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Asia PacificMathematics NewsletterOctober 2013 Volume 3 Number 4

www.asiapacific-mathnews.com

Sangaku from the Sozume Shrine (page 28)

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]

Myung-Hwan KimDepartment of MathematicsSeoul National UniversitySeoul 151-747, [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]

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

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

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

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]

Graham WeirIndustrial Research Ltd69 Gracefield RoadPO Box 31310, Lower Hutt 5040New Zealand [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 2013

Asia PacificMathematics Newsletter

Volume 3 Number 4

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

Editor-in-Chief

Phua Kok Khoo

Editor

S C Lim

Production

Tan Rok Ting

Kwong Lai Fun

Zhang Ji

Artist

Jimmy Low

Editorial

What are p-Adic Numbers? What are They Used for? .............................................1

The Twin Prime Problem and Generalisations ................................................................................. 7

Discrepancy, Graphs, and the Kadison–Singer Problem ................................................15

Journalist in Residence (JIR) Programme in Mathematics in Japan.................21

Gonit Sora: The Two Year Journey ................................................................................................................25

Book Review — Secular Mathematics in Sacred Precincts ..........................................28

Interview with Hidetoshi Fukagawa ..........................................................................................................30

Interview with Tony Rothman ............................................................................................................................37

Problem Corner .....................................................................................................................................................................42

Michio Jimbo and Tetsuji Miwa Awarded the Dannie Heineman Prize for Mathematical Physics...........................................................................................................................................44

News in Asia Pacific Region ....................................................................................................................................45

Conferences in Asia Pacific Region...............................................................................................................62

Mathematical Societies in Asia Pacific Region ..............................................................................73

Electronic – ISSN 2010-3492

Editorial

This publication has completed its third year of

existence with 12 issues published. I hope it has

played a role in the dissemination of news on

mathematics-related activities, and in fostering better

communication links within the mathematics community in

the Asia Pacific region. As I have mentioned in the inaugural

issue, the APMN aims to provide a platform for discussion on

issues faced by the mathematics community, but regrettably

the responses from readers were rather poor. It is hoped that

more readers will put in some effort to start the ball rolling

in future issues of APMN.

In addition to the introductory article by Rozikov on

p-adic numbers, this issue features two articles on recent

important results on the twin prime problem and the

Kadison–Singer conjecture. Ram Murty in “The Twin

Prime Problem and Generalisations” gives an exposition

of this long-standing problem and a recent breakthrough

obtained by Yitang Zhang. The previous issue of APMN

has reported briefly on the work of Zhang and featured an

interview with him. The Kadison–Singer conjecture was

formulated in 1959 by mathematicians Richard Kadison

and Isadore Singer. This conjecture has a remarkably large

number of equivalent formulations in operator algebras,

high-dimensional geometry and linear algebra; and it has

important implications for many areas of mathematics,

computer science and quantum mechanics. In a paper

posted in June this year, Adam Marcus and Daniel A

Spielman of Yale University, together with Nikhil Srivastava

of Microsoft Research India, announced a proof of this

conjecture. One of the authors of this paper, Srivastava gives

an exposition of the result in “Discrepancy, Graphs and the

Kadison–Singer Problem”.

In the article “Journalist in Residence (JIR) Programme in

Mathematics in Japan”, Koji Fujiwara introduces a special

programme which allows journalists and writers to reside

at mathematics departments to explore and know more

about mathematics and to interact with mathematicians.

Such a programme aims to improve science writing and

science journalism.

Gonit Sora is a multilingual website which plays the role of

online mathematics magazine for students. A description

of this website, its goals and future prospects are given in

“Gonit Sora: The Two Year Journey”.

A book review on “Sacred Mathematics: Japanese Temple

Geometry” and interviews with Hidetoshi Fukagawa and

Tony Rothman, authors of the book, are featured in this issue.

I hope you will enjoy reading the articles and news covered

in this issue. Please send in your comments and suggestions

so that APMN can be improved to serve you better.

I wish you in advance a merry Christmas and happy New

Year.

