australian Mathematical Sciences Institute (AMSI) tenth anniversary celebra-tions, the AMSI Board has introduced the

AMSI Medal for Distinguished Service. This medal will be awarded to those who have demonstrated both sustained and exceptional service to AMSI and leader-ship in one or more of AMSI’s portfolio areas of research and higher education, school education and industry engagement, or in advocacy for the broad discipline. The inaugural medallists, along with their citations, are:

Jim Lewis

As the Foundation Chairman of the Board, Jim Lewis guided AMSI through its first 10 years with the vigour and expertise that comes only from experience. A BHP executive, a successful busi-nessman, a chemical engineer and a distinguished university lecturer, Jim was exactly the sort of over-achiever that AMSI’s architects wanted as independent chair of the board. Jim relentlessly pursued AMSI interests, providing advice and inspiration to AMSI’s staff and providing the business orientation that led to our significant successes with government and industry.

To quote from the AMSI Review report:

AMSI was fortunate to attract the services of Jim Lewis, a former BHP executive, as Chair of its Board. Jim has been inspirational in his un-flagging efforts on behalf of AMSI. A brief summary of his contributions include maintaining AMSI’s relationship with the University of Melbourne, appointing and mentoring a series of AMSI Directors, negotiating complex contracts such as BlueScope Steel’s involvement in the ICE-EM outreach program, taking a hands-on leadership role when there was no director and direct involvement in negotiations to bring significant funding to AMSI. The Panel salutes this massive contribution without which AMSI’s survival would have been jeopardised.

Jim is held in the highest esteem and affection by AMSI’s staff, past and present.

Garth Gaudry

AMSI and ICE-EM (International Centre of Excellence for Educa-tion in Mathematics) owe much to Garth and to the contribution that he made over the five years from 2003 to 2007. Garth, with Tony Guttmann and Jan Thomas, drove the vision and commitment to establish AMSI. As foundation director Garth put in place the basic structure upon which AMSI has been built. His most significant achievement was obtaining and leading the ICE-EM grant in 2004. This grant funded not only AMSI’s remarkably successful school education program but also many innovations in research and higher education including AMSI’s flag-ship programs and our Access Grid network. ICE-EM’s impact cannot be underestimated. Garth moved to the position of Director of ICE-EM to oversee the major initiative to improve mathematics education, especially in schools. Garth recruited first class staff and a team of authors to work with him on producing a remarkable series of texts. These texts, now in their second edition and marketed by CUP, have had a seminal influence on school mathematics education in Australia. ICE-EM’s work has established AMSI as an influential policy maker and a provider of school educational materials second to none.

Garth’s vision and strength of character continue to be an inspiration to AMSI members and staff.

Jan Thomas

Jan Thomas was instrumental to the establishment of AMSI.

In 2001, she saw an opportu-nity to set up a national centre in the mathematical sciences with a $1 million grant provided by the Victorian Government’s Science, Technology and Innova-tion Programme. This specialist centre was a recom-mendation of the 1995 report Mathematical Sciences:

Geoff Prince



Adding to Australia, a review to which she had made important contributions. Jan and Tony Guttmann co-wrote the grant application and coordinated the support of the foundation members of AMSI, with a common purpose to turn around the decreasing supply of mathematics teachers and subsequent loss of students and staff across university schools of mathematics. The grant application was successful and AMSI was established in 2002 with a mission to “promote and strengthen understanding and use of the mathematical sciences in Australia’s culture, science and economy”.

As the Executive Officer for AMSI until her retire-ment in 2011, Jan was the government and member liaison person at AMSI, continually pushing the message of the importance of quality mathematics education to Australia’s national interest, through her participation in reviews and submissions. Her deep knowledge of the mathematics education landscape spanning over 20 years, her contributions to gathering the necessary data to reinforce subjective observations of the health of the discipline, and her active involve-ment in pursuit of positive change has been an asset to the advancement of mathematics education.

Jan has worked closely with all the AMSI Directors and the Board. She has extensive experience in dealing with politicians, the press and bureaucrats, and has brought this to bear to AMSI’s considerable benefit. She has been deeply involved in almost all aspects of AMSI’s activities and has been tireless in communicating with our members. Occupying an honorary position at AMSI, Jan continues to support AMSI with her sound advice.

Jan Thomas is an iconic figure in Australian math-ematics. Few individuals in the last 20 years have had such an impact on the discipline.

Tony Guttmann

Tony Guttmann was one of the original architects of AMSI and together with Jan Thomas wrote the original expression of interest proposal to the Victorian Govern-ment for a Strategic Technology Initiative grant in 2001. This was followed by the preparation of the full business plan and the final success of the application. This process involved very significant negotiation with the future Joint Venture Partners in order to produce a proposal of truly national benefit. Tony followed this with the negotiation and

project management of the University of Melbourne’s fit out of the AMSI offices. He also negotiated the provision of the University’s legal and administrative services in setting up AMSI. During this period Tony was AMSI’s interim director and was heavily involved in establishing AMSI’s board. He can take the credit, along with Jan, for the many aspects of the formation of AMSI.

Tony followed this by becoming the Director of the Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS) and leading its long formal partnership with AMSI. As MASCOS Director he has been an active AMSI board member ever since and has given indispensible advice to successive AMSI Directors. Recently he has been heavily involved in the planning phase of the proposed national research institute in the mathematical sciences.

Peter Hall

Peter Hall was instrumental to the establishment and success of AMSI’s scientific program.

In 2003, the first full year of AMSI’s operation, Peter Hall, as one of Australia’s most respected and active mathematical scien-tists, accepted the position of chair of the Scientific Advisory Committee. This is an advi-sory committee to the AMSI Board whose membership comprises eminent mathematicians and statisticians of international repute and includes Professor Terry Tao, Australia’s only Fields medallist.

For the next seven years Peter was architect and custodian of AMSI’s scientific program. This program annually delivers between 15 and 20 workshops in mathematics, statistics and cognate disciplines around Australia. It has been instrumental in bringing hundreds of scientists to Australia from the world’s strongest research communities. Peter worked tire-lessly with workshop organisers to realise their vision, mentoring them on their applications and the execution of their meetings. His remarkable work ethic and deep experience along with the expert advice of the members of the committee has had a considerable impact on our research output and the grant success of our discipline over the last 10 years. The program itself has developed a strong sense of national identity amongst the researchers and research students at AMSI’s 30-odd member institutions.

All the AMSI Directors have relied heavily on Peter



Geoff PrinceAustralian Mathematical Sciences Institute, The University of Melbourne, Australia

[email protected]

Geoff Prince was a Monash undergraduate and took out a La Trobe PhD in 1981 in geometric mechanics and Lie groups. This was followed by a postdoc at the Institute for Advanced Study in Dublin. He enjoyed teaching at RMIT, UNE and La Trobe. His research interests lie mainly in differential equations, differential geometry and the calculus of variations. He is a proud Fellow of the Society, currently a Council and Steering Committee Member. He became AMSI director in September 2009.

for policy advice in pursuing the Institute’s mission. He can quite rightly take considerable credit for our success.

Of course, his service to the discipline extends far beyond his work at AMSI. His ability to be both one of our most respected and prolific scientists and a servant to his discipline commands the respect of everyone who knows him.

Peter Taylor (Australian Mathematics Trust)

Peter Taylor chaired the AMSI Education Advisory Committee (EAC) from its inception and was deeply involved in the planning and execution of the seminal workshops “Teacher Content Knowledge and Materials for Schools”. Work in the following years, including the first edition of the ICE-EM Mathe-matics books, was based on these early initiatives. Peter guided this work with an awareness of its importance

Reproduced from Gazette of Australian Mathematical Society, July 2012

and an ability to encourage others to become involved.He has overseen AMSI’s response to the Australian

Curriculum; the creation of the teacher resource modules; the launch of the “Maths: Make your career count” campaign; the collaboration with CSIRO to produce “Maths by Email”; the support of the “Mathematicians in Schools” program; and of course the new edition of the ICE-EM Mathematics series of textbooks. Peter has given wonderful support to the staff of AMSI and has made a major contribution to each of the projects undertaken during his chairing of the EAC.

Peter has been a great friend to AMSI and has supported Garth Gaudry, Phil Broadbridge and Geoff Prince each in their turn as AMSI Director. Many AMSI staff, particularly Janine McIntosh and Michael Evans, have been fortunate to work with Peter in his time as Chair of the EAC.

The Australian mathematical sciences community owes a considerable debt of gratitude to these far-sighted and dedicated individuals. Without them AMSI would not have reached its tenth anniversary or its track record of achievement and influence.



On August 18, 2012, Opzoon Science and Technology and Tianjin University held the signing ceremony for the “Joint Laboratory

of Applied Mathematics” at the Tianjin Saixiang Hotel. NPC vice chairman, chairman of Central Committee of China Association for Science and Technology Han Qide sent congratulatory letter for the formation of the Applied Mathematics Centre. Academician of the Chinese Academy of Sciences, Professor Ge Molin of Nankai University and academician Chen Yongchuan were appointed respectively as the honorary laboratory director and director.

Ten members of the Chinese Academy of Sciences, Chinese top mathematicians Wu Wentsun, Ma Zhiming, Li Tatsien, Hao Bailin, Zhou Heng, Zhang Chunting, Weinan E, Zhang Weiping, Ge Molin, Chen Yongchuan, etc. attended the ceremony. In addition, President of Tianjin University Li Jiajun, President of Nankai University Gong Ke, Opzoon Science and Technology Chairman Peng Haifan, and other dignities, cooperate leaders, experts with a total of nearly 100 people attended the signing ceremony. Vice president of Tianjin University, academician of Chinese Academy of Engineering Zhong Denghua presided over the ceremony.

Tianjin University President Li Jiajun and Opzoon Science and Technology Chairman Peng Haifan, representing Tianjin University and Opzoon Science and Technology, signed the agreement on “Joint

China's First “Joint Laboratory of Applied Mathematics”

Leaders and academicians at the inaugural ceremony

Laboratory of Applied Mathematics”. Opzoon Science and Technology will support the “Applied Mathematics Laboratory” with no less than 2 million Yuan each year, and not less than 10 million Yuan for five years in research funding. Starting from the advanced and mature technology currently exist in both parties, the laboratory will explore the direction of research and development, and to improve the technological productivity and transformation through sharing and transfer of research results and achievements.

Han Qide, Xing Yuanmin, Li Jiajun and Peng Haifan in their messages stressed the importance of setting up the applied mathematics laboratory and its potential role in promoting national and international collabo-rative research and innovation, training of young scientists and consolidating and strengthening the Centre of Applied Mathematics in Tianjin University as international centre of excellence in the subject. In particular, this Joint laboratory will make use of applied mathematics to solve the key technical problems of information technology, thereby strengthening in cloud computing and mobile internet technology both in application and innovation.

The collaboration between Opzoon Science and Technology and Tianjin University in establishing the “Applied Mathematics Laboratory” can be considered as the first joint venture between a private enterprise and a Chinese university in carrying out applied mathematics research.



The Japanese number theorist Haruzo Hida turned 60 this year, and there was a conference entitled “p-adic Modular Forms and Arith-

metic” for his 60th birthday at University of California, Los Angeles, held during June 18–23, 2012. It was one of the signature events of the year in the number theory conference schedule, both in terms of the enthusiasm it evoked, and the strong array of speakers it drew. This was largely because of the respect and admiration with which Hida and his work is viewed in the community.

The conference was organised by Blasius, Harris, Khare, Skinner, Taylor, Tilouine and Urban. It was supported by an NSF-FRG grant held between UCLA and Columbia and most unusually by the well-known Indian software company Infosys, which provided roughly a third of the funding. Infosys gave funding to this conference held in the US, when most of the usual extra-mural sources of funding for math conferences within the US have dried up, and was a testament to the commitment Infosys has to support academic research even on a global scale. The fact than an Indian corporate supported a research conference in Los Angeles left an impact on the minds of those who attended the conference.

Hida’s fundamental work in the 1980’s, what is called Hida theory these days, created a remarkable theory which put ordinary classical cusp forms in families

Conference In Honour of Haruzo Hida on His 60th Birthday

thus giving number theorists in the field almost another dimension to work in.

It has been tremendously influential! Almost as soon as it was discovered, Greenberg and Stevens made fundamental use of it in their solution of the Mazur–Tate–Teitelbaum conjecture. Mazur set it in the context of deformation theory of Galois representa-tions. Hida’s work had a profound influence on Wiles’ attack on Fermat’s Last Theorem. The proof at several points had Hida’s work as an inspiration. One of the key elements in the proof is a technique to replace Hida’s λ-adic Hecke algebras with patched versions that are still free over a power series ring.

Because of the great influence Hida’s work has had on algebraic number theory, more than 130 leading experts, younger researchers and students attended the conference. In fact the organisers faced a situation where there were more people volunteering to speak than could be accommodated in the 6-day schedule of the conference! Many of the lectures began with an account of how influential Hida’s work had been to the speaker.

The topics exposed ranged from construction of Galois representations, to p-adic L-functions to torsion in cohomology of arithmetic groups. Barry Mazur of Harvard University opened the conference with an account of Hida’s work illustrating its breadth



and significance. Richard Taylor, of the Institute of Advanced Study, paid tribute to Hida’s influence on his own mathematical development, and Hida’s prophetic vision. John Coates of the University of Cambridge pointed out how Hida’s work brought together the work of two Japanese number theorists, Goro Shimura and

Kenkichi Iwasawa, to great effect. There were a number of stimulating talks and much animated discussion amongst the participants.

The conference was felt by those who attended to be a fitting tribute to Hida’s work, its decisive influence and its growing current relevance.

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The aim of the series of the Pan Asian Number Theory (PANT) conferences is to promote collaboration in research between Asian

mathematicians working in any branch of Number Theory. The first PANT conference was held in POSTECH, Pohang, South Korea during January 8–11, 2009. The second conference in the series took place at the Research Institute of Mathematical Sciences (RIMS), Kyoto, between September 13–17, 2010. The third conference was held at the Morningside Institute, Beijing during August 22–26, 2011. PANT 2012 was held at Indian Institute of Science Education and Research (IISER), Pune, India between July 23–27, 2012, and it will be in Vietnam in 2013.

Humankind’s first tentative steps along the difficult road to Number Theory almost certainly began in Asia, probably within the civilisations of Babylon, China and India. Many mathematicians of Asian origin have made great contributions to research in Number Theory since then, especially in the last 150 years. Today, the rapid development of Mathematics departments in universities and research institutes in Asia augurs well for the prosperity of the future of this ancient discipline within Asia. It is also worth noting that including the forthcoming 2014 International

Pan Asian Number Theory Conference 2012

Pune, July 23–28, 2012

R Sujatha

Congress of Mathematicians (ICM) in Seoul, three out of four most recent ICMs have taken place in Asia.

The Scientific Committee consisted of J Coates (chair) (Cambridge, UK), Y Choie (POSTECH, Korea), T Ikeda (Kyoto University, Japan), K Kato (Chicago, USA), M Kim (Oxford, UK), M Kurihara (Keio University, Tokyo, Japan), J Liu (Shandong University, China), B C Ngo ( Chicago, USA), R Sujatha (University of British Columbia, Canada), Y Tian (Chinese Academy of Sciences, Beijing), Winnie Li (NCTS, Taiwan) and Wee Teck Gan (NUS, Singapore). The local Organising Committee consisted of S Maity (IISER Pune), A Raghuram (IISER Pune), A Saikia (IIT Guwahati) and R Sujatha. The conference was generously supported by funds from the International Centre for Theoretical Sciences.

Like the previous PANT Conferences, this one too had lectures that covered current developments in all major areas of research in Number Theory.

The conference itself was preceded by a Workshop on the Bloch–Kato conjecture. The goal of the workshop was to provide a detailed proof (up to powers of 2) of the Bloch–Kato and Lichtenbaum conjectures on the values of the Riemann zeta function at the odd positive integers.



The city of Pune being the cultural capital of the state of Maharashtra added to making the conference a great delight non-mathematically as well. There were excursions to ancient forts and other spots of great scenic beauty in the nearby Sahyadri mountain ranges.

The enthusiastic participation and the depth and range of the mathematical lectures contributed to the success of the event. It was announced that the next PANT conference would be held in Hanoi, Vietnam in the summer of 2013.




Asia Pacific Mathematics NewsletterAsia Pacific Mathematics Newsletter

The 5th International Workshop on Optimal Network Topologies (IWONT 2012), organ-ised by the Expert Group in Combinatorial

Mathematics in the Faculty of Mathematics and Natural Sciences in Institute of Technology Bandung (FMIPA-ITB) and the Indonesian Combinatorial Society, was held during July 27–29, 2012 in ITB. This Conference, which aims to improve the quality of research in particular combinatorial mathematics as well as strengthen the research collaboration with foreign mathematicians, was officially opened by the Rector of ITB, Professor Akhmaloka.

The series of IWONT conferences were previously held in Australia (2005), Czech Repubic (2007), Spain (2010), and Belgium (2011). IWONT 2012 Conference is supported by the International Mathematical Union (IMU) and the Abdus Salam International Centre for Theoretical Physics (ICTP). This shows the increasing international recognition of the development of the field of combinatorics and graph theory in Indonesia. IWONT 2012 Conference was chaired by Dr Rinovia Simanjuntak. There were about 70 participants came from different countries which include USA, United Kingdom, Belgium, Denmark, Spain, Australia, Japan, Slovakia, the Czech Republic, Pakistan, Malaysia, India,

the Philippines, Iran and Indo-nesia. The topics discussed at the Conference include IWONT problems related to optimal network topolo-gies in theoretical studies and applications. Keynote speakers were Dominique Shucks (Universite Libre de Bruxelles, Belgium), Leif Jorgensen (Aalborg Univer-

sity, Denmark), Margarida Mitjana (Universitat Politecnica de Catalunya, Spain), Akira Saito (Nihon University, Japan) and Jozef Siran (Open University, United Kingdom). Papers presented in this conference will be selected and published in the International Journal of AKCE Graphs and Combinatorics and ITB Journal of Sciences, which are indexed in Mathematical Reviews, Zentralblatt MATH, and SCOPUS. This will add to the knowledge and improve the quality of the publication of the international landscape in Indonesia.