Swee Cheng Lim

Editor

Asia Pacific Mathematics Newsletter welcomes contributions on the following areas:

• Expository articles on mathematical topics of general interest• Articles on mathematics education• Introducing centres of excellence in mathematical sciences• News of mathematical societies in the Asia Pacific region• Introducing well-known mathematicians from the Asia Pacific region• Book reviews• Conference reports and announcements held in Asia Pacific countries• Letters from readers on relevant topics and issues• Other items of interest to the mathematical community

What are p-Adic Numbers?What are They Used for?

U A Rozikov

1

What are p-Adic Numbers? What areThey Used for?

U A Rozikov

Abstract. In this short paper we give a popular intro-duction to the theory of p-adic numbers. We give someproperties of p-adic numbers distinguishing them to“good” and “bad”. Some remarks about applicationsof p-adic numbers to mathematics, biology and physicsare given.

1. p-Adic Numbers

p-adic numbers were introduced in 1904 by the

German mathematician K Hensel. They are used

intensively in number theory. p-adic analysis was

developed (mainly for needs of number theory)

in many directions, see, for example, [20, 50].

When we write a number in decimal, we can

only have finitely many digits on the left of the

decimal, but we can have infinitely many on the

right of the decimal. They might “terminate” (and

become all zeros after some point) but they might

not. The p-adic integers can be thought of as

writing out integers in base p, but one can have

infinitely many digits to the left of the decimal

(and none on the right; but the rational p-adic

numbers can have finitely many digits on the

right of the decimal). For example, the binary

expansion of 35 is 1·20+1·21

+0·22+0·23

+0·24+1·25,

often written in the shorthand notation 1000112.

One has 1 = 0, 111111111 . . .2 = 0, (1)2. But what is

. . . 111111, 02 = (1), 02? Compute (1), 02 + 1:

. . . 111111, 02

+. . .000001, 02

. . . 000000, 02

Hence (1), 02 = −1. This equality can be written as

(1), 02 = limn→∞

n−1

i=0

2i= lim

n→∞(2n − 1) = −1. (1)

This limit equivalent to limn→∞ 2n= 0. In real

case one has limn→∞ qn= 0 if and only if absolute

value |q| is less than 1. Remember that to define

real numbers one considers all limit points of

sequences of rational numbers, using the absolute

value as metric.

To give a meaning of the limit (1), one has

to give a new absolute value | · |∗, on the set of

rational numbers, such that |2|∗ < 1. This is done

as follows. Let Q be the field of rational numbers.

Every rational number x 0 can be represented

in the form x = pr nm , where r, n ∈ Z, m is a positive

integer, ( p, n) = 1, ( p, m) = 1 and p is a fixed prime

number. The p-adic absolute value (norm) of x is

given by

|x|p =

p−r, for x 0,

0, for x = 0.

The p-adic norm satisfies the so called strong

triangle inequality

|x + y|p ≤ max|x|p, |y|p, (2)

and this is a non-Archimedean norm.

This definition of |x|p has the effect that high

powers of p become “small”, in particular |2n|2 =1/2n. By the fundamental theorem of arithmetic,

for a given non-zero rational number x there is a

unique finite set of distinct primes p1, . . . , pr and

a corresponding sequence of non-zero integers

a1, . . . , an such that x = pa1

1. . . par

r . It then follows

that |x|pi= p−ai

ifor all i = 1, . . . , r, and |x|p = 1 for

any other prime p p1, . . . , pr.For example, take 63/550 = 2−1 · 32 · 5−2 · 7 · 11−1

we have

63

550

p=

2, if p = 2,

1/9, if p = 3,

25, if p = 5,

1/7, if p = 7,

11, if p = 11,

1, if p ≥ 13.

We say that two norms · 1 and · 2 on Q are

equivalent if there exists α > 0 such that

· α1 = · 2.

It is a theorem of Ostrowski (see [41]) that

each absolute value on Q is equivalent either

to the Euclidean absolute value | · |, the trivial

absolute value, or to one of the p-adic absolute

values for some prime p. So the only norms on

October 2013, Volume 3 No 4 1

Asia Pacific Mathematics Newsletter

2

Q modulo equivalence are the absolute value,

the trivial absolute value and the p-adic absolute

value which means that there are only as many

completions (with respect to a norm) of Q.

The p-adic absolute value defines a metric

|x − y|p on Q. Two numbers x and y are p-adically

closer as long as r is higher, such that pr divides

|x − y|p. Amazingly, for p = 5 the result is that 135

is closer to 10 than 35.

The completion of Q with respect to p-adic

norm defines the p-adic field which is denoted

by Qp. Any p-adic number x 0 can be uniquely

represented in the canonical form

x = pγ(x)(x0 + x1p + x2p2+ · · · ),

where γ = γ(x) ∈ Z and xj are integers, 0 ≤ xj ≤p − 1, x0 > 0, j = 0, 1, 2, ... (see more detail [31,

50, 54]). In this case |x|p = p−γ(x). The set of p-adic

numbers contains the field of rational numbers Q

but is different from it.

Using canonical form of p-adic numbers, simi-

larly as real numbers, one makes arithmetic oper-

ations on p-adic numbers (see for example, [41]).

2. “Good” Properties of p-Adic Numbers

The ultra-metric triangle inequality, i.e. (2), under-

lies many of the interesting differences between

real and p-adic analysis. The following properties

of p-adic numbers make some directions of the

p-adic analysis more simple than real analysis:

1. All triangles are isosceles.

2. Any point of ball D(a, r) = x ∈ Qp : |x−a|p ≤ ris center. Each ball has an empty boundary. Two

balls are either disjoint, or one is contained in the

other.

3. | · |p1 | · |p2

if p1 p2. This means that each

prime number p generates its own field of p-adic

numbers Qp.

4. x2= −1 has a solution x ∈ Qp if and only if

p = 1 mod 4.

5. A sequence xn in Qp is a Cauchy sequence

if and only if |xn+1 − xn|p → 0 as n→ ∞.

This has the useful corollary that a sum con-

verges if and only if the individual terms tend to

zero:

6. (A student’s dream)∑∞

n=1 an < ∞ if and only

if an → 0.

Since |n!|p → 0 we have, for example,

∞∑

n=0

( − 1)nn!(n + 2) = 1,∞∑

n=0

( − 1)nn!(n2 − 5) = −3.

The sum∑∞

n=0 n! exists in every Qp. The follow-

ing problem has been open since 1971.

Problem. Can∑∞

n=0 n! be rational for some

prime p?

It is not known if∑∞

n=0 n! 0 in every Qp.

7. For any x ∈ Q, we have

|x|∏

p:prime

|x|p = 1.

This formula have been used to solve several

problems in number theory, many of them us-

ing Helmut Hasse’s local-global principle, which

roughly states that an equation can be solved

over the rational numbers if and only if it can be

solved over the real numbers and over the p-adic

numbers for every prime p.

3. “Bad” Properties of p-Adic Numbers

1. Qp is not ordered.

2. Qp is not comparable with R, for example√7 Q5, but i =

√−1 ∈ Q5.

3. Qp is not algebraically closed.

But | · |p can be extended uniquely to the

algebraic closure Qap and the completion of (Qa

p, |·|p)

is called Cp, the field of the p-adic complex num-

bers. Cp is no locally compact, but separable and

algebraically closed.

Now define the functions expp (x) and logp (x).

Given a ∈ Qp and r > 0 put

B(a, r) = x ∈ Qp : |x − a|p < r.

The p-adic logarithm is defined by the series

logp(x) = logp(1 + (x − 1)) =∞∑

n=1

( − 1)n+1 (x − 1)n

n,

which converges for x ∈ B(1, 1);

The p-adic exponential is defined by

expp (x) =∞∑

n=0

xn

n!,

which converges for x ∈ B(0, p−1/(p−1)).

Let x ∈ B(0, p−1/(p−1), then

| expp(x)|p=1, | expp(x)−1|p= |x|p, | logp(1+x)|p= |x|p,

logp( expp(x)) = x, expp( logp(1 + x)) = 1 + x.

4. Some “good” functions become “bad”. For

example exp (x) is very “good” function on R, but

as we seen above expp(x) is defined only on ball

B(0, p−1/(p−1)).

October 2013, Volume 3 No 42


3

4. Remarks about Applications

When the p-adic numbers were introduced they

considered as an exotic part of pure mathematics

without any application (see for example [41,

42, 50, 56] for applications of p-adic numbers

to mathematics). Since p-adic numbers have the

interesting property that they are said to be close

when their difference is divisible by a high power

of p the higher the power the closer they are.