In the opening speech, President of the Indonesian Combinatorial Society, Professor Edy Tri Karimuddin, who at one time was also Chairman of the Expert Group in Combinatorial Mathematics at FMIPA-ITB, stated his continued effort to organise an international conference on this subject. He emphasised that it is the Society’s commitment to foster the growth of the quality papers in the study of mathematics, developing interna-tional collaboration and enhance the competitiveness of the nation. He added that history has shown that great nations always exhibit their strong commitment to the development of mathematics as a major source of new technological inventions, as well as generating viewpoints and new mindset in solving the national and international problems.

The 5th IWONT 2012

Thailand-Japan Joint Conference on Computational Geometry and Graphs (TJJCCGG 2012) will be held on December 6 - 8, 2012 at Department of Mathematics, Srinakharinwirot University, Bangkok, Thailand. TJJCCGG 2012 is mainly intended to provide a forum for researchers working in compu-tational geometry, graph theory/algorithms and their

Participants of the 5th IWONT 2012

Thailand-Japan Joint Conference on Computational Geometry and Graphs

applications. Original research papers in these areas and their applications are sought. Applied and experi-mental papers are expected to show convincingly the usefulness and efficiency of algorithms discussed in a practical setting. The topics include, but are not limited to, Computational Geometry, Discrete Geometry, Graph Algorithms, and Graph Theory.

Book Reviews


Understanding Probability (3rd Edition)

Henk TijmsCambridge University Press, 2012, 572 pp

The third edition of “Under-standing Probability” by Henk Tijms is an introduc-tory book on probability theory. It is written at the level at which one requires, at most, a first course in calculus to read it. The book is split into two parts, the first consisting of an intro-duction to probability, by the means of motivating

examples (as aptly described by the author “to provide a feel for probability”). These motivating examples cover quite technical issues, for example the Black Scholes model, but at a mathematical level that is intuitive rather than technical. The second details the topics for a first course on (non measure-theoretic) probability theory, that might be taught at the first or second year undergraduate level at most mathematics or statistics departments. The topics of these latter sections are perhaps mathematically sophisticated, but introduced in a very readable manner, that provides the reader a very gentle introduction. Roughly, on the non-technical side of the book, the author covers: “laws of large numbers”, “rare-events”, “random walks”, “Brownian motion” and “Bayes Theorem” (in 6 chapters). These concepts are enhanced with a collection of more-or-less well known examples such as the “St. Petersburg paradox” and the “Monty–Hall problem” that are staples in undergraduate probability courses. On the technical side, the author covers: “foundations of probability”, “standard introduction to discrete and continuous random variables” (including the multivariate normal distribution and conditioning), “generating functions” and “Markov chains in discrete and continuous-time” (in 10 chapters). There are also exercises with solutions to odd-numbered questions. In addition, in comparison to previous editions of the book, the author adds further exercises and examples, including Markov chain Monte Carlo and Brownian motion.

Previous to reading this textbook, I had been unfamiliar with Henk Tjims’ work and in particular his books. I approached the book, with the idea that it might be a routine textbook and that essentially, I would skim through the book with little interest, revisiting concepts I already knew, forgotten or already taught. However,

I was very wrong! The book was engaging and the first half, as is claimed on the book jacket and preface, is not only easily accessible but very interesting. There are many real well-known examples, which add a dimen-sion of motivation which is often alluded to by many authors, but is followed through by this author. I have the feeling that this book should be recommended to high-school students that have the misconception that probability is either too easy or boring. In addition, I feel that this first half of the book is particularly useful for industrial professionals, for example in the pharmaceu-tical industry or finance, who have long forgotten their undergraduate training, but need to brush up for a new project. I cannot recommend this first half of the book more highly. Even more, what I find quite astonishing, is the ability to make quite complex mathematical objects (such as Brownian motion or the bootstrap method of Efron) seem “easy” by clear and intuitive explanation that one would assume can only be gained by a deep understanding of these concepts. Clearly, however, for the more technical minded (which includes this reviewer) one can find the lack of mathematical detail frustrating, but, of course this is not the intention of the author at this stage.

Moving onto the second half of the book, where the author starts to take a more mathematical look into probability, the one issue which gave me an initial skeptism was as follows. From my own experience as both student and teacher, I am used to probability being taught as a branch of mathematics; with a strict definition-theorem-proof format, that, whilst poten-tially intimidating, provides a clear way to understand the ideas; this is also the format of every textbook that I have used for probability. This is not the approach of the author (although there are sometimes definitions and “rules”) and the general route of explanation is one of first intuition or word commentary and then technical details, but only to the level at which they are required. The extent to which this works will depend on the reader, but I have the feeling that most readers who begin reading about a concept to which they have not read before looking at the book, will leave the book with the notion of some understanding. That is, it is very clear, without reaching technical details which would be required at the graduate level (which, again, is not the book’s intention). The reader of this review should not make the mistake that the book is not completely rigorous; within the confines of undergraduate probability, the author is generally very accurate mathematically.

From the perspective of the new material, I spent

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some time looking at these aspects, particularly Markov chain Monte Carlo (MCMC), this lying within my own research interests. The idea of MCMC is routinely used by researchers and industry professionals for statistical inference and until recently is seldom covered in undergraduate courses, mainly because the theory of Markov chains on general state-spaces is relatively new in probability theory. The author provides an introduc-tion to this algorithm which allows one to understand how to construct an algorithm of their own, which, given the level of the text is highly commendable. This explanation can easily be used by researchers in fields outside statistics or probability, seeking to gain an understanding in MCMC and to develop their own ideas further. In relation to this, I particularly liked the way the author discussed self-normalised importance sampling, which I have rarely seen outside a research level book. This topic is amazingly well demystified: “Why does this work. The explanation is simple” — and indeed it is and so was that of the author’s. I found this new part of the third edition very satisfying and in-line with the research that is currently being undertaken in simulation methodology.

The potential audience of this book, who I have frequently alluded to during my review, not only includes undergraduate students in multiple disciplines (such as statistics, economics or engineering) but those in industry seeking to gain an initial understanding in probability (or revisit long forgotten concepts) and espe-cially those seeking to teach an introductory course in probability. For the latter, whilst there may be a shortage of mathematics, the intuition that could be taken from this text, would greatly enhance your lectures, in this reviewer’s opinion. The book should definitely be read by undergraduates who leave each class with a feeling that they do not understand what just happened; they certainly will understand after this book — which makes the title entirely appropriate.

If this review feels very enthusiastic, then indeed that is my intention. My own feelings on “Under-standing Probability” are that it is an extremely useful book that makes probability understandable to a wide audience.

A JasraNational University of Singapore

[email protected]

Figurate Numbers

Elena Deza and Michel Marie DezaWorld Scientific, 2011, xviii + 456 pp

This book is about special types of numbers (inte-gers) that have geometric associations and that have intriguing spatial proper-ties. The ancient Greeks were perhaps the first to study what are called “figu-rate numbers” — numbers that can be represented by regular geometric patterns of points in the plane or in

space, such as triangular, polygonal and polyhedral numbers. The first two chapters contain a lot of formulae for all kinds of figurate numbers that arise from geometric patterns in 2 and 3 dimensions. Properties and relations between such figurate numbers and their connections with Diophantine equations have been studied by classical mathematicians like Euler, Fermat, Lagrange, Legendre, Cauchy, Gauss and Dirichlet.

Chapter 3 extends the construction of figurate numbers to dimension 4 and beyond. Examples of such numbers are the pentatope numbers which are 4-dimensional analogues of triangular and tetrahedral numbers, and the biquadratic numbers which are the 4-dimensional analogues of square and cubic numbers. Despite the lack of visual pictures and physical intuition, multitudes of formulae are presented and proved.

Chapter 4 contains much interesting material on the role of certain figurate numbers in classical number theory. One finds connections with well-known numbers associated with the names of Catalan, Mersenne, Fermat, Fibonacci, Lucas, Stirling, Bernoulli, Bell and so on. Certain types of Diophantine equa-tions inevitably turn up — the Fermat equation, Pell equation, Ramanujan–Nagell equation. We get to see some recreational aspects of prime numbers in terms of square arrangements of their digits. Most people have come across magic squares and magic cubes, but probably not magic hexagons. There is a brief mention of unrestricted partitions and Waring’s problem.

The first four chapters may appear to be a collec-tion of results and properties about “exotic” numbers and lack a general theory. However, from a number-theoretic point of view, Chapter 5 is the most interesting

Book Reviews


and modern. It revolves around Fermat’s polygonal number theorem which was mentioned in a letter from Fermat to Mersenne as the statement that every integer is a sum of at most 3 triangular numbers, 4 squares, 5 pentagonal numbers and so on. In his usual style, Fermat hints at a proof for which he would need to devote an entire book, but such a book or proof has yet to be discovered. Unlike Fermat’s more famous “Last Theorem”, his polygonal number theorem was proved by Cauchy around 1813 and a simplified proof was given by T Pepin in 1892. Apparently the book under review is the first book to present the full details of the proof. Before that, results about the polygonal number theorem are scattered among hard to access publications and defunct journals. In the classical connection, we also come across the names of illustrious mathemati-cians like Gauss, Lagrange, Legendre, Jacobi, Dirichlet and Minkowski. The bridge between the classical and the modern setting was perhaps provided by L E Dickson, and the final coup de grace was delivered by M B Natanson in 1987.

There is a list of figurate-related numbers in Chapter 6 — a kind of zoo of numbers with “exotic” and unusual numerical properties, like rare trophies of number hunters and collectors; for example, the largest known prime that cannot be expressed as a sum of 3 hexagonal numbers, or a prime that can be

represented as a sum of a triangular number and a perfect square in 27 distinct ways. The list is probably not exhaustive; there must be numerous puzzles in recreational mathematics that would be a good test bed for arithmetic ingenuity and computer skills. In fact, the last chapter contains 155 problems (with solu-tions given) to indulge in one’s fascination for curious numerical properties which could have also occupied mathematicians as a pastime.

This book offers a potential source of information for those interested in numbers and numerical properties associated with geometric configurations. It collects together a wide range of results scattered throughout the literature and gives numerous references to books on recreational mathematics as well as elementary number theory. However, there are many typographical errors in language — the proof reading could have been more thorough. In many places also, the language is awkward and sometimes incorrect (probably due to the fact that the authors are not English native-speaking) though this may not be mathematically significant. All in all, it is good to know that there is a book one can turn to if you need to check up some lesser known things about numbers associated with geometric patterns.

Y K Leong National University of Singapore

The Best Writing on Mathematics 2010

Mircea Pitici (editor)Princeton University Press, 2011

Mircea Pitici is a math-ematics education specialist at C ornel l Univers ity. He also teaches writing courses and has edited this anthology as a way of presenting nontechnical expositions of mathematical topics to a general audience. The articles are organised somewhat arbitrarily into six broad categories: “Math-

ematics Alive”, illustrating the versatility of math-ematical writing; “Mathematicians and the Practice of Mathematics”, challenging stereotypes of mathemati-cians; “Mathematics and Its Applications”, including networks, probability and homology; “Mathematics

Education”, ranging from high school to post-graduate level; “History and Philosophy of Mathematics”; and “Mathematics in the Media”.

The sources vary from popular mathematical journals such as The American Mathematical Monthly and The Mathematical Intelligencer, journals of record like The Bulletin and Notices of the American Mathematical Society, to blogs and columns from The New Yorker, The Guardian and The New York Times. The articles are presented without critical commentary and on the whole are well chosen and written to appeal to a wide mathematically literate audience. A few, however, especially those on education, are of limited relevance outside of North America.

There are far too many articles to review individually, so I will just comment on ones that I found particularly appealing. In “Mathematics Alive”, there is an amusing but serious discussion by the geometer Branko Grünbaum, called “An enduring error”, concerning the enumeration of the Archimedean Polyhedra: are there 13 or 14? The ambiguity dates right back to Kepler, who in different places claimed both. It

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persists in research papers and textbooks right up to the present, and Grünbaum gleefully traces its passage. Of course, he also discusses the reason: there are two incompatible definitions of an Archimedean Polyhedron, that is, a convex polyhedron having regular polygons for faces. One definition states that it has isomorphic vertex figures (this is the source of the 14), and the other that its automorphism group acts transitively on the vertex figures (this eliminates one of the 14). Grünbaum carefully describes the two possible rhombicuboctahedra, one of which is transitive on the vertices and the other not.

The section on “Mathematicians and the Practice of Mathematics” contains an essay by Phillip J Davis, published in a popular Swedish mathematical journal, on the mathematical jottings in the notebooks of the Symbolist poet and philosopher Paul Valéry (1871–1945). Valéry read widely in mathematics and physics, and was acquainted with both E Borel and Hadamard. He was au fait with contemporary developments in relativity and quantum physics. While Davis finds nothing mathematically noteworthy in his notes, he points out that Valéry was obsessed with clarity of language and saw mathematics as a model for defining concepts precisely and relating them in a coherent way.

This section also contains the curious history, by Alicia Dickenstein, of the lost cover page in the English 1920 translation of Einstein’s main article on the Theory of General Relativity, published in 1916. This page, which Dickenstein found in the online Einstein archives from the Hebrew University of Jerusalem, contains unstinting praise of the mathematicians who developed the absolute differential calculus on which the theory is based.

There are several novel results in the “Mathematics and Its Applications” section. In “Mathematics and the Internet”, Willinger, Anderson and Doyle debunk the popular “scale-free” or power law model of the

Internet, pointing out that it is based on easily obtained but unreliable data. Brian Hayes, in “The Higher Arithmetic”, shows how to use different number scales to make sense of the very large numbers that pop up in computing, finance and astronomy. In “Knowing When to Stop”, Theodore P Hill discusses the mathematical justification of optimal stopping rules in various practical situations.

A controversial article in the “History and Philosophy of Mathematics” section is “Kronecker’s algorithmic mathematics” by Harold M Edwards. He demolishes popular legends concerning Kronecker’s non-belief in the existence of objects like non-constructible irrational numbers. He points out that Kronecker’s algorithms (in the absence of computers) are intended to be theoretically, not practically, computable. Finally, as a strong adherent of Kronecker’s version of constructive mathematics, Edwards pours scorn on Brouwer’s lawless sequences as well as Hilbert’s proof of the existence of integral bases of algebraic number fields. One may feel the desire to argue with Edwards, but there is no doubt that he presents interesting ideas in an intriguing way.

In the “Mathematics and the Media” section, the classical and jazz musician Vijay Iyer, in a column from The Guardian newspaper called “Strength in numbers”, describes the way in which mathematical ideas have explicitly influenced musicians. For example, he traces harmonic rhythms based on initial segments of the Fibonacci sequence in the music of Karnatak India, West Africa, Bartok and even Michael Jackson’s “Billie Jean”!

In summary, I recommend this book to the readers as enjoyable bedside reading.

Phill SchultzThe University of Western Australia

[email protected]

Reproduced from Gazette of Australian Mathematical Society, July 2012

News in Asia Pacific Region

News from Australia

Scientists and Mathematicians in Schools

“Scientists and Mathematicians in Schools” is a national program that seeks to bring volunteer scientists/mathematicians together with teachers into an ongoing professional partnership, with the aims of inspiring and motivating students, bringing real world science and mathematics into classrooms and increasing awareness of science and maths related careers.

“Scientists and Mathematicians in Schools” is funded by the Australian Government Department of Education, Employment and Workplace Relations and Commonwealth Scientific and Industrial Research Organisation (CSIRO), and managed by CSIRO Education. In the Australian Government budget of May 8, 2012, “Scientists and Mathematicians in Schools” received $6.5 million over four years to continue the good work being done since 2007. The funding is part of a $54 million package for science and mathematics education and the result of a review undertaken by the Chief Scientist, Professor Ian Chubb. This is a vote of confidence in the positive difference the program makes and in its ability to bring real-life science and maths into classrooms.

At present there are over 1400 partnerships across Australia, 180 of these are mathematics partnerships. However, there are many teachers who are currently registered and waiting for their mathematician. Currently, we have approximately 30 mathematicians registered with the program who have identified themselves as being members of the Australian Mathematical Society. It should be noted that this number is likely to be an underestimate, as providing information on professional association membership is voluntary when registering.

ContactCarla Hall, Senior Project Officer, Scientists in School, CSIRO EducationPhone: +61 2 6276 6376Email: [email protected]: http://www.scientistsinschools.edu.au/

News from China

Sino-French Seminar on Diophantine Geometry

S i n o - Fre n c h S e m i n a r o n Diophantine Geometry took place during August 27–31, 2012 at the Beijing Interna-tional Centre for Mathematical Research (BICMR). This meeting was the first academic activity in China held under the Sino-French Mathematical Research Cooperation Project (SFRPM). Director of BICMR, Professor Gang Tian, and the French representative Professor Sinnou David, delivered speeches during the opening ceremony.

This seminar was organised to discuss the joint research program (Sino-French Research Program in Diophantine Geometry) focusing on rational points on modular curves, an important research topic in Diophantine geometry. This topic is closely linked with the theory of modular forms, Diophantine approxima-tion theory, Galois theory, and many other subjects.