This property enables p-adic numbers to encode

congruence information in a way that turns out

to have powerful applications in number theory

including, for example, in the famous proof of

Fermat’s Last Theorem by Andrew Wiles (see [42,

Chap. 7]).

What is the main difference between real and

p-adic space-time? It is the Archimedean axiom.

According to this axiom any given large segment

on a stright line can be surpassed by successive

addition of small segments along the same line.

This axiom is valid in the set of real numbers and

is not valid in Qp. However, it is a physical axiom

which concerns the process of measurement. To

exchange a number field R to Qp is the same as

to exchange axiomatics in quantum physics (see

[31, 56]).

In 1968 two pure mathematicians, A Monna

and F van der Blij, proposed to apply p-adic

numbers to physics. In 1972 E Beltrametti and

G Cassinelli investigated a model of p-adic valued

quantum mechanics from the positions of quan-

tum logic. Since 80th p-adic numbers are used in

applications to quantum physics. p-adic strings

and super strings were the first models of p-adic

quantum physics (see, for example, [17, 29, 50,

54]). The interest of physicists to p-adic numbers

is explained by the attempts to create new models

of space-time for the description of (fantastically

small) Planck distances.

There are some evidences that the standard

model based on real numbers is not adequate

to Planck’s domain. On the other hand, some

properties of fields of p-adic numbers seem to

be closely related to Planck’s domain. In partic-

ular, the fields of p-adic numbers have no order

structure.

The pioneer investigations on p-adic string

theory induced investigations on p-adic quantum

mechanics and field theory (see the books [31, 54,

55]). This investigations induce a development of

p-adic mathematics in many directions: theory of

distributions [6, 31], differential and pseudodif-

ferential equations [32, 56], theory of probability

[31, 56] spectral theory of operators in a p-adic

analogue of a Hilbert space [7, 8, 33].

The representation of p-adic numbers by se-

quences of digits gives a possibility to use this

number system for coding of information. There-

fore p-adic models can be used for the description

of many information processes. In particular, they

can be used in cognitive sciences, psychology and

sociology. Such models based on p-adic dynamical

systems [3–5].

The study of p-adic dynamical systems arises

in Diophantine geometry in the constructions

of canonical heights, used for counting rational

points on algebraic varieties over a number field,

as in [21].

There most recent monograph on p-adic dy-

namics is Anashin and Khrennikov [9]; nearly a

half of Silverman’s monograph [52] also concerns

p-adic dynamics.

Here are areas where p-adic dynamics proved

to be effective: computer science (straight line

programs), numerical analysis and simulations

(pseudorandom numbers), uniform distribution

of sequences, cryptography (stream ciphers, T-

functions), combinatorics (Latin squares), au-

tomata theory and formal languages, genetics.

The monograph [9] contains the corresponding

survey. For a newer results see recent papers and

references therein: [10, 14, 15, 28, 36, 37, 38, 48, 51].

Moreover, there are studies in computer science

and cryptography which along with mathematical

physics stimulated in 1990th intensive research in

p-adic dynamics since it was observed that major

computer instructions (and therefore programs

composed of these instructions) can be considered

as continuous transformations with respect to the

2-adic metric, see [11, 12].

In [33, 53] p-adic field have arisen in physics in

the theory of superstrings, promoting questions

about their dynamics. Also some applications

of p-adic dynamical systems to some biological,

physical systems has been proposed in [3, 4, 5,

22, 23, 33, 35]. Other studies of non-Archimedean

dynamics in the neighborhood of a periodic point

and of the counting of periodic points over global

fields using local fields appear in [39, 47]. It is

known that the analytic functions play important

role in complex analysis. In the p-adic analysis



4

the rational functions play a role similar to that of

analytic functions in complex analysis [49]. There-

fore, there naturally arises a question on study the

dynamics of these functions in the p-adic anal-

ysis. On the other hand, these p-adic dynamical

systems appear while studying p-adic Gibbs mea-

sures [26, 24, 44–46]. In [18, 19] dynamics on the

Fatou set of a rational function defined over some

finite extension of Qp have been studied, besides,

an analogue of Sullivan’s no wandering domains

theorem for p-adic rational functions which have

no wild recurrent Julia critical points was proved.