Recently there was a major breakthrough. Yuri Bilu, Pierre Parent and Marusia Rebolledo, who in a series of work have proved that when the prime number p is not equal to or less than 17 or p = 11, and r > 0, modular curves X0

+(pr) have only trivial rational points of the ordinary. The most impressive places of work are the traditional method of Diophan-tine approximation theory in conjunction with tools of modern arithmetic geometry combined in an organic way. Such a method is expected to continue to play an important role in the study of modular curves.

This workshop has a dual purpose. First, the conference

Gang Tian, Director of the Beijing Interna-tional Centre for Math-ematical Research

Professor Mehdi Fabien Pazuki, the representa-tive from France



Fang Guanghua, President of Northwestern University delivering the welcoming speech

invited Bilu, Parent, Rebolledo to explain their recent results. In order to prepare the audience to have a better understanding of the technical lectures, the conference also invited a group of scholars to provide introductory lectures on theories of Galois, Diophantine approxima-tion, modular curves, etc. In addition, some number theorists from the two countries also presented reports on their recent work during the seminar. Students from Peking University, Capital Normal University, the Chinese Academy of Sciences, Université de Bordeaux I and Université Paris VII enthusiastically participated in the seminar. For a period of one week, both students and teachers conducted extensive exchanges and discussion.

2012 Annual Meeting of CMS

Chinese Mathematical Society Annual Conference in 2012 was held during August 31 to September 2 in Xi’an, hosted by the Northwestern University (NWU). There were about 200 Chinese and foreign participants attended this meeting. Chinese Academicians present include Wang Shicheng, Wen Lan, Shi Zongci, Cui Junzhi, Tian Gang, Xi Nanhua, and Xu Zongben.

Fang Guanghua, the President of Northwestern Univer-sity, briefed the participants the history of the university in his welcoming speech. He also expressed his hope that the department of mathematics of NWU could make use of this meeting to improve its cooperation and interaction with Chinese and overseas mathematicians.

Professor Xu Zongben from Xi’an Jiaotong University presented a report on “Several theoretical questions about the sparse information processing”. Professor Zong Chuanming from Peking University talked about “Mysterious tetrahedral”, and Professor Guo Kunyu of Fudan University gave a talk on “Operator theory on the Bergman Space”. Subsequently, the analysis group, applied mathematics group and algebra, number

theory, topology, geometry group conducted a total of 30 group reports.

Dur ing the meet ing , 10 mathematicians including academicians Wang Shicheng, Wen Lan, Shi Zongci, Cui Junzhi, Tian Gang visited and gave talks at Shaanxi Normal University, Northwestern Polytechnical University, Xi’an Jiaotong University, and Northwestern University. The public lectures include “Talking from the Knot” by Wang Shicheng, “Cantor theorem and barber paradox” by Wen Lan, “The development of computational mathematics in China” by Shi Zongci, “From scientific computing to digital engineering” by Cui Junzhi, and “Mathematics is useful” by Tian Gang.

The entire meeting provided a useful platform for academic exchanges involving various areas of mathematics, showcased the latest research results in mathematics, and also allowed the analysis of the future prospects for the development of Chinese mathematics.

A Vietnam Delegation Visited MSC of Tsinghua University

A delegation of five Vietnamese scholars visited Math-ematical Sciences Center (MSC) of Tsinghua University in September 17, 2012. The delegate includes Professor Ngo Viet Trung, Director of Institute of Mathematics, Vietnamese Academy of Science and Technology, Professor Le Tuan Hoa, Executive Director of Vietnam Institute of Advanced Study in Mathematical Sciences, and Professor Ha Huy Khoai, Chair of Department of Mathematics, Thang Long University.

In the exchange conference, Associate Director of MSC, Professor Yat Sun Poon introduced the present situation and future outlook of MSC, including members and primary activities. When talked about the successful experience of attracting talented person, Professor Poon said, “The professors come to our centre for two reasons: one is that we have excellent students here. The professors are all love teaching, because the students are stimulative. Another is that the centre itself is very much open to any research programs. We don’t really care which area that you are in. Good people bring a good research area. So we give people the freedom to do their research.”

Academician Shi Zongci lectures on the develop-ment of computational mathematics



National University of Singapore, and is a Distinguished Visiting Professor of the University of Hong Kong.

Peter Hall’s Course at Peking University

Invited by the Centre for Statistical Science at Peking University, Professor Peter Hall from The University of Melbourne, Australia, delivered a short course on “Methodology and Theory for the Bootstrap” from March 15 to 24, 2012. The short course comprised 16 lectures, and attracted more than 100 graduate students and faculty members from schools across China, and many of them came from outside Beijing. It took place at the newly built Beijing International Centre for Mathematics (which co-sponsored the short course).

The course was well received by the participants. The President of Peking University, Professor Qifeng Zhou, met Professor Hall, and they had lively exchanges of ideas and views on developing statistics in the campus of Peking University and beyond.

On the occasion of Peter’s 60-and-a-quarter birthday, a surprise birthday party was staged, which was well attended by the participants of the short course, as a way to express their gratitude to Peter for his extremely hard work in delivering the 16 lectures, as well as his scholarship — and, more importantly, to celebrate a milestone in a distinguished career in Statistics. We are sure Peter’s visit and short course would be long remembered by those students and faculty members.

Peking University Alumnus Wins COPSS Presidents’ Award

At the Joint Statistical Meetings (JSM) held during July 28 to August 2 this year, we learned that Samuel Kou of Harvard’s Department of Statistics won the Committee of Presidents of Statistical Societies (COPSS) President’s award.

After that, Vice Chair of Department of Mathematical Sciences, Professor Wenming Zou introduced the history and present situation of Department of Mathematical Sciences. Besides, Director of Department of Math-ematical Sciences, Professor Jie Xiao gave an introduc-tion to visitors about students of Tsinghua University.

The five Vietnam scholars spoke highly of MSC and Tsinghua University. They also introduced the situation of Vietnam Institute of Advanced Study in Mathematical Sciences and exchanged the experience with MSC. This visit provides a better understanding between Tsinghua University and Vietnamese math-ematicians.

ICSA Distinguished Service Award

H o w e l l To n g r e c e i v e d a Distinguished Achievement award at the 2012 Joint Statistical Meeting in San Diego on August 1, 2012 from the International Chinese Statistical Association (ICSA). This award honours his achievements and leadership in statistical research, education and statistical applications. Howell is an IMS Fellow and former Council member. He was a Council member and Chair of the European Section, Bernoulli Society, 1999–2001. He is known for his pioneering and authoritative work in nonlinear time series analysis and chaos, for which he was honoured with a National Natural Science Prize (Class 2) from the People’s Republic of China in 2000 and a Guy Medal in Silver from the UK Royal Statistical Society in 2007. He was elected a Foreign Member of the Norwegian Academy of Science and Letters in 2000. Howell retired from his chair of statistics at the London School of Economics in 2009 and is now an emeritus professor of statistics. He was the 2009 and 2010 Saw Swee Hock Professor of the

Professor Hall (centre front row) with students and faculty members. Peking University faculty members present in front row: Gang Tian (fourth from right), Song Xi Chen (fifth from left)

Professor Yat Sun Poon introduced MSC to Vietnamese delegates

Howell Tong



The citation for the aw a rd re a d s , “f or g r o u n d b r e a k i n g c o n t r i b u t i o n s t o stochastic modeling and statistical infer-ence in single mole-cule biophysics; for pioneering the equi-energy sampler; for fundamental contribu-tions to Bayesian, empirical Bayes and nonparametric methods; and for outstanding service to the statistical profession and contribution to statistical education.”

Kou is an alumnus of Peking University. He was admitted to Peking University in 1993 and started pursuing his PhD at Stanford University in 1997. In 2001, he took a faculty position at Harvard University and was promoted to a full professor in 2008.

COPSS sponsors and presents the Presidents’ Award to a young member of the statistical community in recog-nition of an outstanding contribution to the profession of statistics. The Presidents’ Award, established in 1976, is jointly sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Biometric Society ENAR, the Biometric Society WNAR, and the Statistics Society of Canada operating through COPSS. The award consists of a suitable certificate and cash award in the sum of $1000 and is given during the joint meetings of the sponsoring socie-ties. The first award was made in 1979, and is awarded yearly. The recipient of the Presidents’ Award shall be a member of at least one of the participating societies. The candidate may be chosen for a single contribution of extraordinary merit, or an outstanding aggregate of contributions, to the profession of statistics. The President’s Award is granted to an individual who has not yet reached his or her 41st birthday during the calendar year of the award.

2012 Turing Year in China

The Turing Year in China was hold successfully during May 16–21, 2012 at Building 5, fourth floor lecture hall in the Institute of Software Chinese Academy of Sciences (ISCAS). In this connection, a series of activities was held to commemorate the centenary of renowned scientist Alan Turing: 2012 Turing Lectures, the 9th Annual Conference on Theory and Applications of Models of Computation (TAMC 2012), China Forum

on Algorithm and Information 2012 and 2012 China Science Future Star, which all took place during May 16–21 at the ISCAS.

The highlight of the Turing Year in China is the Turing Lectures given by a number of distinguished speakers, including three Turing Award winners. They were S Barry Cooper (Leeds, Chair Turing Centenary Committee), John E Hopcroft (Cornell, 1986 Turing Award Winner), Richard M Karp (Berkeley, 1985 Turing Award Winner), Jon Kleinberg (Cornell, 2006 Nevanlinna Prize), Li Deyi (Chinese Academy of Engineering, Beijing, China), Wei Li (BUAA, Beijing, China), and Andrew Chi-Chih Yao (Tsinghua, 2000 Turing Award Winner).

The titles of the lectures given were: “Impact of Turing Machines” by John E Hopcroft, “From Turing Machine to Morphogenesis — Forming and Informing Compu-tation” by S Barry Cooper, “Theory of Computation as an Enabling Tool for the Sciences” by Richard M Karp, “The Convergence of Social and Technological Networks” by Jon Kleinberg, “Interaction and Collective Intelligence on the Internet” by Deyi Li, “R-Calculus: A Logical Inference System for Scientific Discovery” by Wei Li, and “Quantum Computing: A Great Science in the Making” by Andrew C Yao. These presentations are open to domestic scholars and students. There were nearly 200 scholars from home and abroad and several news media attended the event. The meeting was presided over by Angsheng Li from ISCAS.

News from India

Indo-French Number Theory Symposium at IISER Pune

The Indo French Centre for the Promotion of

Left: Xihong Lin, Chair of COPSS, right: Presidents’ Award winner, Samuel S Kou



Advanced Research (IFCPAR) was set up in 1987 by the Governments of India and France to promote collaboration between researchers in both countries in all areas of Science and Technology. The Centre also funds research level seminars in various disciplines. One such meeting was held from September 3–7, 2012 at IISER Pune.

The focus of this symposium was on Number Theory and more specifically on topics relating to Automorphic forms, Galois representations and L-functions. The Indian Coordinator for this event was Professor A Raghuram (IISER Pune) and the French Coordinator was Professor Jacques Tilouine (Paris 13). The local organiser from the host institution was Dr Baskar Balasubramanyam.

The meeting was well attended with 25 Indian participants and 7 French participants. There were a total of 24 research level talks and a colloquium by Professor Jean-Marc Fontaine.

For further details, please visit the website https://sites.google.com/site/cefipramath2012/

Ramanujan Prize Announcement

The 2012 Ramanujan Prize for Young Mathemati-cians from Developing Countries will be awarded to Professor Fernando Codá Marques (32), Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil. The prize is awarded jointly by The Abdus Salam International Centre for Theoretical Physics, The Niels Henrik Abel Memorial Fund, and The International Mathematical Union.

The Prize is in recognition of Professor Fernando Codá Marques’ several outstanding contributions to Differential Geometry. Together with his coauthors, Fernando Codá Marques has solved long standing open problems, and obtained important results, including results on the Yamabe problem, the complete solution of Schoen’s conjecture, counterexamples to the rigidity conjecture of Min-Oo, connectivity of the

space of positive curvature metrics on an orientable 3-manifold, and most recently, a proof of the Willmore conjecture.

The Selection Committee consisted of Ngô Bảo Châu, Helge Holden, Maria José Pacifico, Vasudevan Srinivas and Lothar Göttsche (Chair). The Prize is supported financially by the Norwegian Niels Henrik Abel Memo-rial Fund, with the participation of the International Mathematical Union.

Students Celebrate National Year of Mathematics

BANGALORE – Infosys Science Foundation in association with Sishu Griha Montessori and High School organised an inter-school mathematics fest “Limit Infinity — The Number Games”. The day-long event on Saturday witnessed participation from over 160 students from 25 schools in the city.

“The Limit Infinity fest was aimed at inspiring a love for Mathematics and to help eliminate the fear of Math in young minds. With the year 2012–2013 being celebrated as the ‘National Year of Mathematics’ in India in honour of the renowned mathematician Srinivasa Ramanujan’s 125th birth anniversary, we thought it apt to organise this fest to demystify Math and overcome the myths and fallacies associated with numbers. The aim was also to encourage students to pursue the field of Math in future,” said Sujatha Mohandas, the principal of Sishu Griha School.

The event hosted interesting sessions that focused on combining Math and fun, while engaging youngsters in group discussions, quizzes, and relay of problem solving sessions. Presentations and a skit on the life of Ramanujan by the Sishu Griha students were also organised to help children understand the application of Math in day-to-day lives.

K Dinesh, co-founder Infosys said, “It is important to encourage and influence the young minds in our country to pursue Math at advanced levels and bring back the romance in this field of study. Limit Infinity, organised by Sishu Griha and Infosys Science Foundation, is our effort in this direction. I am sure it demonstrated how exciting a subject Mathematics can be.”

Zhiwei Yun Receives 2012 SASTRA Ramanujan Prize

The 2012 SASTRA Ramanujan Prize will be awarded to Dr Zhiwei Yun, who has just completed a C L E Moore Instructorship at the Massachusetts Institute of Technology and will be taking up a faculty posi-tion at Stanford University in California this fall.



The SASTRA Ramanujan Prize was established in 2005 and is awarded annually for outstanding contributions by very young mathematicians to areas influenced by the genius Srinivasa Ramanujan. The age limit for the prize has been set at 32 because Ramanujan achieved so much in his brief life of 32 years. Because 2012 is the 125th anniversary of the birth of Srinivasa Ramanujan, the prize will be given in New Delhi (India’s capital) on December 22 (Ramanujan’s birthday), during the concluding ceremony of the International Confer-ence on the Legacy of Ramanujan conducted by the National Board of Higher Mathematics of India and co-sponsored by SASTRA University and Delhi University. Dr Yun will also be invited to speak at the International Conference during December 14–16 at SASTRA University in Kumbakonam (Ramanujan’s hometown) where the prize has been given annually in previous years.

Yun’s PhD thesis on global Springer theory at Princeton University, written under the direc-tion of Professor Robert MacPherson of The Institute for Advanced Study, is opening up whole new vistas in the Langlands program, which represents one of the greatest developments in mathematics in the last half-century. Springer theory is the study of Weyl group actions on the cohomology of certain subvarieties of the flag manifold called Springer fibers. Yun’s global Springer theory deals with Hitchin fibers instead of Springer fibers (taking the lead from earlier work on Hitchin fibers by Gérard Laumon and the 2010 Fields Medalist Ngô Bảo Châu) which he uses to determine the actions of affine Weyl groups on cohomolgy. His work is expected to lead to a geometric and functorial understanding of the Langlands program. Many papers by him on global Springer theory have arisen from his PhD thesis; one has appeared in 2011 in Advances in Mathematics and another will soon appear in Compo-sitio Mathematica.

Ngô Bảo Châu was awarded the 2010 Fields Medal for his proof of the Fundamental Lemma in the Langlands Program. Yun has made a major breakthrough in the study of the Fundamental Lemma formulated by

Jacquet and Rallis in their program of proving the Gross–Prasad conjecture on relative trace formulas. Yun’s understanding of Hitchin fibrations enabled him to reduce the Jacquet–Rallis fundamental lemma to a cohomological property of the Hitchin fibration. This work, considered a gem of mathematics, appeared in 2011 in the Duke Mathematical Journal.

Yun has collaborated with Ngô and Jochen Heinloth on a seminal paper on Kloosterman sheaves for reductive groups which will appear in the Annals of Mathematics. In this wonderful joint paper, Ngô, Heinloth and Yun reprove a unicity result of Gross on automorphic representations over the rational func-tion field, and use the geometric Langlands theory to the construction of l-adic local systems.

Yun has also done significant work in algebraic geom-etry. His recent article with Davesh Maulik on the Macdonald formula for curves with planar singularities will appear in The Journal für die Reine und Angewandte Mathematik. Yun’s most recent work on the uniform construction of motives with exceptional Galois groups is considered to be a fundamental breakthrough. A construction like Yun’s was sought by Fields Medalists Serre and Grothendieck for over 40 years, and Yun’s work is considered one of the most exciting develop-ments in the theory of motives in the last two decades.

Zhiwei Yun was born in Changzhou, China in 1982. He showed his flair for mathematics early by winning the Gold Medal in the 41st Mathematical Olympiad in 2000 in Korea. He joined Peking University in 2000 on a Ming-De Fellowship and obtained a bachelor’s degree there in 2004. He continued his studies at Princeton University, where he received his PhD in 2009. He was Visiting Member at the Institute for Advanced Study in 2009–2010, and held the C L E Moore instructorship at MIT during 2010–2012. In fall 2012, he will join the mathematics faculty at Stanford University. At the age of 30, he has established himself as one of the young leaders of modern mathematics.

The international panel of experts who formed the 2012 Prize Committee were: Krishnaswami Alladi (chair), University of Florida; Frits Beukers, University of Utrecht; Kathrin Bringmann, University of Cologne; Benedict Gross, Harvard University; Kenneth Ribet, University of California, Berkeley; Robert Vaughan, The Pennsylvania State University; Ole Warnaar, University of Melbourne.

Previous winners of the SASTRA Ramanujan Prize

Dr Zhiwei Yun has made fundamental contributions to several areas that lie at the interface of representation theory, algebraic geometry and number theory



include Manjul Bhargava and Kannan Soundararajan in 2005 (two full prizes), Terence Tao in 2006, Ben Green in 2007, Akshay Venkatesh in 2008, Kathrin Bringmann in 2009, Wei Zhang in 2010 and Roman Holowinsky in 2011. Thus Zhiwei Yun joins an impressive list of brilliant mathematicians who have made monumental contributions at a very young age.

News from Japan

The 2012 MSJ Spring Prize

The 2012 MSJ Spring Prize was awarded to Dr Shin-ichi OHTA, an associate professor at Department of Mathematics, Kyoto University. Dr Ohta is recognised for his outstanding contributions to “Geometric analysis on metric measure spaces and Finsler manifolds”.

The Spring Prize and the Autumn Prize of the Society are the most prestigious prizes awarded by the MSJ to its members. The Spring Prize is awarded to those of age below 40 who have obtained outstanding mathematical results.

Mathematical research in curved spaces (Riemannian manifolds) has a long history and its principal method is global analysis, that is, analysis of functions or mappings defined on spaces in question and/or of mappings targeted to them. Conversely, in order to fully develop global analysis, we need to know detailed geometry of underlying spaces.

Theory of metric measure spaces grew out of the close interaction between geometry and analysis as a logical consequence of them and new research subject of importance of its own. A metric measure space is a (singular) space equipped with a distance function and a measure. It is a natural framework to apply various analytic methods, specifically probabilistic methods.

Typical examples of metric measure spaces are “Alexandrov spaces”. Alexandrov spaces naturally appear as limits of families of Riemannian manifolds of bounded curvature and diameter. Alexandrov spaces, which were originally introduced in order to better understand Riemannian manifolds, are now recognised as fascinating research objects in their own right.

Probabilistic methods are powerful machinery for the

study of metric measure spaces. One of such example is geometry via Wasserstein spaces. It is related to the optimal transportation problem of Monge and Kantorovich, which asks the most economical way to transport a pile of soil from one place to another place. The Wasserstein space associated with a metric space is the set of probability measures on the space equipped with the distance defined as follows. We may think of a probability measure as a distribution of soil on the space. Then we define the distance of two measures to be the infimum of the transportation cost for changing the first distribution of soil to the second one.

The importance of Wasserstein spaces in geometry was first illustrated by epoch-making papers by J Lott and C Villani, and by K Th Sturm to the effect that for a Riemannian manifold of dimension bounded from above, the convexity properties of the entropy function can be used to characterise a lower Ricci curvature bound. Their result can be extended to a wider class of spaces, turning Wasserstein spaces to a powerful tool for the study of metric measure spaces such as Alexandrov spaces.

In the situation explained above, Dr Ohta has been conducting energetic researches in geometry and analysis of metric measure spaces, and eventually succeeded in extending most of the important results known in the category of Riemannian manifolds to a bigger category of metric measure spaces. His outstanding achievements include a series of papers on Wasserstein spaces associated with Alexandrov spaces as well as significant contributions to the theory of Finsler manifolds by giving proper formulations and proofs of associated Wasserstein spaces, uniform convexity/smoothness and the Borel–Brascamp–Lieb inequality.

Two achievements are particularly outstanding among Dr Ohta’s works. The first is a joint work with K Th Sturm on the (nonlinear) Laplacian and heat equations on Finsler manifolds. The second is the construction of gradient flows of the relative entropy on Wasserstein spaces associated with Alexandrov spaces.

The standard argument to show that the heat equation on a Riemannian manifold always has solutions heavily depends on the linearity of the Laplacian. On a Finsler manifold, the Laplacian is not linear any more, which causes serious troubles. Dr Ohta together with K Th Strum overcame technical difficulties due to the non-linearity, and showed that the Laplacian is absolutely continuous with respect to the measure of the



Finsler manifold. As for Wasserstein spaces associated with Alexandrov spaces, Dr Ohta proved that a gradient flow of a lower semicontinuous convex function has a solution in arbitrary time, and that a solution is unique when the underlying Alexandrov space has curvature 0. In fact, the existence of a solution was previously proved by L Ambrosio, N Gigli and G Savaré, but Dr Ohta’s method, completely different from theirs, is highly appreciated as a useful alternative method. The uniqueness is a new original result.

On top of the results above, Dr Ohta’s recent joint paper with N Gigli and K Kuwada shows that the heat flow on an Alexandrov space is essentially identical with the gradient flow of the relative entropy on the associated Wasserstein space. A comparison of the two different equations on two different spaces, provides non-trivial information, which is rich enough to immediately elicit the Lipschitz continuity of solutions of the heat equation and eigenfunctions of the Laplacian.

As said above, the contribution of Dr Ohta to the development of the geometry and analysis of metric measure spaces is quite outstanding and well deserves the Spring Prize of the Mathematical Society of Japan.

Takashi Kumagai to Receive the 8th JSPS Prize

Dr Takashi KUMAGAI was awarded the 8th JSPS Pr ize by Japan S o cie ty for the Promotion of Science. Dr Kumagai, a professor in RIMS, Kyoto University, is honoured for his work on “Analysis and Theory of Stochastic Processes on Disordered Media”. He is also the 2004 MSJ Spring Prize awardee.

The objective of JSPS Prize is to recognise and support excellent young researchers under 45 years of age.

Yoshinori Gongyo to Receive the Second JSPS Ikushi Prize

Yoshinori Gongyo was awarded the second JSPS Ikushi Prize by Japan Society for the Promotion of Science. Yoshinori Gongyo, a PhD student in the Graduate School of Mathematical Sciences, the University of Tokyo, is honoured for his work on “minimal models and abundance”.

JSPS Ikushi Prize has been established upon an imperial donation to encourage young researchers, especially PhD students.

Videos Launched for MSJ Seasonal Institute 2012 “Schubert Calculus”

The MSJ has launched the vidoes of lectures delivered in MSJ Seasonal Institute (MSJ-SI) “Schubert Calculus” held in Osaka City University in July, 2012: http://www.math.ed.okayama-u.ac.jp/msjsi12/

Vist the MSJ webpagehttp://mathsoc.jp/videos/2012msj-si.html

to enjoy the lectures:Equivariant Schubert polynomials (I–IV) by Takashi Ikeda (Okayama Univ.), Schubert calculus and puzzles (I–IV) by Allen Knutson (Cornell Univ.), Consequences of the Lakshmibai–Sandhya Theorem; the ubiquity of permutation patterns in Schubert calculus and related geometry (I–IV) by Sara Billey (Univ. of Washington), Affine Schubert calculus (I–IV) by Thomas Lam (Univ. of Michigan) and Experimentation in the Schubert Calculus (I–IV) by Frank Sottile (Texas A&M Univ.) and also research expositories by many prominent speakers in the area.

News from Korea

ICM Preparatory Workshop

“ICM Preparatory Workshop” was held on July 9, 2012 at COEX, Seoul in which Korean LOC members reported the status of various activities to examine ongoing preparations and to get feedback.

Special invitees include Professor Ingrid Daubechies, President of the International Mathematical Union (IMU) and Chairs of 4 preceding ICMs’ who are Professor Martin Grötschel from Germany, Professor Zhi-Ming Ma from China, Professor Manuel de Leon from Spain and Professor M S Raghunathan from India.

For the beginning of the workshop, Professor Hyungju Park, Chairman of the Organising Committee of Seoul ICM 2014 delivered opening remarks and Professor Dong-Yup Suh, President of the Korean Mathematical Society delivered the welcome remarks.



The President of IMU Visits Korea

Professor Ingrid Daubechies, President of the Interna-tional Mathematical Union (IMU) visited Korea in July 2012 on an invitation from the Organising Committee of Seoul ICM 2014.

The Organising Committee of Seoul ICM 2014 held a “ICM Preparatory Workshop” on July 9 in which Professor Daubechies shared her observations and expectations as a host of the Congress and LOC members had opportunities to examine ongoing preparations and status of various activities and to get feedback.

As a sign of solidarity, Professor Daubechies also attended the 12th International Congress on Math-ematical Education (ICME-12) Opening Ceremony and ICME-12 related events.

• July 8: Lecture on “Art and Mathematics” for Korean high school mathematics teachers, Interview with Dong-A Daily News and the JoongAng Ilbo

• July 9: ICME-12 Opening Ceremony, ICM Prepara-tory Workshop, ICM Welcome Reception

• July 10: Visit Minister of Education, Science and Technology, Open KIAS Symposium

• July 11: Inspect IMU General Assembly venue, Visit UNESCO Cultural Heritage sites in the city of Gyeongju

• July 12: Visit Chairman of the Education, Science and Technology Committee, Visit Mayor of Seoul

• July 13: WISET Roundtable

Korea Ranks the 1st in the 53rd IMO

Korea ranks the 1st in the 53rd International Math-ematical Olympiad (IMO), with 6 gold medals scoring total of 209 points, which is the best record ever since Korea participated IMO in 1988. The IMO is the world championship mathematics competition for high school students and is held annually in a different

For the main program, there was a very special time to hear the experiences from Chairs of 4 preceding ICMs’ under the title of “Organising an ICM, Fun Moments and Pitfalls”. Chairs of 4 preceding ICMs’ advised ICM LOC what should be considered before the Congress, during the Congress, and after the Congress to hold a successful event.

After then, subcommittee Chairs of Seoul ICM 2014 reported on the subjects of travel assistance program to invite 1000 mathematicians from developing countries and the status of preparations for the 17th General Assembly of IMU.

It was followed by a presentation on overview of status of preparations for Seoul ICM 2014 from Professor Hyungju Park, Chairman of the Organising Committee of Seoul ICM 2014. And, on the discussion, they got feedback, suggestions, and thoughts from 4 Chairs of past ICMs.

For the closing of the workshop, Professor Ingrid Daubechies, President of IMU, gave a speech, and the ICM Reception was followed at the Oakwood premier Coex centre.

Chairs of 4 Preceding ICMs’ Visit Korea

Chairs of 4 preceding ICMs’ who are Professor Martin Grötschel from Germany, Professor Zhi-Ming Ma from China, Professor Manuel de Leon from Spain and Professor M S Raghunathan from India visited Korea in July 2012 on an invitation from the Organising Committee of Seoul ICM 2014.

The Organising Committee of Seoul ICM 2014 held a “ICM Preparatory Workshop” on July 9 in which Chairs of 4 preceding ICMs’ shared their precious experiences from past ICMs.

As a sign of solidarity, Chairs of 4 preceding ICMs’ also attended the 12th International Congress on Math-ematical Education (ICME-12) Opening Ceremony and ICME-12 related events.

• July 9: ICME-12 Opening Ceremony, ICM Prepara-tory Workshop, ICM Welcome Reception

• July 10: Visit Minister of Education, Science and Technology, Open KIAS Symposium

• July 11: Inspect IMU General Assembly venue, Visit UNESCO Cultural Heritage sites in the city of Gyeongju



country. This year, IMO was held in Mar del Plata, Argentina during July 4–16, with 548 participants from 100 countries.

News from New Zealand

Les Woods Memorial Lecture

On the evening of May 1, Professor Emeritus John Ockendon, University of Oxford, delivered the third annual Les Woods M e m o r i a l L e c t u r e , entit led Mathematics under the Bonnet. This was held in the Engineering Building of the University

of Auckland. In this lecture John captured the spirit of his deceased (in 2007) colleague Professor Les Woods, covering gems from many years of novel applications of mathematics. Les Woods was arguably one of New Zealand’s best real-world applied mathematicians, and was regarded highly for his work in the theory of plasmas. The latter led to some controversy concerning the obtaining of energy from plasmas.

The lecture series has been a joint venture between the University of Auckland (the Departments of Mathematics, Statistics, and Engineering Science) and Massey University Auckland (the Institute of Information and Mathematical Sciences) since it was launched in late 2009. Previous speakers have been: Professor Gil Strang of MIT (2010) and Professor Peter Hunter of UoA (2011).

(By Graeme Wake, Massey University at Albany, New Zealand)Reproduced from New Zealand Mathematical Society, 115, August 2012

Professor Les Woods

Professor John Ockendon

News from Pakistan

13th International Pure Mathematics Conference

ISLAMABAD – Deputy Prime Minister Chaudhry Pervaiz Elahi and Federal Minister for Ministry of Education & Training has inaugurated the 13th Inter-national Pure Mathematics Conference (13th IPMC 2012) on algebra, geometry, analysis, and mechanics on September 1.

The 13th IPMC 2012 (September 1–3, 2012) was organised by Quaid-i-Azam University and Preston University in collaboration with Higher Education Commission (HEC), Pakistan Science Foundation (PSF) and Pakistan Mathematical Society.

The IPMC series, held annually since the year 2000, was the brainchild of Professor Dr Qaiser Mushtaq, Dean Faculty of Natural Sciences (QAU) who founded the Pakistan Mathematical Society. The rationale behind this annual activity was to provide impetus to the math-ematicians to do research in all areas of mathematics, research being a global activity and conferences are important in helping mathematicians to keep abreast with the latest research trends.

The conference deliberations were split into two parallel sessions consisting of 9 keynote lectures and 62 short communications. Over 90 well known mathematicians from 26 countries, including the US, China, India, Japan, South Korea, Italy, Iran and Uzbekistan, attended this conference.

Keynote speakers were Professor Steven Bleiler from Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, USA, Dr Sobirov Abdujalil from Tajikistan, Professor Wenbin Guo from China, Dr Sherali Kosimov from Tajikistan, Professor Fang Li from China, Professor Alexander

Participants of 13th IPMC 2012



Makin from Russia, Professor Sant Sharan Mishra and Professor Chayan Kumar from India, Professor Mohammad Reza R Moghaddam from Iran.

On the first day, Federal Minister for Education and Training Sheikh Waqas Akram announced 5 million rupee on behalf of Deputy Prime Minister Parvez Elahi for Pakistan Mathematical Society to promote Mathematics.

News from Singapore

Singapore Mathematical Society (SMS) Activities

(a) The annual SMS Mathematics Project Festival for schools was held in February and March 2012.

(b) Teo Yik Ying (NUS) gave an invited lecture in the SMS Lecture Series on “The foundational role of statistics in the future of medicine” on March 7, 2012.

(c) The Association of Mathematical Educators (AME) and SMS held a one-day joint AME–SMS Confer-ence on May 30, 2012 on “Nurturing reflective learners”. Keynote lectures were given by Frank Voon (NUS), John Mason (Open University and Oxford University), Berinderjeet Kaur (National Institute of Education), Anne Watson (Oxford University), Yeap Ban Bar (Marshall Cavendish Institute and Pathlight School).

(d) SMS held its annual Singapore Mathematics Olym-piad in June 2012 for primary, secondary and high schools at 3 levels of competition (Open, Senior and Junior).

(e) The Singapore national team to the 53rd Inter-national Mathematical Olympiad held in Mar del Plata, Argentina on July 10–11, 2012 bagged one gold, 3 silvers and 2 bronzes and team member Lim Jeck (National University of Singapore High School of Mathematics and Science) was ranked first.

(f) The 3rd Singapore Mathematics Symposium organ-ised by SMS was held on September 28, 2012 at the Department of Mathematics, NUS with invited talks by Shen Zuowei (NUS), Xing Chaoping (NTU), Dmitrii Pasechnik (NTU) and Zhu Chengbo (NUS). A poster exhibition and competition for graduate students was also held.

News from Taiwan

Sun-Yung Alice Chang, Ker-Chau Li and Jing Yu Elected Academicians of Academia Sinica

Academia Sinica held its biennial Convocation of Academicians from July 2 to July 5, 2012, culminating in the announcement of the 2012 list of Academicians on July 5, 2012. This year, a total of 20 new Academicians and one Honorary Academician were elected. Among those elected were Professors Sun-Yung Alice Chang, Ker-Chau Li and Jing Yu.

Professor Chang is the Eugene Higgins Professor of Mathematics at Princeton University. She was awarded the Satter Prize by the American Mathematical Society in 1995 and a Guggenheim Memorial Foundation Fellowship from 1999–2000. She has been a member of the American Academy of Arts and Sciences and a fellow of the National Academy of Sciences USA since 2008 and 2009, respectively.

Professor Li is a distinguished fellow at the Institute of Statistics of Academia Sinica. Professor Li was awarded a Guggenheim Fellowship in 1993 and the ICSA Distin-guished Award in 2010. Furthermore he was invited to give an IMS Medallion Lecture in 2003.Professor Yu is currently a distinguished professor at the Department of Mathematics of the National Taiwan University. He has served as the director of the NCTS from 2006–2009 and was a plenary speaker at the Inter-national Conference of Chinese Mathematicians in both 2001 and 2010. Among his many other honours are the 1994 Academic Award and the 2003 and 2009 National Chair Professorships by the Ministry of Education.

Yau High School Mathematics Awards

The Yau High School Mathematics Awards (YHMA) was established in 2008 to encourage high school students in the greater China area to participate in project-based competitions in mathematical sciences. 2012 is the fifth year of this competition. This year’s winner of the 2012 YHMA in Taiwan is Mr Su Tse-Kuan from the Affiliated High School of the National Taiwan Normal University. During the award ceremony held on August 11 at the National Taiwan University, Professor Shing-Tung Yau personally presented the gold medal to Mr Su for his project entitled “Circle Cut by a Zigzag line”, which he completed under the guidance of his teacher Mr Yun-Dong Hong.