In [27] the behaviour and ergodicity of a p-adic

dynamical system f (x) = xn in the fields of p-adic

numbers Qp and complex p-adic numbers Cp was

investigated. Firstly, the problem of ergodicity of

perturbed monomial dynamical systems which

was posed in these papers and which stimulated

intensive research, was solved in [13]. Secondly,

quite recently a far-going generalisation of the

problem for arbitrary 1-Lipschitz transformations

of 2-adic spheres was also solved in [16]. Finally,

we note that not only polynomial and rational

p-adic dynamical systems has been studied: In

past decade, a significant progress was achieved

in a study of a very general p-adic dynamical

systems like non-expansive, locally analytic, shift-

like, etc.

It is also known [33, 41, 43, 56] that a num-

ber of p-adic models in physics cannot be de-

scribed using ordinary Kolmogorov’s probabil-

ity theory. In [34] an abstract p-adic probability

theory was developed by means of the theory

of non-Archimedean measures. Applications of

the non-Kolmogorov theory of probability can

be considered not only in physics, but in many

other sciences, especially in biology and possibly

in sociology. The general principle of statistical

stabilisation of relative frequencies is a new pos-

sibility to find a statistical information in the

chaotic (from the real point of view) sequences

of frequencies [31, 1, 2].

We refer the reader to [30, 24, 44–46] where

various models of statistical physics in the context

of p-adic fields are studied.

A non-Archimedean analogue of the Kol-

mogorov theorem was proved in [25]. Such

a result allows to construct wide classes of

stochastic processes and the possibility to de-

velop statistical mechanics in the context of p-adic

theory.

References

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[2] S. Albeverio and X. Zhao, Measure-valued branch-ing processes associated with random walks onp-adics, Ann. Probab. 28 (2000) 1680–1710.

[3] S. Albeverio, U. A. Rozikov and I. A. Sattarov,p-adic (2, 1)-rational dynamical systems, J. Math.Anal. Appl. 398(2) (2013) 553–566.

[4] S. Albeverio, A. Khrennikov and P. E. Kloeden,Memory retrieval as a p-adic dynamical system,BioSys. 49 (1999) 105–115.

[5] S. Albeverio, A. Khrennikov, B. Tirozzi and S.De Smedt, p-adic dynamical systems, Theor. Math.Phys. 114 (1998) 276–287.

[6] S. Albeverio, A. Y. Khrennikov and V. M.Shelkovich, Theory of p-Adic Distributions: Linearand Nonlinear Models (Cambridge University Press,2010).

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[8] S. Albeverio, R. Cianci and A. Yu. Khrennikov, Arepresentation of quantum field Hamiltonians ina p-adic Hilbert space, Theor. Math. Phys. 112(3)(1997) 355–374.

[9] V. Anashin and A. Khrennikov, Applied AlgebraicDynamics, de Gruyter Expositions in Mathematics,Vol. 49 (Walter de Gruyter, Berlin, New York,2009).

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U A Rozikov is a professor in Institute of Mathematics, Tashkent, Uzbekistan. He gradu-ated from the Samarkand State University (1993). He otained PhD (1995) and Doctor of Sciences in physics and mathematics (2001) degrees from the Institute of Mathematics, Tashkent. He is known for his works on the theory of Gibbs measures of models on trees of statistical mechanics (recently he published a book: Gibbs Measures on Cayley Trees (World Scientific, 2013)). He developed a contour method to study the models on trees and described complete set of periodic Gibbs measures. Rozikov has (with F Mukhamedov) an important contribution to non-Archimedean theory of phase transitions and dynamical systems. He has important results on non-Volterra quadratic operators. N Ganikhodjaev and Rozikov gave a construction of a quadratic operator which connects phases of the models of statistical mechanics with models of genetics. His most recent works are devoted to evolu-tion algebras of sex-linked populations. He was invited to several leading universities and research centres in the UK, France, Italy, Germany, Spain etc. His (more than 100) papers are published in front-line journals.

U A RozikovInstitute of Mathematics, Tashkent, [email protected]




Asia Pacific Mathematics Newsletter1

The Twin Prime Problemand Generalisations

(apres Yitang Zhang)

M Ram Murty

We give a short introduction to the recent break-

through theorem of Yitang Zhang that there are

infinitely many pairs of distinct primes (p, q)

with |p− q|< 70 million.

The twin prime problem asks if there are in-

finitely many primes p such that p + 2 is also

prime. More generally, one can ask if for any even

number a, there are infinitely many primes p such

that p + a is also prime. This problem inspired

the development of modern sieve theory. Though

several sophisticated tools were discovered, the

problem defied many attempts to resolve it until

recently.

On April 17, 2013, a relatively unknown math-

ematician from the University of New Hampshire,

Yitang Zhang, submitted a paper to the Annals

of Mathematics. The paper claimed to prove that

there are infinitely many pairs of distinct primes

(p, q) with |p − q| < 7 × 107. This was a major step

towards the celebrated twin prime conjecture! A

quick glance at the paper convinced the editors

that this was not a submission from a crank.

The paper was crystal clear and demonstrated a

consummate understanding of the latest technical

results in analytic number theory. Therefore, the

editors promptly sent it to several experts for

refereeing. The paper was accepted three weeks

later.

In this article, we will outline the proof of

this recent breakthrough theorem of Yitang Zhang

[1]. Even though this article is only an outline, it

should help the serious student to study Zhang’s

paper in greater detail. An essential ingredient in

Zhang’s proof is the idea of smoothness which

allows him to extend the range of applicability

of earlier theorems. (A number is said to be y-

smooth if all its prime factors are less than y.)

The rudimentary background in analytic number

theory is readily obtained from [2] and [3]. This

can be followed by a careful study of [4] and the

three papers [5–7].

1. Introduction and History

Let p1, p2, ... be the ascending sequence of prime

numbers. The twin prime problem is the ques-

tion of whether there are infinitely many pairs

of primes (p, q) with |p − q| = 2. This problem

is usually attributed to the ancient Greeks, but

this is very much Greek mythology and there is

no documentary evidence to support it. The first

published reference to this question appeared in

1849 by Alphonse de Polignac who conjectured

more generally that for any given even number

2a, there are infinitely many pairs of primes such

that |p − q| = 2a.

In a recent paper [1] in the Annals of Mathemat-

ics, Yitang Zhang proved that there are infinitely

many pairs of distinct primes (p, q) with

|p − q| < 7 × 107.

His proof depends on major milestones of 20th

century number theory and algebraic geometry.

Thus, it is definitely a 21st century theorem! Un-

doubtedly, his paper opens the door for further

improvements and it is our goal to discuss some

of these below.

After de Polignac’s conjecture, the first serious

paper on the subject was by Viggo Brun in 1915,

who, after studying the Eratosthenes sieve, de-

veloped a new sieve, now called the Brun sieve,

to study twin primes and related questions. He

proved that∑

p:p+2 prime

1

p< ∞.

By contrast, the sum of the reciprocals of the

primes diverges and so, this result shows that

(in some sense) if there are infinitely many twin

primes, they are very sparse.

A few years later, in 1923, Hardy and Little-

wood [8], made a more precise conjecture on the

number of twin primes up to x. They predicted

The Twin Prime Problemand Generalisations

(aprés Yitang Zhang)

M Ram Murty


Asia Pacific Mathematics Newsletter 2

that this number is (see [9, p. 371])

∼ 2

p>2

1 − 1

(p − 1)2

x

log2 x.

Here, the symbol A(x) ∼ B(x) means that A(x)/B(x)

tends to 1 as x tends to infinity.

They used the circle method, originally discov-

ered by Ramanujan and later developed by Hardy

and Ramanujan in their research related to the

partition function. After Ramanujan’s untimely

death, it was taken further by Hardy and Little-

wood in their series of papers on Waring’s prob-

lem. (The circle method is also called the “Hardy–

Littlewood method” by some mathematicians.) In

the third paper of this series, they realised the

potential of the circle method to make precise con-

jectures regarding additive questions, such as the

Goldbach conjecture and the twin prime problem.

Based on heuristic reasoning, it is not difficult

to see why such a conjecture should be true. The

prime number theorem tells us that the number

of primes π(x), up to x, is asymptotically x/ log x.