The Taiwan Society for Industrial and Applied Mathematics Established

The Taiwan Society for Industrial and Applied Mathematics (TWSIAM) was established in Taipei on June 26, 2012. The establishment of such a society was proposed twenty years ago by Professor Mei-Chang Shen, who was then a professor at the University of Wisconsin at Madison. Professor Shen has been enthusiastically promoting applied mathematics in Taiwan throughout the years. Although it was not established at that time, the seed for TWSIAM had been sown then. Twenty years later, after efforts of several local applied mathematicians, including Professors Ming-Chih Lai, Shu-Ming Chang, Sze-Bi Hsu, and many others, the society was finally established. There are 81 start-up members. The goals of TWSIAM are to build communication between the mathematics community and the industrial and scientific community, and to promote and popularise research in applied and industrial mathematics. The ceremony on June 26 was attended by Professor Jyh-Yang Wu, the President of National Chung Cheng University, and Professor Gerard Jennhua Chang, the President of the Mathematical Society of the Republic of China. The current president and vice president of TWSIAM are respectively Professors I-Liang Chern and Tony Wen-Han Sheu. The main office of the society is located at the National Chiao Tung University in Hsinchu, Taiwan. Further information can be found at http://www.twsiam.org.

News from Vietnam

VMS–SMF Joint Congress

The VMS–SMF Joint Congress took place from August 20–24, 2012 at Hue University, Hue City.

This was the first international joint congress between Vietnam Mathematical Society (VMS) and a foreign Mathematical Society (French Mathematical Society — SMF). The important event attracted about 90 French mathematicians, 350 Vietnamese mathematicians and 20 mathematicians from others countries (two of them awarded Fields Medal).

The congress was held in order to strengthen and promote the cooperation in mathematical research between France and Vietnam, as well as between Vietnam and other countries. The most remarkable

The first plenary talk was given by Professor Yoccoz — 1994 Fields Medalist

Professor Lionel Schwartz (representing SMF) giving his welcoming speech at the Opening Ceremony

Professor Le Tuan Hoa — Chairman of VMS giving the opening speech

event in the cooperation was the work awarded Fields Medal in 2010 of Professor Ngo Bao Chau.

Prestigious mathematicians attended the congress include: Jean Christophe Yoccoz (Collége de France, Paris; Fields Medalist in 1994), Ngo Bao Chau (Mich-igan, USA; Fields Medalist in 2010), B Gross (Harvard, USA), Hélène Esnault (University of Duisburg-Essen), Vu Ha Van (Yale, USA), and Pierre Cartier (IHÉS, Paris).



There were 13 plenary talks and one public lecture given by the leading mathematicians in the fields.

Besides the plenary talks and public lecture, partici-pants at the congress were divided into 15 parallel sessions to discuss. There were more than 150 reports in parallel sessions during 5 days.

Mathematician Vu Ha Van Receives Fulkerson Prize

Professor Vu Ha Van of Yale University, who is also a member of the Scientific Council of Vietnam Institute for Advanced Study in Mathematics, has been awarded the prestigious Fulkerson Prize 2012 for his work determining the threshold of edge density above which a random graph can be covered by disjoint copies of any given smaller graph.

Professor Vu Ha Van and his two collaborators Swede Anders Johansson and American Jeff Kahn, were named the winners of the Fulkerson Prize by the Mathematical Optimisation Society and the American Mathematical Society at the 21st International Sympo-sium on Mathematical Programming, held in Berlin, Germany during August 19–24, 2012.

The Fulkerson Prize was established in 1979 to honour outstanding papers in the area of discrete mathematics. Up to three awards of US$1500 each are presented every three years. The prize is sponsored by the Mathematical Programming Society and the American Mathematical Society.

The winning paper of Van and coworkers “Factors in random graphs” was published in the journal Random Structures and Algorithms, issue No. 33 in 2008.

Van, 42, was a gifted mathematics student in Vietnam before attending university in Hungary and receiving his PhD from Yale University in the US. He has worked in many research institutes in the US including IAS and Microsoft Research, as well as at Rutger and Santiago universities.

Van, who is currently in Vietnam to attend a math-ematical symposium in Hue City, also received the George Polya award, presented by the US Society for Industrial and Applied Mathematics (SIAM), in 2008.

Activities of VIASM

• VIASM Annual Meeting 2012

VIASM Annual Meeting 2012 took place at VIASM Lecture Hall, 7th floor Ta Quang Buu Library, Hanoi University of Science and Technology during August 25–26, 2012.

Annual Meeting is an official event of VIASM which is held every year.

VIASM is inviting prestigious mathematicians from all over the world to come to the meeting to give the lectures on some of the focus research in contemporary mathematics.

The lecturers for this year are:• Dinh Tien Cuong (Paris 6): Automorphism groups of

compact Kaehler manifolds• Jean-Pierre Demailly (Grenoble): Hyperbolic alge-

braic varieties and holomorphic differential equations• Hélène Esnault (Duisburg-Essen): Finiteness and

companions, after P. Deligne and V. Drinfeld• Benedict Gross (Harvard): On the arithmetic of

hyperelliptic curves• Lionel Schwartz (Paris 13): Realising unstable modules

as the cohomology of spaces, a survey

Professor Dinh Tien Cuong giving his lecture

Professor Benedict Gross in his lecture on arithmetic of hyper-elliptic curves

Vu Ha Van



Students at summer school

Professor John Lafferty and Professor Ho Tu Bao in a discussion

Participants at the annual meeting can find here some related issues to their studies and research. Young mathematicians and students studying mathematics can find out from the lectures the preferable directions of study as well.

Mathematicians at the meeting also discussed and planned for the next annual meeting in terms of fields of studies, visiting guests and lecturers.

More about the event, visit: http://viasm.edu.vn/?p=7014&lang=en

• Seminars on Modern Statistical Methods in Machine Learning

The seminar series on modern statistical methods in machine learning took place from June 18 to August 18. The seminars were split in three parts which were hosted by Professor Ho Tu Bao (JAIST, Tokyo), Professor Nguyen Xuan Long (Michigan, US) and Professor John Lafferty (Chicago, US) who have done excellent work on contemporary machine learning.

The seminars covered most of the popular issues in machine learning such as statistical and graphical models, fully sparse topic models, regression, and Nonparametric Methods, etc. The seminars attracted more than 100 academic participants (mostly from computer science field). More than 60 researchers were regular participants at VIASM for that.

Lectures by Professor Ho Tu Bao include Machine Learning: What It Can Do, Recent Directions and Some Challenges, Model Assessment and Selection in Multiple and Multivariate Regression, Kernel Methods and Support Vector Machines, Dimensionality Reduc-tion and Manifold Learning, Graphical Models and Topic Modelling, and Fully Sparse Topic Models.

Lectures by Professor John Lafferty are Regression, Structure and Sparsity, and Nonparametric Methods.For more about the lectures, please visit: http://viasm.edu.vn/?page_id=6763&lang=en

• Summer School on Some Basic Theorems in Analytic Number Theory

About 20 excellent Vietnamese students studying mathematics from all across Vietnam and from the US, Canada and South Korea attended the summer school on analytic number theory, taught by Professor Ngo Bao Chau. The course equipped students with some basic theorems in analytic number theory based on a book written by Komaravolu S Chandrasekharan, a 92-year-old Indian professor emeritus at the Swiss Federal Institute of Technology Zurich.

The school took place in two months (July and August 2012) at VIASM. The methodology of studying was that Professor Ngô Bảo Châu gave lectures and guidelines, and students helped each other to study.

Lectures at the school were noted and collected by the students, after that they are printed so that many other students could take the printout as a reference for their studies.




Conferences in Asia Pacific Region

OCTOBER 2012

1 – 4 Oct 2012 The 13th Conference of the New Zealand Association of Mathematics TeachersWellington, New Zealandhttp://www.nzamt.org.nz/

1 Oct 2012 – 30 Apr 2013Semester on Curves, Codes, CryptographyIstanbul, Turkeyhttp://sccc.sabanciuiv.edu.tr

2 – 5 Oct 2012Australian Computers in Education ConferencePerth, Australiahttp://acec2012.acce.edu.au/news/see-you-perth-acec2012

2 – 5 Oct 2012International Symposium on Communications and Information Technologies (ISCIT2012)Gold Coast, Australiahttp://www.iscit2012.org/

3 – 6 Oct 2012International Conference on Applied andComputational Mathematics (ICACM)Ankara, Turkeyhttp://www.iam.metu.edu.tr/icacm

3 – 5 Oct 20123rd International Conference on Computational Systems-Biology and BioinformaticsBangkok, Thailand http://www.csbio.org/

3 – 5 Oct 2012International Neural Network Society Winter Conference 2012 (INNS-WC2012) Bangkok, Thailandhttp://inns.sit.kmutt.ac.th/wc2012/

3 – 6 Oct 2012International Conference on Applied and Computational Mathematics (ICACM) Ankara, Turkeyhttp://www.iam.metu.edu.tr/icacm/

5 – 6 Oct 2012Fall Meeting of Korean Mathematical SocietyDaejeon, Koreahttp://www.kms.or.kr/meetings/fall2012

5 – 7 Oct 20124th International Conference on Graphic and Image Processing (ICGIP2012)Singaporehttp://www.icgip.org/index.htm

6 – 7 Oct 2012International Conference on Future Trends in Computing and Communication (FTCC)Bangkok, Thailandhttp://theired.org/ftcc/

6 – 8 Oct 20122nd International Conference on Communication, Computing and SecurityRourkela, Indiahttp://www.icccs.co.in/

9 – 11 Oct 2012Algerian-Turkish International days on Mathematics 2012 (ATIM2012)Annaba, Algeriahttp://www.univ-annaba.org/ATIM2012/

10 – 12 Oct 2012International Conference on Geometry, Number Theory and RepresentationTheoryIncheon, Koreahttp://www.numbertheory.org/jpgs/conference_poster.jpg

11 – 13 Oct 2012Managing Under Uncertainty: Paradigms for Developed and Emerging Economies(JAMC 2012)Noida, Indiahttp://jaipuria.ac.in/noida/conference-detail.aspx?pageid=87&cid=3

11 – 13 Oct 20128th International Symposium of Statistics (IGS2012)Eskisehir, Turkeyhttp://igs2012.anadolu.edu.tr/index.php?lang=en

11 – 13 Oct 20128th International Symposium ofStatistics (IGS2012)Eskisehir, Turkeyhttp://igs2012.anadolu.edu.tr/index.php?lang=en

12 – 13 Oct 20121st Workshop on Complex Dynamical Systems and Their Applications (CDS2012)Ankara, Turkeyhttp://www.kds2012.etu.edu.tr

12 – 14 Oct 2012Istanbul Workshop on Teichmüller TheoryIstanbul, Turkeyhttp://math.gsu.edu.tr/2012iwtt.html

13 – 14 Oct 20122nd International Conference on Intelligent Computational Systems (ICS2012)Bali, Indonesiahttp://psrcentre.org/listing.php?subcid=135 &mode=detail

13 – 15 Oct 20121st International Conference on Numerical Physics (ICNP1)Oran, Algeriahttp://sites.google.com/site/icnp1ustomb/

14 – 17 Oct 2012The 2012 IEEE International Conference on Systems, Man, and Cybernetics (IEEESMC2012)Seoul, Koreahttp://www.smc2012.org/

14 – 18 Oct 2012Conference on Computational Physics 2012 (CCP2012)Kobe, Japanhttp://www.ile.osaka-u.ac.jp/CCP2012/index.html

14 – 18 Oct 2012Horizons of Quantum Physics: From Foundations to Quantum-Enabled TechnologiesTaipei, Taiwanhttp://www.quantumhorizons.org/

14 – 28 Oct 2012FEM on The Foundation of Functional Analysis (FFFA)Varanasi, Indiahttp://www.bdu.ac.in/ncfade

15 – 19 Oct 2012Multiscale Materials Modeling 2012Conference (MMM)Singaporehttp://www.mrs.org.sg/mmm2012/

15 – 19 Oct 2012HEPiX Fall 2012 WorkshopBeijing, Chinahttp://indico.cern.ch/conferenceDisplay.py?ovw=True&confId=199025

15 – 19 Oct 2012IGA/AMSI Workshop on Geometry of SupermanifoldsAdelaide, Australiahttp://www.austms.org.au/Conferences

16 – 17 Oct 20122nd Cloud Computing World Forum IndiaMumbai, Indiahttp://www.cloudcomputinglive.com/india/

16 – 18 Oct 20125th International Congress on Image and Signal Processing (CISP2012)Chongqing, Chinahttp://cisp-bmei.cqupt.edu.cn/

18 – 20 Oct 2012Carthage Meeting on StatisticsHammamet, Tunisiarcs2012.atistat.com/

Conference CALENDAR


18 – 20 Oct 2012IEEE 5th International Conference on Advanced Computational Intelligence (ICACI2012)Nanjing, Chinahttp://www.iwaci.org/

18 – 21 Oct 20121st International Conference on Analysis and Applied Mathematics (ICAAM2012)Gumushane, Turkeyhttp://icaam2012.gumushane.edu.tr 18 – 21 Oct 20125th International Workshop on Chaos-Fractals Theories and Applications (IWCFTA2012)Dalian, Chinahttp://www.chaos-fractal.cn/

19 – 21 Oct 2012International Conference on Computational Problem-Solving (ICCP2012)Leshan, Chinahttp://www.ic-cp.org/2012

20 – 21 Oct 2012The 1st International Conference on Parallel, Distributed Computing and Applications (IPDCA2012)Jakarta, Indonesiahttp://airccse.org/ipdca/index.html

20 – 22 Oct 2012Integrable Systems and Geometric PDEsTaipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=141

20 – 23 Oct 2012 The 27th Annual Meeting of the Ramanujan Mathematical SocietyUttar Pradesh, Indiahttp://www.ramanujanmathsociety.org/

21 – 24 Oct 20123rd International Conference on Networking and Distributed Computing (ICNDC2012) Hangzhou, Chinahttp://www.inetdc.org/meeting/icndc2012/

21 – 25 Oct 201211th International Conference on Signal Processing (ICSP2012)Beijing, Chinahttp://icsp.bjtu.edu.cn/

21 – 26 Oct 2012International Conference on Inverse Problems and Related Topics 2012 (ICIP2012)Nanjing, Chinahttp://math.seu.edu.cn/ICIP2012/

22 – 23 Oct 20123rd Annual International Conference on Advanced Topics in Artificial Intelligence (ATAI 2012)Singaporehttp://www.aiconf.org/

23 – 25 Oct 2012 Fundamental Technologies of the Next-Generation Computational Science Kyoto, Japanhttp://www.kurims.kyoto-u.ac.jp/~kyodo/workshop-en.html

24 – 26 Oct 2012International Conference onApplied Mathematics and Computer Sciences (ICAMCS 2012)Bali, Indonesiahttp://www.waset.org/conferences/2012/bali/icamcs/

24 – 26 Oct 2012International Conference on Applied Mathematics, Mechanics and Physics (ICAMMP 2012 )Bali, Indonesiahttp://www.waset.org/conferences/2012/bali/icammp/

24 – 26 Oct 2012International Conference in Number Theoryand Applications 2012 (ICNA 2012)Bangkok, Thailandhttp://www.maths.sci.ku.ac.th/icna2012/

26 – 28 Oct 201210th Asian Symposium on Computer MathematicsBeijing, Chinahttp://www.mmrc.iss.ac.cn/ascm/ascm2012/

28 – 29 Oct 20125th International Symposium on Computational Intelligence and Design (ISCID2012)Hangzhou, Chinahttp://iukm.zju.edu.cn/iscid/

29 Oct – 2 Nov 20122012 International Conference on Nonlinear Analysis: Evolutionary PDE and Kinetic TheoryTaipei, Taiwanhttp://www.math.sinica.edu.tw/www/file_upload/conference/201210PDE/home.jsp

29 Oct – 3 Nov 2012Workshop on Mathematical FinanceGuwahati, Indiahttp://math.iisc.ernet.in/~imi/MFWS.php

NOVEMBER 2012

1 – 2 Nov 2012International Conference on Speech, Image, Biomedical and Information Processing 2012 (SIBIP 2012)Chandigarh, Indiahttp://sibip2012.chitkara.edu.in/

1 Nov – 23 Dec 2012Optimization: Computation, Theory and ModelingSingaporehttp://ims.nus.edu.sg/Programs/012opti/index.php

4 – 7 Nov 20127th International Conference on Science, Mathematics and Technology EducationMuscat, Omanhttp://smec.curtin.edu.au/index2.cfm

5 – 6 Nov 2012International Conference on Complex Systems (ICCS12)Agadir, Moroccohttp://iccs12.org/

7 – 8 Nov 2012The 2nd International Conference on Computational Mechanics and Design Engineering (ICCMDE2012)Shanghai, Chinahttp://www.iccmde.org/

7 – 9 Nov 2012International Conference on Advancement in Science and Technology 2012 “Contemporary Math, Mathematical Physics and Applications” (ICAST2012)Kuantan, Malaysiahttp://iium.edu.my/icast/2012/

7 – 9 Nov 2012Joint IAPR International Workshops on Structural and Syntactic Pattern Recognition (SSPR 2012) and Statistical Techniques in Pattern Recognition(SPR 2012)Sendai, Japanhttp://www.icpr2012.org/

8 Nov 2012Cahit Arf Lecture 2012 by David E. Nadler titled Traces and LoopsAnkara, Turkeyhttp://www.matematikvakfi.org.tr/en/arf-lectures

9 – 11 Nov 20122012 Image Analysis and Signal Processing International Conference (IASP2012)Hangzhou, Chinahttp://iasp2012.zjicm.edu.cn/