Thus, the probability that a random number in

[1, x] is prime is 1/ log x and so the probability that

both n and n + 2 are prime is about 1/ log2 x. The

constant is a bit more delicate to conjecture and

is best derived using the theory of Ramanujan–

Fourier series expansion of the von Mangoldt

function as in a recent paper of Gadiyar and

Padma [10] (see also [11] for a nice exposition).

However, it is possible to proceed as follows. By

the unique factorisation theorem of the natural

numbers, we can write

log n =

d|n

Λ(d),

where Λ(d) = log p if d is a power of a prime p and

zero otherwise. This is called the von Mangoldt

function. By the Mobius inversion formula, we

have for n > 1

Λ(n) =

d|n

µ(d) logn

d= −

d|n

µ(d) log d,

since

d|n µ(d) = 1 if n = 1 and zero otherwise.

Thus, to count twin primes, it is natural to study

p≤x

Λ(p + 2),

where the sum is over primes p less than x. Using

the formula for Λ(n), the sum above becomes

−

p≤x

d|p+2

µ(d) log d = −

d≤x+h

µ(d) log d

p≤x,p≡−2(mod d)

1.

The innermost sum is the number of primes p ≤ x

that are congruent to −2 (mod d), which for d odd

is asymptotic to π(x)/φ(d), where π(x) is the num-

ber of primes up to x, and φ is Euler’s function.

Ignoring the error terms, our main term now is

asymptotic to

−π(x)

d≤x+2,d odd

µ(d) log d

φ(d).

This suggests that

p≤x

Λ(p + 2) ∼ π(x)

−

d>1,d odd

µ(d) log d

φ(d)

.

The infinite series in the brackets is not absolutely

convergent. However, it converges conditionally

and can be evaluated as follows.

Consider the Dirichlet series

F(s) :=∞

d=1

µ(d)

φ(d)ds,

which converges absolutely for ℜ(s) > 0. Now,

F(s) admits an Euler product

p,(p,2)=1

1 − 1

ps(p − 1)

which resembles 1/ζ(s+1) (with the 2-Euler factor

removed) and so it is natural to write the product

as

ζ(s+1)−1(1−2−s−1)−1

p>2

1 −1

ps+1

−1

1 −1

ps(p − 1)

.

It is now easy to see that the Euler product

converges absolutely for ℜ(s) ≥ 0 and this gives

an analytic continuation of F(s) for ℜ(s) ≥ 0. The

twin prime constant is now F′(0) and because

ζ(s + 1) has a simple pole at s = 0 with residue

1, the term ζ(s+1)−1 has a zero at s = 0. Thus, our

heuristic reasoning gives

p≤x

Λ(p + 2) ∼ 2π(x)

p>2

1 −1

(p − 1)2

,

which agrees with the Hardy–Littlewood conjec-

ture (after applying partial summation). A similar

argument provides the conjectured formula of

Hardy and Littlewood for the number of prime

pairs that differ by an even number 2h.

The reader will note that one can make the

above argument precise by introducing the error

terms

E(x, d, a) := π(x, d, a) − π(x)

φ(d)



and it is easy to see that the error term in our

calculation is

d≤x+2

E(x, d,−2).

The Bombieri–Vinogradov theorem states that

d≤Q

|E(x, d,−2)| ≪ x

logA x

for any A > 0 and Q ≤ x1/2 log−B x, where B = B(A)

is a function of A. In fact, one can take B(A) = A+5

(see [3, p. 161]). Elliott and Halberstam [12] have

conjectured that the result is valid for any Q <

x1−ǫ for any ǫ > 0. Even admitting this conjecture,

we see that the interval [x1−ǫ , x] still needs to be

treated. It is this obstacle that motivates the use

of truncated von Mangoldt functions:

ΛD(n) :=

d|n,d<D

µ(d) log (D/d)

and more generally

ΛD(n; a) :=1

a!

d|n,d<D

µ(d) loga (D/d)

as will be indicated below.

2. The Basic Strategy of Zhang’s Proof

Let θ(n) = log n if n is prime and zero otherwise.