9 – 11 Nov 20125th International Congress on Image and Signal Processing (CISP2012)Chongqing, Chinahttp://cisp-bmei.cqupt.edu.cn

9 – 12 Nov 2012Cultures of Mathematics and LogicGuangzhou, Chinahttp://www.math.uni-hamburg.de/home/loewe/Guangzhou2012/

11 – 15 Nov 201221st International Conference on Pattern Recognition (ICPR 2012 )Tsukuba, Japanhttp://www.icpr2012.org

Conference CALENDAR


12 – 15 Nov 2012Modeling and Computation in Musculoskeletal Engineering (MCME)Brisbane, Australiahttp://www.amsi.org.au/events/archived-events/911-modeling-and-computation-in-musculoskeletal-engineering/

12 – 15 Nov 20122012 Haifa Matrix Theory ConferenceHaifa, Israelhttp://www.math.technion.ac.il/cms/decade_2011-2020/year_2012-2013/matrix/

12 – 16 Nov 2012 Mal’tsev MeetingNovosibirsk, Russiahttp://www.math.nsc.ru/conference/malmeet/12/index.html

12 Nov 2012 – 03 Mar 2013A Fixed Point Theorem for Meir-Keeler Contractions and Its Applications to Integral Equations in Ordered Modular Function SpacesSemnan, Iranhttp://Semnan.ac.ir

15 – 17 Nov 20124th International Conference for Young Mathematicians on Differential Equations and Applications Dedicated to Ya. B. LopatinskiiDonetsk, Ukrainehttp://www.math.donnu.edu.ua/conference/?lang=en

17 – 18 Nov 20122nd International Workshop on Computer Science for Environmental Engineering and EcoInformatics 2012Hong Kong, Chinahttp://www.iasht.org/cseee

17 – 18 Nov 2012 2012 International Conference on Intelligent Control, Optimization and System (ICICOS)Shanghai, Chinahttp://conference.researchbib.com/?eventid=16704

19 – 21 Nov 2011International Conferences on Mathematics, Statistics and Its ApplicationsBali, Indonesiahttp://icmsa2012.org/home.php

19 – 24 Nov 2012 Canberra Symposium on Regularisation – Integrating the Chemnitz Symposium on Inverse Problems on TourCanberra, Australia http://math-old.au/events/regularisation12/index.html

20 – 24 Nov 2012The 6th International Conference on Soft Computing and Intelligent Systems, The 13th International Symposium on Advanced Intelligent Systems (SCIS-ISIS 2012)Kobe, Japanhttp://scis2012.j-soft.org/?file=home

21 – 24 Nov 2012International Conference on History and Development of Mathematical Sciences (ICHDMS2012)Rohtak, Indiahttp://www.mdurohtak.ac.in/international_conference/

22 – 23 Nov 2012The 3rd International Conference on Recent Trends in Information Processing and Computing (IPC 2012)Kuala Lumpur, Malaysiahttp://ipc.theides.org/2012/

23 – 24 Nov 20122012 Korean Society for Industrial and Applied Mathematics (KSIAM) Annual MeetingDaegu, Koreahttp://www.ksiam.or.kr

23 – 25 Nov 2012Workshop on the Effective use of Visualization in the Mathematical Sciences (EviMS)Newcastle, Australiahttp://cama.newcastle.edu.au/meetings/evims/

24 – 25 Nov 20122012 International Conference on Networks and InformationBangkok, Thailandhttp://www.icni.org/

24 – 26 Nov 2012Workshop of Quantum Dynamics and Quantum Walks (QDQW)Okazaki, Japanhttp://qm.ims.ac.jp/qdqw/

24 – 27 Nov 2012 2nd International Science, Technology, Engineering and Mathematics (STEM) in Education ConferenceBeijing, Chinahttp://stem2012.bnu.edu.cn/index.html

24 – 29 Nov 2012International Conference “Arithmetic as Geometry: Parshin Fest”Moscow, Russiahttp://www.mathnet.ru/php/conference.phtml?confid=325&option_lang=eng

25 – 27 Nov 20124th International Conference onComputational Methods (ICCM2012)Gold Coast, Australiahttp://www.iccm-2012.org/

26 – 29 Nov 2012The 19th International Conference on Neural Information Processing(ICONIP2012)Doha, Qatarhttp://www.iconip2012.org

26 – 29 Nov 2012 2012 International Conference on Control, Automation and Information Sciences (ICCAIS)Ho Chi Minh City, Vietnamhttp://www.iccais2012.irobotics.ac.vn/

27 – 28 Nov 2012International Conference on Computer Science and Network Security(ICCSNS2012) Penang, Malaysiahttp://psrcentre.org/listing.php?subcid=147 &mode=detail

27 – 28 Nov 2012International Conference on Geography, Mathematics and Economics (ICGME2012)Penang, Malaysiahttp://psrcentre.org/listing.php?subcid=152 &mode=detail

28 – 30 Nov 20124th International Conference on Computational Collective Intelligence: Technologies and Applications (ICCCI2012)Ho Chi Minh City, Vietnamhttp://iccci.pwr.wroc.pl/iccci2012

28 – 30 Nov 2012The 15th Annual International Conference on Information Security and CryptologySeoul, South Koreahttp://www.icisc.org/

28 Nov – 1 Dec 2012The 8th China International Conference on Information Security and Cryptology (Inscrypt’2012) Beijing, Chinahttp://www.inscrypt.cn/2012/inscrypt2012cfp.html

29 – 30 Nov 2012NZSA 2012 ConferenceDunedin, New Zealandhttp://www.maths.otago.ac.nz/nzsa2012/

29 – 30 Nov 2012 International Conference on Mathematical Sciences and Computer EngineeringKuala Lumpur, Malaysiahttp://www.icmsce.net/cms/

29 Nov – 1 Dec 20123rd International Conference on Emerging Applications of Information Technology (EAIT2012)Kolkata, Indiahttp://sites.google.com/site/csieait2012

29 Nov – 2 Dec 2012International School on Quantum and Nano Computing Systems and Applications (QANSAS2012)Agra, Indiahttp://www.dei.ac.in/ConferenceWeb/qansas2012/index.html

DECEMBER 2012

1 – 2 Dec 20123rd International Conference on Theoretical and Mathematical Foundations of Computer Science (ICTMF2012)Bali, Indonesiahttp://www.ictmf-conf.org/

Conference CALENDAR Conference CALENDAR


1 – 5 Dec 2012The 2nd Cross-Straight Workshop in AlgebraTainan, Taiwanhttp://www.ncts.ncku.edu.tw/math/workshop/121201/transportation.html

1 – 31 Dec 201224th International Conference on Computational Linguistics (COLING 2012 )Mumbai, Indiahttp://www.coling2012-iitb.org

2 – 5 Dec 2012Inaugural Meeting of the Australian and New Zealand Association of Mathematical Physics (ANZAMP)Lorne, Victoria, Australiahttp://www.anzamp.austms.org.au/meetings/2012/

2 – 6 Dec 2012Asiacrypt 2012Beijing, Chinahttp://cis.sjtu.edu.cn/asiacrypt2012/

2 – 7 Dec 20122012 BioInfoSummerAdelaide, Australiawww.amsi.org.au/BIS12.php

3 – 5 Dec 20122nd International Conference on Theory and Practice of Algorithms in (Computer) Systems (TAPAS2012)Ein Gedi, Israelhttp://tapasconference.org/2012/show/home

3 – 5 Dec 20128th International Conference on Computing and Convergence Technology (ICCCT, ICCIT, ICEI and ICACT2012)Seoul, Koreahttp://www.aicit.org/iccct

3 – 5 Dec 2012International Conference on Digital Image Computing: Techniques and Applications (DICTA2012)Fremantle, Australiahttp://dicta2012.aprs.org.au

3 – 6 Dec 20122nd Biomarker Discovery Conference (BDC2012)Shoal Bay, Australiahttp://bdc.mtci.com.au/

3 – 6 Dec 2012IEEE 4th International Conference on Cloud Computing Technology and ScienceTaipei, Taiwanhttp://grid.chu.edu.tw/cloudcom2012/index.html

3 – 7 Dec 201218th Australasian Fluid Mechanics ConferenceLaunceston, Tasmania, Australiahttp://www.18afmc.com.au/

3 – 7 Dec 2012Asia-Pacific Conference and Workshop in Quantum Information SciencePutrajaya, Malaysiahttp://einspem.upm.edu.my/6APCWQIS/website.php

3 – 7 Dec 2012Trilateral (Australia-Italy-Taiwan) Meeting on Nonlinear Partial Differential Equations and ApplicationsWollongong, Australiahttp://www.uow.edu.au/informatics/maths/trilateral/index.html/

3 – 16 Dec 2012 ICTS Program: Groups, Geometry and DynamicsUttarakhand, Indiahttp://www.icts.res.in/program/details/318/

3 – 20 Dec 2012ICTS Program: Winter School on Stochastic Analysis and Control of Fluid FlowThiruvananthapuram, Indiahttp://www.icts.res.in/program/details/322/

4 – 6 Dec 2012 New Zealand Mathematical Society Colloquium Palmerston North, New Zealand http://nzmathsoc.org.nz/colloquium/home.php

4 – 7 Dec 2012Australasian Applied Statistics ConferenceQueenstown, New Zealandhttp://aasc2012.com/

6 – 7 Dec 20122nd International Conference on Mechatronics and Applied Mechanics (ICMAM2012)Hong Kong, Chinahttp://www.ttp-icmam.org/

6 – 7 Dec 2012International Conference on Mathematical, Computational and Statistical Sciences, and Engineering (ICMCSSE2012)Perth, Australiahttp://www.waset.org/conferences/2012/perth/icmcsse/

6 – 7 Dec 2012International Conference on Computational Mathematics, Statistics and Data Engineering Penang, Malaysiahttp://www.waset.org/conferences/2012/penang/iccmsde/

6 – 8 Dec 2012 Thailand – Japan Joint Conference on Computational Geometry and Graphs (TJJCCGG 2012)Bangkok, Thailandhttp://www.tjjccgg2012.com/index.htm

7 – 8 Dec 2012International Conference on Data Analysis and Learning SymbolicGreater Noida, Indiahttp://www.gbu.ac.in/SOM/SOM_InternationalConferenceDataAnalysis_8Sept12.pdf

7 – 9 Dec 20122012 Annual Meeting of the Mathematics Society of the Republic of ChinaHsinchu, Taiwanhttp://www.taiwanmathsoc.org.tw/

7 – 9 Dec 2012International Conference on Frontiers of Mathematical Sciences with Applications (ICFMSA2012)Kolkata, Indiahttp://www.calmathsoc.org/downloads/ICFMSA-2012.pdf

7 – 9 Dec 2012Taipei Density Matrix Renormalization Group Winter School (DMRG101)Taipei, Taiwanhttp://web.phys.ntu.edu.tw/dmrg101

8 – 9 Dec 2012International Conference on Frontiers of Mathematical Sciences with Applications (ICFMSA2012)Kolkata, Indiahttp://www.calmathsoc.org/downloads/ICFMSA-2012.pdf

8 – 9 Dec 2012International Conference on Advanced Computational Technologies (ICACT2012)Pattaya, Thailandhttp://psrcentre.org/listing.php?subcid=156 &mode=detail

8 – 15 Dec 201224th International Conference on Computational Linguistics (COLING2012)Mumbai, Indiahttp://www.coling2012-iitb.org/

9 – 12 Dec 2012Indocrypt 2012Kolkata, Indiahttp://www.isical.ac.in/~indocrypt/

9 – 12 Dec 2012Reservoir Characterisation, Simulation and ModellingAbu Dhabi, United Arab Emirateshttp://www.reservoirme.com

10 – 11 Dec 201246th Annual ORSNZ ConferenceWellington, New Zealandhttps://secure.orsnz.org.nz/conf46/

10 – 13 Dec 2012Regional Annual Fundamental Science Symposium 2012Johor Bahru, Malaysiahttp://www.ibnusina.utm.my/rafss2012

10 – 14 Dec 201236th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (36ACCMCC)Sydney, Australiahttp://conferences.science.unsw.edu.au/36accmcc/

10 – 14 Dec 2012 International Conference on Advances on Fractals and Related TopicsHong Kong, Chinahttp://www.math.cuhk.edu.hk/conference/afrt2012/index.html

Conference CALENDAR


10 – 21 Dec 2012VI-MSS Event: Winter School and Conference on Computational Aspects of Neural EngineeringBangalore, Indiahttp://icerm.brown.edu/vi-mss

12 – 13 Dec 2012International Conference on Computer Science and Data Mining (ICCSDM12)Batam, Indonesiahttp://www.isaet.org/listing.php?subcid=204 &mode=detail#204

12 – 14 Dec 201218th IEEE International Conference on Networks (ICON2012)Singaporehttp://www.ieee-icon.org/2012/

12 – 14 Dec 2012Baum FestCanberra, Australiahttp://www.amsi.org.au/events/archived-events/935-baum-fest

12 – 14 Dec 2012Istanbul Workshop on Teichmüller TheoryIstanbul, Turkeyhttp://math.gsu.edu.tr/2012iwtt.html

12 – 14 Dec 2012The 23rd International Conference on Genome Informatics Workshop (GIW2012)Tainan, Taiwanhttp://conf.ncku.edu.tw/giw2012/

13 – 15 Dec 2012International Conference on Signal and Image Processing (ICSIP2012)Coimbatore, Indiahttp://www.icsip2012.org/

14 – 16 Dec 2012International Conference on Computational and Statistical Sciences (ICCSS2012)Istanbul, Turkeyhttp://www.waset.org/

14 – 16 Dec 2012International Conference on Mathematical and Computational Biology (ICMCB2012)Istanbul, Turkeyhttp://www.waset.org/

14 – 16 Dec 2012International Conference on Mathematical and Statistical Sciences (ICMSS2012)Istanbul, Turkeyhttp://www.waset.org/

15 – 16 Dec 2012 2nd International Conference on Mathematical Sciences and ApplicationsNew Delhi, Indiahttp://ijmsa.yolasite.com/upcoming-conferences.php

15 – 17 Dec 201221st International Conference on Interdisciplinary Mathematics, Statistics and Computational Techniques (IMSCT2012-FIMXXI)Chandigarh, Indiaimsct2012.puchd.ac.in/

15 – 19 Dec 2012Imaging Science: A Workshop in Honor of Stanley OsherBeijing, Chinahttp://msc.tsinghua.edu.cn/imaging2012/

16 – 19 Dec 2012The 9th International Conference on Simulated Evolution And Learning (SEAL 2012)Hanoi, Vietnamhttp://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=16916&copyownerid=23956

16 – 20 Dec 2012 2nd International Conference on Mathematical Sciences and ApplicationsNew Delhi, India http://atcm.mathandtech.org/

16 – 20 Dec 2012The 17th Asian Technology Conferencein MathematicsBangkok, Thailandhttp://atcm.mathandtech.org/

17 – 21 Dec 2012International Conference on “Analysis and Singularities” Dedicated to the 75th Birthday of Arnol’dMoscow, Russiahttp://www.mathnet.ru/php/conference.phtml?confid=352&option_lang=eng

17 – 21 Dec 2012Workshop on Algebraic Number TheoryWellington, New Zealandhttp://homepages.ecs.vuw.ac.nz/~bdkim/Workshop2012.htm

18 – 20 Dec 2012International Conference on Statistics and Informatics in Agricultural Research: 66th Annual Conference of Indian Society of Agricultural StatisticsNew Delhi, Indiahttp://www.isas.org.in/icsi2012/

19 – 20 Dec 2012National Conference on Frontiers in Analysis and Differential Equations (NCFADE)Tiruchirappalli, Indiahttp://www.bdu.ac.in/ncfade

20 – 23 Dec 20122013 ICSA International ConferenceHong Kong, Chinahttp://icsa.org/meetings/co-sponsorship/index.html

21 – 23 Dec 20126th International Conference of IMBIC on “Mathematical Sciences for Advancement of Science and Technology” (MSAST 2012)http://imbic.org/forthcoming.html

22 – 23 Dec 2012International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA)Bhubaneswar, Indiahttp://ficta.in

22 – 23 Dec 2012International Conference on Mathematical, Computational and Statistical Sciences, and Engineering (ICMCSSE2012)Bangkok, Thailandhttp://www.waset.org/conferences/2012/bangkok/icmcsse/

22 – 24 Dec 2012The International Congress on Science and TechnologyAllahabad, Indiahttp://sites.google.com/site/intcongressonsciandtech/

24 – 25 Dec 2012International Conference on Bioinformatics and Bioengineering (ICBB2012)Phuket, Thailandhttp://www.waset.org/conferences/2012/phuket/icbb/

24 – 25 Dec 2012International Conference on Bioinformatics, Computational Biology and Biomedical Engineering (ICBCBBE2012)Phuket, Thailandhttp://www.waset.org/conferences/2012/phuket/icbcbbe/

24 – 25 Dec 2012International Conference on Fluid Dynamics and Thermodynamics (ICFDT2012)Phuket, Thailandhttp://www.waset.org/conferences/2012/zurich/icfdt/

24 – 25 Dec 2012International Conference on Mathematical and Computational Biology (ICMCB2012)Phuket, Thailandhttp://www.internationaluniversity.me/conferences/2012/phuket/icmcb/

24 – 25 Dec 2011International Conference on Mathematical and Statistical Sciences (ICMSS2012)Phuket, Thailandhttp://www.waset.org/conferences/2012/phuket/icmss/

24 – 25 Dec 2012International Conference on Mathematical, Computational and Statistical Sciences, and Engineering (ICMCSSE2012)Phuket, Thailandhttp://www.waset.org/conferences/2012/phuket/icmcsse/

24 – 25 Dec 2012International Conference on Modeling and Simulation (ICMS 2012)Phuket, Thailandhttp://www.allconferences.com/conferences/ 2011/20110917042810



24 – 25 Dec 2012Young Statisticians Meet- An International ConferenceBurdwan, Indiahttp://www.buruniv.ac.in/Notices/UBUR_2012032_NOT_WEBPAGE.pdf

26 Dec 2012 – 1 Jan 2013 International Conference: Mathematical Science and Applications (ICMSA 2012)Abu Dhabi, United Arab Emirateshttp://www.adu.ac.ae/en/section/international-conference-mathematical-sciences-and-applications

27 – 29 Dec 20126th Conference of the Indian Subcontinent Decision Sciences InstituteHyderabad, Indiahttp://ibsindia.org/conference/ISDSI-IBS/index.htm

27 – 29 Dec 2012Statistics in Planning and Development Bangladesh PerspectiveDhaka, Bangladeshhttp://www.isrt.ac.bd/node/1379

27 – 29 Dec 2012International Conference on Mathematics – Trends and Developments (ICMTD12)Cairo, Egypthttp://etms-eg.org/

27 – 30 Dec 20128th International Triennial CalcuttaSymposium on Probability and Statistics (caltri8)Kolkata, Indiahttp://triennial.calcuttastatisticalassociation.org/sympBrochure.php

27 Dec 2012 – 4 Jan 2013Descriptive Set Theory and Model Theory Workshop and ConferenceKolkata, Indiahttp://www.isical.ac.in/~dst.model/

28 – 30 Dec 2012Statistical Concepts and Methods for theModern WorldColombo, Sri Lankahttp://www.maths.usyd.edu.au/u/shelton/SLSC2011/

28 – 31 Dec 2012 International Conference on Mathematical Sciences (ICMS 2012) Nagpur, India http://icms2012.org/

28 Dec 2012 – 11 Jan 2013Recent Advances in Operator Theory and Operator AlgebraBangalore, Indiahttp://www.isibang.ac.in/~jay/rota.html

JANUARY 2013

1 – 4 Jan 2013Descriptive Set Theory and Model TheoryKolkata, Indiahttp://www.isical.ac.in/~dst.model/index.htm

1 – 9 Jan 2012 VI-MSS Event: Workshop and Conference on Limit Theorems in ProbabilityBangalore, Indiahttp://icerm.brown.edu/vi-mss

2 – 5 Jan 2013 International Indian Statistical Association Conference: Statistics, Science and Society: New Challenges and Opportunities Chennai, India www.iisaconference.info

2 – 8 Jan 2013Workshop on Limit Theorems in ProbabilityBangalore, Indiahttp://math.iisc.ernet.in/~imi/LTPWS.php

4 – 8 Jan 2013Third Conference of Tsinghua Sanya International Mathematics ForumSanya, Chinahttp://msc.tsinghua.edu.cn/forum2013/

6 – 10 Jan 2013ISBA Regional Meeting in Conjunction with International Workshop/Conferenceon Bayesian Theory and Applications (IWCBTA)Varanasi, Indiahttp://www.bhu.ac.in/isba/

7 – 11 Jan 2013The 5th International Conference to Review Research on Science, Technology and Mathematics Education (epiSTEME 5)Mumbai, Indiahttp://conf.hbcse.tifr.res.in/index.php/episteme5/5/announcement/view/1

7 – 13 Jan 20135th International Conference to Review Research on Science, Technology and Mathematics Education (ISTEME5)Mumbai, Indiahttp://episteme5.hbcse.tifr.res.in/index.php/episteme5/5

7 Jan – 1 Feb 2013AMSI Summer School 2013Melbourne, Australiahttp://www.ms.unimelb.edu.au/~amsi2013/index.php

8 – 9 Jan 20133rd International Conference on Emerging Trends in Computer and Image Processing (ICETCIP2013)Kuala Lumpur, Malaysiahttp://psrcentre.org/listing.php?subcid=192 &mode=detail

8 – 10 Jan 20132013 Quantitative Economics ConferenceSanya, Chinahttp://www.engii.org/qec2013/

8 – 10 Jan 2013International Congress on Natural Sciences and Engineering (ICNSE2013)Taipei, Taiwanhttp://www.icnse.org/

9 – 10 Jan 20132nd International Conference on “Advances in Communication and Computing” (ICACC2013) in collaboration with Asian Institute of Technology, ThailandCoimbatore, Indiahttp://www.tejaashakthi.org/conference/

9 – 11 Jan 20132013 International Conference on Computer Communication and InformaticsCoimbatore, Indiahttp://srishakthiinstitute.com/siet_iccci/

9 – 11 Jan 2013Conference on Limit Theorems in ProbabilityBangalore, Indiahttp://math.iisc.ernet.in/~imi/LTPConf.php

9 – 11 Jan 2013The 1st Asian Quantitative Finance Conference (AQFC2013)Singaporehttp://cqf.nus.edu.sg/AQFC2013/aqfc2013.htm

10 – 12 Jan 2013Indian Conference on Logic and its Applications (ICLA2013)Chennai, Indiahttp://www.imsc.res.in/~icla

11 – 12 Jan 2013International Conference on Computation and Communication Advancement (IC3A)Kalyani, Indiahttp://www.jiscollege.ac.in/ic3a/

13 – 19 Jan 2013NZMRI Summer Workshop 2013: Geometric Mechanics and ShapeWhakatane, New Zealandhttp://seat.massey.ac.nz/NZMRI13

16 – 17 Jan 2013Big Data Analytics Asia 2013Singaporehttp://www.bigdata-asia.com/Event.aspx?id=806044&MAC=ACC

17 – 18 Jan 2013International Conference on Advances in Computing, Communication and Control 2013Mumbai, Indiahttp://icac3.frcrce.ac.in/

18 – 19 Jan 201321th Annual Workshop on Differential EquationsChungli, Taiwanhttp://2013de.math.ncu.edu.tw/index.html

21 – 24 Jan 2013International Conference on Computing, Management and Telecommunications (ComManTel2013)Ho Chi Minh City, Vietnamhttp://commantel.net/2013

22 – 25 Jan 2013The 78th Annual Conference of the Indian Mathematical Society (IMS)Varanasi, Indiahttp://www.indianmathsociety.org.in/

Conference CALENDAR


24 – 25 Jan 20132013 International Conference on Science and Engineering in Mathematics, Chemistry and PhysicsJakarta, Indonesiahttp://scietech.org/

29 – 31 Jan 2013International Conference on Reliability, Infocom Technologies and Optimization (ICRITO2013): Trends and Future DirectionsNoida, Indiahttp://www.amity.edu/aiit/icrito2013/

29 – 31 Jan 2013 Research on the Behavior of Semi-Equilibrium Solutions Arising in Mathematical Models of Nonlinear PhenomenaKyoto, Japan http://www.kurims.kyoto-u.ac.jp/~kyodo/workshop-en.html

29 Jan – 1 Feb 2013Computing: The Australasian Theory Symposium (CATS2013)Adelaide, Australiahttp://cis.unimelb.edu.au/cats

29 Jan – 1 Feb 2013The 9th Asia-Pacific Conference on Conceptual Modeling (APCCM2013)Adelaide, Australiahttp://2013.apccm.org/

29 Jan – 2 Feb 2013Mathematics in Industry Study Group (MISG) 2013 WorkshopBrisbane, Australiahttp://mathsinindustry.com/

30 – 31 Jan 2013 International Conference on Probability and Statistics (ICPS 2013)Dubai, United Arab Emirates http://www.waset.org/conferences/2013/dubai/icps/

FEBRUARY 2013

2 – 3 Feb 20132nd International Conference on Educational and Information Technology (ICEIT2013)Hong Kong, Chinahttp://www.iceit.org/

3 – 7 Feb 2013ANZIAM 2013 ConferenceNewcastle, Australiahttp://anziam2013.newcastle.edu.au/

4 – 5 Feb 20132nd Annual Conference on Computational Mathematics, ComputationalGeometry and Statistics (CMCGS2013)Singaporehttp://www.mathsstat.org/

4 – 7 Feb 20133rd Bar-Ilan Winter School on Crypto: Bilinear Pairings in CryptographyTel-Aviv area, Israelhttp://crypto.biu.ac.il/winterschool2013/

4 – 8 Feb 20132nd Biennial International Group Theory ConferenceIstanbul, Turkeyhttp://istanbulgroup2013.dogus.edu.tr/

5 – 7 Feb 2013International Conference on Mathematical Sciences and Statistics (ICMSS2013)Kuala Lumpur, Malaysiahttp://math.upm.edu.my/icmss2013/

5 – 8 Feb 20139th International Conference on Distributed Computing and Internet TechnologyBhubaneswar, Indiahttp://icdcit.ac.in

7 – 8 Feb 2013The Young Statistician ConferenceMelbourne, Australiahttp://www.ysc2013.com/

9 – 12 Feb 2013South Pacific Optimization Meeting (SPOM2013)Newcastle, Australiahttp://carma.newcastle.edu.au/meetings/spom/

11 – 14 Feb 2013Graph C*-Algebras, Leavitt Path Algebras and Symbolic DynamicsSydney, Australiahttp://www.amsi.org.au/events/archived-events/898-graph-c-algebras-leavitt-path-algebras-and-symbolic-dynamics

14 – 16 Feb 20137th International Workshop on Algorithms and Computation (WALCOM2013)Kharagpur, Indiahttp://cse.iitkgp.ac.in/conf/walcom2013/

17 – 25 Feb 2013Cass Workshop 2013: Networks of lifeArthur’s Pass, New Zealandhttp://www.math.canterbury.ac.nz/bio/events/cass/

18 – 22 Feb 2013The Arithmetic of Function Fields and Related TopicsBusan, Koreahttp://asarc.kaist.ac.kr/bbs/view.php?board_id=conference1&no=40

20 – 21 Feb 2013Workshop “Special Functions and Orthogonal Polynomials”Riyadh, Saudi Arabiahttp://spconf.ksu.edu.sa/node/61

22 – 23 Feb 20133rd IEEE International Advance Computing Conference (IACC2013)Ghaziabad, Indiahttp://akgec.org/iacc2013/

22 – 24 Feb 2013 2013 Indo-Slovenia Conference on Graph TheoryThiruvanathapuram, Indiahttp://indoslov2013.wordpress.com/

23 – 24 Feb 20135th International Conference on Computer Research and Development (ICCRD2013)Ho Chi Minh City, Vietnanhttp://www.iccrd.org/

26 Feb – 1 Mar 2013The 16th International Conference on Practice and Theory in Public-Key Cryptography (PKC2013)Nara, Japanhttp://ohta-lab.jp/pkc2013/

MARCH 2013

3 – 6 Mar 2013The 10th Theory of Cryptography Conference (TCC2013)Tokyo, Japanhttp://tcc2013.com/

4 – 6 Mar 2013The 1st International Conference on Green Computing, Technology and Innovation (ICGCTI2013)Kuala Lumpur, Malaysiahttp://sdiwc.net/conferences/2013/Malaysia4/

4 – 6 Mar 2013 The 2nd International Conference on Mathematics, and Technology in Mathematics Education 2013 Phnom Penh, Cambodiahttp://www.cambmathsociety.org/Conference2013/conferen2013.htm

10 – 16 Mar 2013Workshop and Conference on Stochastic Processes in EngineeringMumbai, Indiahttp://math.iisc.ernet.in/~imi/SPEWS.php

11 – 13 Mar 2013 The 20th International Workshop on Fast Software Encryption Singaporehttp://fse2013.spms.ntu.edu.sg/

12 – 14 Mar 2013NatStats 2013Brisbane, Australiahttp://www.nss.gov.au/blog/natstats.nsf

13 – 15 Mar 2013IAENG International Conference on Operations Research 2013 (ICOR’13)Hong Kong, Chinahttp://www.iaeng.org/IMECS2013/ICOR2013.html

13 – 15 Mar 2013International Conference on Data Mining and Applications 2013 (IAENG)Hong Kong, Chinahttp://www.iaeng.org/IMECS2013/ICDMA2013.html

15 – 16 Mar 2013International Conference on Mathematics and Information TechnologyChennai, Tamilnadu, Indiahttp://www.worldairco.org/ICMIT%20Mar%202013/ICMIT.html



17 – 22 Mar 2013The 6th East Asia Regional Conference on Mathematics Education (EARCOME6)Phuket, Thailandhttp://home.kku.ac.th/earcome6/

20 – 23 Mar 2013 MSJ Spring Meeting 2013 Kyoto, Japanhttp://mathsoc.jp/en/

22 – 23 Mar 2013International Multi Conference on Automation, Computing, Control, Communication and Compressed SensingKerala, Indiahttp://www.imac4s.org/

25 – 27 Mar 2013First International Conference Human Machine InteractionChennai, Indiahttp://hmi2013.in/

25 – 28 Mar 2013The Computer Applications and Quantitative Methods in Archaeology (CAA)Perth, Australiahttp://www.caa2013.org/drupal/

25 – 29 Mar 201312th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA12)Port El Kantaoui, Sousse, Tunisiahttp://matematicas.uc3m.es/index.php/seminarios/intern-meet-menu/12th-opsfa

APRIL 2013

1 – 5 Apr 2013Financial Crypto (FC13)Okinawa, Japanhttp://fc13.ifca.ai/

6 – 7 Apr 20133rd International Conference on Advanced Computing and Communication Technologies (ACCT13)Rohtak, Indiahttp://www.rgsociety.org/acct13/

13 – 14 Apr 2013International Conference on Advanced Data Analysis, Business Analyticsand Intelligence (The 3rd IIMA)Ahmedabad, Indiahttp://www.iimahd.ernet.in/icadabai2013/

16 – 19 Apr 2013IEEE Symposium on Computational Intelligence for Engineering Solutions (CIES2013)Singaporehttp://www.ntu.edu.sg/home/epnsugan/index_files/SSCI2013/CIES2013.htm

16 – 19 Apr 2013IEEE Symposium Series on Computational Intelligence (SSCI 2013)Singaporehttp://www.ntu.edu.sg/home/epnsugan/index_files/SSCI2013/index.html

22 – 23 Apr 20133rd Annual International Conference on Operations Research and Statistics (ORS2013)Singaporehttp://orstat.org/

22 – 25 Apr 20137th Meeting of the Eastern Mediterranean Region of the International Biometric Society (EMR-IBS)Tel-Aviv, Israelhttps://event.pwizard.com/ims/

27 – 29 Apr 2013International Conference on Information and Communications Technologies (IET2013)Beijing, Chinahttp://www.ietict.org/index.html

MAY 2013

10 – 12 May 2013Workshop on Super Representation TheoryTaipei, Taiwanhttp://www.math.sinica.edu.tw/chengsj/super_2013.htm

16 – 21 May 201315th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT2013)Beijing, Chinahttp://acat2013.ihep.ac.cn

19 – 21 May 20137th International Conference on Bioinformatics and Biomedical Engineering (ICBBE2013)Beijing, Chinahttp://www.icbbe.org/2013/

30 May – 4 Jun 2013New Directions in ProbabilityBangalore, Indiahttp://www.isibang.ac.in/~athreya/ndp/

JUN 2013

3 Jun – 12 Jul 2013Nonlinear Expectations, Stochastic Calculus under Knightian Uncertainty, and Related TopicsSingaporehttp://ims.nus.edu.sg/Programs/013wnlinear/index.php

10 – 14 Jun 20137th International Conference on Computational Methods and Function Theory (CMFT2013)Shantou, Chinahttp://math.stu.edu.cn/cmft/

17 – 21 Jun 2013 Istanbul Summer School in Algebraic GeometryIstanbul, Turkeyhttp://homepages.math.uic.edu/~coskun/istanbulAG.html

19 – 21 Jun 2013Symposium on Manufacturing Modeling, Management, and Control (MIM2013 IFAC)St Petersburg, Russiahttp://mim2013.org

19 – 21 Jun 2013The 9th Conference of East Asia Section of SIAM (EASIAM 2013)Bandung, Indonesiahttp://www.math.itb.ac.id/~easiam2013

20 – 21 Jun 2013International Conference on Mathematical and Computational Biology (ICMCB2013)Istanbul, Turkeyhttp://www.waset.org/conferences/2013/istanbul/icmcb/

20 – 24 Jun 2013Asymptotic Geometric Analysis IISt Petersburg, Russiahttp://www.pdmi.ras.ru/EIMI/2013/aga/index.html

24 – 28 Jun 2013The 2nd Pacific Rim Mathematical Association Congress (PRIMA2013)Shanghai, Chinahttp://www.pims.math.ca/scientific-event/130624-spc

26 – 30 Jun 2013The 22th Summer St Petersburg Meeting onMathematical AnalysisSt Petersburg, Russiahttp://www.pdmi.ras.ru/EIMI/imiplanC.html

28 – 30 Jun 20131st International Conference on SmarandacheMultispace and MultistructureBeijing, Chinahttp://www.ams.org/meetings/calendar/2013_jun28-30_beijing100190.html

30 Jun – 4 Jul 20132013 Asian Mathematical Conference (AMC)Busan, Koreahttp://www.kms.or.kr/meetings/amc2013

30 Jun – 4 Jul 2013The 4th IMS China International ConferenceChengdu, Chinaimscn2013.swufe.edu.cn

JULY 2013

1 – 5 Jul 2013 6th Pacific Rim Conference on Mathematics Sapporo, Japan http://www.math.sci.hokudai.ac.jp/sympo/130701/

2 – 5 Jul 20134th International Conference on Matrix Analysis and ApplicationsAnkara, Turkeyhttp://icmaa2013.selcuk.edu.tr/

Conference CALENDAR


2 – 6 Jul 2013The 5th St Petersburg Conference in SpectralTheory Dedicated to The Memory of M. Sh. BirmanSt Petersburg, Russiahttp://www.pdmi.ras.ru/EIMI/2012/ST/index.html

3 – 6 Jul 2013International Conference Anatolian Communications in Nonlinear Analysis (ANCNA2013)Bolu, Turkeyhttp://ancna.net/

7 – 10 Jul 2013IEEE International Conference on Fuzzy Systems (FUZZ-IEEE2013)Hyderabad, Indiahttp://www.isical.ac.in/~fuzzieee2013

8 – 11 Jul 20133rd Australia New Zealand Applied Probability WorkshopBrisbane, Australiahttp://www.smp.uq.edu.au/people/YoniNazarathy/AUSTNZworkshop/2013/main.html

14 – 19 Jul 2013The Sixth International Congress of Chinese Mathematicians (ICCM 2013)Taipei, Taiwanhttp://iccm.tims.ntu.edu.tw/

22 – 26 Jul 201325th IUPAP International Conference on Statistical Physics (STATPHYS25)Seoul, Koreahttp://www.statphys25.org

22 Jul – 4 Aug 2013 CIMPA-UNESCO-MESR-MINECO Philippines Research School 2013 Manila, Philippineshttp://www.math.upd.edu.ph/cimpa_research_school2013/

AUGUST 2013

3 – 9 Aug 2013The 2013 International Joint Conference on Artificial Intelligence (IJCAI 2013)Beijing, Chinahttp://www.ezconf.net/ijcai13/

5 – 16 Aug 2013Analysis on Minimal Representations,International Summer Research School ofCIMPA 2013 “Hypergeometric Functions andRepresentation Theory”Mongoliahttp://www.cimpa-icpam.org/spip.php?article484&lang=fr

22 – 24 Aug 2013Joint IASE/IAOS Satellite Conference to WSCMacau, Chinahttp://www.conkerstatistics.co.uk/iase2013/index.php

25 – 30 Aug 2013The 59th World Statistics Congress of theInternational Statistical InstituteHong Kong, Chinahttp://www.isi2013.hk/

SEPTEMBER 2013

2 – 6 Sep 2013Joint with the 6th Japan-Mexico Topology SymposiumMatsue, Japanhttp://www.city.matsue.shimane.jp/kankou/en/index.htm

29 Sep – 3 Oct 2013World Conference on Science and Technology EducationKuching, Malaysiahttp://worldste2013.org/

NOVEMBER 2013

24 – 28 Nov 2013The 9th Delta Conference on The Teaching and Learning of Undergraduate Mathematics and StatisticsKiama, Australiahttp://delta2013.net

26 – 28 Nov 2013International Conference on Pure and Applied Mathematics (ICPAM-LAE 2013)Lae, Morobe Province, Paupa New Guineahttp://www.unitech.ac.pg/

DECEMBER 2013

1 – 6 Dec 2013 International Congress on Modelling and Simulation (MODSIM2013)Adelaide, Australiahttp://www.austms.org.au/tiki-calendar.php?editmode=details&calitemId=344

28 – 30 Dec 20133rd International Conference on Mathematics and Information ScienceLuxor, Egypthttp://conf.naturalspublishing.com/

28 – 31 Dec 2013Statistics 2013: Socio-Economic and Sustainable Challenges and SolutionsHyderabad, Indiawww.statistics2013-conference.org.in

MAY 2014

12 – 14 May 2014SIAM Conference on Imaging Science (IS14)Hong Kong, Chinahttp://www.siam.org/meetings/is14/

JUN 2014

16 – 19 Jun 20142nd Joint Meeting with Israel Mathematical UnionTel-Aviv, Israel

Jun (or Jul) 2014CIMPA/TUBITAK/GSU Summer School: Algebraic Geometry and NumberTheoryIstanbul, Turkey

JULY 2014

6 – 11 Jul 2014IEEE World Congress on Computational Intelligence (WCCI2014)Beijing, Chinahttp://www.ieee-wcci2014.org/

7 – 11 Jul 2014IMS Annual MeetingSydney, Australiahttp://www.imstat.org/meetings/submissions/2014/07/07/1309790138141.html

AUGUST 2014

13 – 21 Aug 2014International Congress of Mathematicians 2014Seoul, Koreahttp://www.icm2014.org/

APRIL 2015

19 – 24 Apr 2015IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2015/ICASSP15)Brisbane, Australiahttp://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=17257

MAY 2015

25 – 28 May 2015IEEE Congress on Evolutionary Computation (CEC 2015)Sendai, Japanhttp://www.ourglocal.com/event/?eventid=10249

Conference CALENDAR

The following are conditionally pre-approved ICM Satellite Conferences in Korea

Jul or Aug 2014The 4th Asian Conference on Nonlinear Analysis and Optimization BEXCO or Pukyong National University, Busan, Korea

Jul or Aug 2014Pacific Rim Conference on Complex GeometryVenue to be announced

4 – 8 Aug 2014Symplectic Geometry and Mirror SymmetrySeoul National University or KIAS, Seoul, Korea

4 – 9 Aug 201435th Conference on Quantum Probability and Related TopicsChungbuk National University, Cheongju, Korea

5 – 9 Aug 2014L-functionsYonsei University, Seoul, Korea

4 – 9 Aug 2014Geometry on Groups and SpacesKAIST, Daejeon, Korea

5 – 8 Aug 2014ICM 2014 Satellite Conference in Harmonic AnalysisSeoul National University, Seoul, Korea

6 – 8 Aug 2014Imaging, Multi-scale and High Contrast PDEInha University, Incheon, Korea

6 – 8 Aug 2014Representation Theory and Related TopicsVenue to be announced

Those who plan to organise Satellite Conferences right before or after the ICM may send the following information to the Parallel Scientific Activity Committee at [email protected]:

• Name(s) of organisers and their affiliation(s) • An email address of the corresponding person • The title and a brief description of the conference • The intended period and the place of the conference

Please note in advance that, there are a small number of requisites for a meeting in order to be accepted as a Satellite Conference, on top of which is the scientific quality and the interest of the research topics proposed, as well as the previous experience of the organisers. Other criteria to be considered are the following:

• The conference must have a strong international projection, and, therefore, should be well balanced with respect to the participation of local and international specialists.

• For strategic reasons, proximity in time to the ICM 2014 is required.

6 – 9 Aug 2014Classification TheoryYonsei University, Seoul, Korea

6 – 9 Aug 2014ILAS (International Linear Algebra Society) 2014Sungkyunkwan University, Suwon. Korea

7 – 11 Aug 2014Arithmetic & Algebraic GeometryKIAS, Seoul, Korea

7 – 11 Aug 2014Integral Quadratic Forms and Related TopicsJeju, Korea

7 – 12 Aug 2014Operator Algebras and ApplicationsGyeongju, Korea

8 – 12 Aug 2014Dynamical Systems and Related TopicsChungnam National University, Daejeon, Korea

11 – 12 Aug 2014ICM Satellite Conference on Differential Geometry and Related FieldsKyungpook National University, Daegu, Korea

11 – 12 Aug 2014Recent Advances in Finite Element MethodsYonsei University, Seoul, Korea

11 – 12 Aug 2014ICM 2014 Satellite Conference on Algebraic Coding TheoryEwha Womans University, Seoul, Korea

Aug 2014Geometric Topology and Related Topics / Hyperboic Geometry and Related Topics (tentative topic)Seoul National University or KIAS, Seoul, Korea

Aug 2014ICWM 2014 (International Conference of Women Mathematicians)Venue to be announced

Date to be announcedTorus Actions and Its ApplicationKAIST, Daejeon, Korea

Date to be announced7th International Conference on Stochastic Analysis and Its Applications 2014Venue to be announced

Date to be announcedGraph TheoryVenue to be announced

The following are conditionally pre-approved ICM Satellite Conferences in neighbouring countries

22 – 25 Jul 2014ISSAC 2014Kobe, Japan

4 – 8 Aug 2014The Geometry, Topology and Physics of Moduli SpacesThe Institute for Mathematical Sciences (IMS), National University of Singapore

6 – 8 Aug 2014The 9th East Asia PDE ConferenceTokyo, Japan

7 – 11 Aug 2014Recent Advances in Computational MathematicsWeihai Campus of Shandong University,China

25 – 29 Aug 2014Sapporo Symposium on Partial Differential EquationsHokkaido University, Sapporo, Japan

25 – 30 Aug 2014Traditional Mathematics of East Asia and Related Topics (Takebe Conference 2014)Ochanomizu University, Tokyo, Japan

International Congress of Mathematics Satellite Conferences



Pure and Applied Communications (PAMC), a high quality, fully open access, electronic-only journal will begin accepting submissions soon.

It features:

• Wide coverage of original research in all areas of pure and applied mathematics, with emphasis on cross-field research of a broad impact.

• Rigorous peer-review. • Flexible length restrictions. • Rapid publication (full citation upon acceptance). • Authors retain copyright (CC-BY License). • Full text database with searches and content alerts. • Papers may be featured as highlights in the Asia Pacific

Mathematics Newsletter (APMN), enabling your research to reach a wider community.

Free global access to all content of PAMC is supported by the article-processing charge (APC), which is waived for 2012–2013.

Aims & ScopePure and Applied Mathematics Communications (PAMC) publishes original research and review articles in all areas of pure and applied mathematics, with emphasis on cross-field research of a broad impact.

Articles are published Open Access under Creative Commons Attribution License.

Editorial Board

Advisory BoardAlice Chang (Princeton University, USA) Yongchuan Chen (Nankai University, China) Weinan E (Princeton University, USA) Molin Ge (Nankai University, China) Daqian Li (Fudan University, China) Yiming Long (Nankai University, China) Zhiming Ma (Institute of Applied Mathematics, Chinese

Academy of Sciences)Yum-Tong Siu (Harvard University, USA) Gang Tian (Princeton University, USA; Beijing

International Center for Mathematics Research, China)Gongqing Zhang (Peking University, China)

Editor-in-ChiefQing Han (Notre Dame University, USA)

Editorial BoardMeng Chen (Fudan University, China) Kunyu Guo (Fudan University, China) Jianshu Li (University of Science and Technology, Hong

Kong, China) Jiayu Li (Institute of Mathematics, Chinese Academy of

Sciences) Pingbing Ming (Institute of Computational Mathematics,

Chinese Academy of Sciences)Ngaiming Mok (Hong Kong University, China) Tao Tang (Hong Kong Baptist University, China) Yuan Yao (Peking University, China) Zongmin Wu (Fudan University, China)

Pure and Applied Mathematics Communications

For more information please visithttp://www.worldscientific.com/worldscinet/pamc

Print ISSN: 2315-439X Online ISSN: 2315-4403

WorldScientific pen



Mathematical Societies in Asia Pacific Region

Australian Mathematical Society

President: P. G. TaylorAddress: Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, AustraliaEmail: [email protected].: +61 (0)3 8344 5550Fax: +61 (0)3 8344 4599http://www.austms.org.au/

Bangladesh Mathematical Society

President: Md. Abdus SattarAddress: Bangladesh Mathematical Society, Department of Mathematics, University of Dhaka, Dhaka - 1000, BangladeshEmail: [email protected].: +880 17 11 86 47 25http://bdmathsociety.org/

Cambodian Mathematical Society

President: Chan Roath Address: Khemarak University Phnom Penh Center Block D Email: [email protected] Tel.: (855) 642 68 68 (855) 11 69 70 38http://www.cambmathsociety.org/

Chinese Mathematical Society

President: Zhiming MaAddress: 55 Zhong Guan Cun East Road, Hai Dian

District Beijing 100080, P.R. China Email: [email protected].: +86-10-62551022http://www.cms.org.cn/cms/

Hong Kong Mathematical Society

President: Tao TangAddress: Department of Mathematics, Hong Kong Baptist University Kowloon Tong, Kowloon, Hong KongEmail: [email protected].: (852)-3411 7011Fax: (852)-3411 5862http://www.hkms.org.hk/

Mathematical Societies in India:

The Allahabad Mathematical ScocietyPresident: D. P. GuptaAddress: 10, C S P Singh Marg, Allahabad – 211001,Uttar Pradesh, IndiaEmail: [email protected]://www.amsallahabad.org/

Calcutta Mathematical SocietyPresident: K. Ramachandra Address: AE-374, Sector I, Salt Lake City, Kolkata - 700064, WB, IndiaEmail: [email protected].: 0091 (33) 2337 8882Fax: 0091 (33) 376290http://www.calmathsoc.org/

The Indian Mathematical SocietyPresident: R. SridharanAddress: Department of Mathematics, University of Pune, Pune – 411007, IndiaEmail: [email protected]://www.indianmathsociety.org.in/

Ramanujan Mathematical SocietyPresident: Phoolan PrasadAddress: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhaba Road, Colaba, Mumbai, IndiaEmail: [email protected]://www.ramanujanmathsociety.org/



Vijnana Parishad of IndiaPresident: G. C. SharmaContact: R.C. Singh Chandel Secretary, Vijnana Parishad of India D.V. Postgraduate College, Orai - 285001, UP, IndiaEmail: [email protected].: +91 11 27495877http://vijnanaparishadofindia.org/

Indonesian Mathematical Society

President: WidodoAddress: Fakultas MIPA Universitas Gadjah Mada, Yogyakarta, IndonesiaEmail: [email protected]://www.indoms-center.org

Israel Mathematical Union

President: Louis H. RowenAddress: Israel Mathematical Union, Department of Mathematics, Bar Ilan University, Ramat Gan 52900, IsraelEmail: [email protected].: +972 3 531 8284Fax: +972 9 741 8016http://www.imu.org.il/

The Mathematical Society of Japan

President: Yoichi MiyaokaAddress: 34-8, Taito 1 Chome, Taito-Ku Tokyo 110-0016, JapanEmail: [email protected] Tel.: +81 03 3835 3483http://mathsoc.jp/en/

The Korean Mathematical SocietyPresident: Dong Youp Suh KAISTAddress: The Korean Mathematical Society, The Korea Science and Technology

Center 202, 635-4, Yeoksam-dong, Kangnam-gu, Seoul 135-703, KoreaEmail: [email protected] [email protected] http://www.kms.or.kr/eng/

Malaysian Mathematical Sciences Society

President: Mohd Salmi Md. NooraniAddress: School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600, Selangor D. Ehsan, MalaysiaEmail: [email protected].: +603 8921 5712Fax.: +603 8925 4519http://www.persama.org.my/

Mongolian Mathematical Society

President: A. MekeiAddress: P. O. Box 187, Post Office 46A, Ulaanbaatar, MongoliaEmail: [email protected]

Nepal Mathematical Society

President: Bhadra Man Tuladhar Address: Nepal Mathematical Society, Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, NepalEmail: [email protected].: 9841 639131 00977 1 2041603 (Res)http://www.nms.org.np/

New Zealand Mathematical Society

President: Charles SempleContact: Alex James SecretaryAddress: Department of Mathematics and

Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New ZealandEmail: [email protected]://nzmathsoc.org.nz/

Pakistan Mathematical SocietyPresident: Qaiser Mushtag Contact: Dr. Muhammad Aslam General SecretaryAddress: Department of Mathematics, Qauid-i-Azam University, Islamabad, PakistanEmail: [email protected]: +92 51 260 1053http://pakms.org.pk/



Mathematical Society of the Philippines

President: Fidel Nemenzo Address: Mathematical Society of the Philippines, c/o Department of Mathematics, University of the Philippines, Diliman, Quezon City, 1101, PhilippinesEmail: [email protected]: 632 920 1009http://www.mathsocietyphil.org/

Mathematical Societies in Russia

Moscow Mathematical SocietyPresident: S. NovikovAddress: Landau Institute for Theoretical Physics, Russian Academy of Sciences, Kosygina 2 117 940 Moscow GSP-1, RussiaEmail: [email protected] [email protected]://mms.math-net.ru/

St. Petersburg Mathematical Society

President: A. M. VershikAddress: St. Petersburg Mathematical Society, Fontanka 27, St. Petersburg, 191023, RussiaEmail: [email protected].: +7 (812) 312 8829, 312 4058Fax: +7 (812) 310 5377http://www.mathsoc.spb.ru/

Voronezh Mathematical Society

President: S. G. KreinAddress: ul. Timeryaseva 6 a ap 35 394 043 Voronezh, Russia

Singapore Mathematical Society

President: Chengbo Zhu Address: Department of Mathematics, National University of Singapore, S17, 10 Lower Kent Ridge Road Singapore 119076Email: [email protected].: (65)-67795452http://sms.math.nus.edu.sg/

Southeast Asian Mathematical Society

President: Le Tuan Hoa Address: Managing Director

VIASM (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: [email protected] http://www.seams-math.org/

The Mathematical Society of ROC

President: Gerard Jennhwa ChangAddress: The Mathematical Society of ROC 5F, Astronomy-Mathematics Building No.1, Sec. 4, Roosevelt Road Taipei 10617, TaiwanEmail: [email protected] [email protected].: 886-2-2367-7625Fax: 886-2-2391-4439http://www.taiwanmathsoc.org.twhttp://tms.math.ntu.edu.tw/

Mathematical Association of Thailand

President: Yongwimon LenburyAddress: Chair, Graduate Program Committee Department of Mathematics Mahidol University Ramab Road, Bangkok 10400, ThailandEmail: [email protected].: (662) 201-5448Fax: (662) 201-5343http://www.math.or.th/mat/

Vietnam Mathematical Society

President: Le Tuan Hoa Address: Managing Director

VIASM (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: [email protected]: (**84) 4 37563474http://www.vms.org.vn/english/vms_e.htm



MICA (P) 157/03/2012

· tony f chan hong kong university of science and technology hong kong [email protected] louis chen...

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