We will use the notation n ∼ x to mean that x <

n < 2x. Now, suppose we can find a positive real-

valued function f such that for

S1 =

n∼x

f (n),

S2 =

n∼x

θ(n) + θ(n + 2)

f (n),

we have

S2 − (log 3x)S1 > 0,

for sufficiently large x. Then we can deduce that

there exists an n such that n and n + 2 are both

prime with x < n < 2x. Such a technique and a

method to choose optimal functions f goes back

to the 1950’s and is rooted in the Selberg sieve.

See for example [2] for a short introduction to the

Selberg sieve.

The problem as posed above is intractable. So

we generalise the problem and consider sets

H = h1, h2, ..., hk.

It is reasonable to expect (under suitable condi-

tions) that there are infinitely many n such that

n+ h1, n+ h2, ..., n+ hk are all prime. This would be

a form of the generalised twin prime problem and

was first enunciated in the paper by Hardy and

Littlewood alluded to above. Clearly, we need to

put some conditions on H . Indeed, if for some

prime p the image of H (mod p) has size p, then

all the residue classes are represented by p so that

in the sequence,

n + h1, n + h2, ..., n + hk

there will always be some element divisible by p

and it is unreasonable to expect that for infinitely

many n all of these numbers are prime numbers.

So a necessary condition is that νp(H ) = |H| (mod

p) < p for every prime p. Under such a condition,

the set is called admissible and we expect this to

be the only local obstruction.

Zhang [1] proves:

Theorem 1. Suppose that H is admissible with k ≥3.5 × 106. Then, there are infinitely many positive

integers n such that the set

n + h1, ..., n + hk

contains at least two primes. Consequently,

lim infn→∞

(pn+1 − pn) < 7 × 107.

In other words, pn+1 − pn is bounded by 7 × 107 for

infinitely many n.

Zhang shows that the second assertion follows

from the first if we choose for H a set of k0 = 3.5×106 primes lying in the interval [3.5× 106, 7× 107].This can be done since

π(7 × 107) − π(3.5 × 106) > 3.5 × 106

from known explicit upper and lower bounds for

π(x) due to Dusart [13]. That such a set of primes

is admissible is easily checked. Indeed, if p > k0,

νp(H ) ≤ k0 < p. If p < k0 and νp(H ) = p, then

one of the prime elements is divisible by p and

hence equal to p, a contradiction since we chose

elements of H to be primes > k0.

The main strategy of the proof goes back to the

paper by Goldston, Pintz and Yildirim [4] where

they consider

S1 =

n∼x

f (n),

S2 =

n∼x

h∈H

θ(n + h)

f (n).

The idea is to show that for some admissible H ,

we have

S2 − (log 3x)S1 > 0.



This would imply that there are at least two

primes among the sequence

n + h1, ..., n + hk.

They choose, f (n) = λ(n)2 with

λ(n) =1

(k + ℓ)!

∑

d|P(n),d<D

µ(d)g(d),

where µ denotes the familiar Mobius function and

g(d) =

(

logD

d

)k+ℓ

,

and

P(n) =∏

h∈H

(n + h).

What is now needed is a good upper bound for S1

and a good lower bound for S2. This is the same

strategy adopted in [4]. To elaborate, let Ci(d) be

the set of solutions (mod d) for P(n− hi) ≡ 0 (mod

d) and define the singular series S by

S =

∏

p

(

1 −νp(H )

p

) (

1 − 1

p

)−k

.

With

T∗1 =1

(k + 2ℓ)!

(

2ℓ

ℓ

)

S(log D)k+2ℓ+ o((log x)k+2ℓ)

and

T∗2 =1

(k + 2ℓ + 1)!

(

2ℓ + 2

ℓ + 1

)

S(log D)k+2ℓ+1

+ o((log x)k+2ℓ+1),

the argument of [4] leads to

S2 − (log 3x)S1 = (kT∗2 − (log x)T∗1)x

+O(x(log x)k+ℓ) +O(E),

where

E =∑

1≤i≤k

∑

d<D2

µ(d)τ3(d)τk−1(d)∑

c∈Ci(d)

∆(θ; d, c)

and

∆(θ; d, c) =∑

n∼x,n≡c(mod d)

θ(n) − 1

φ(d)

∑

n∼x

θ(n).

We write a(x) = o(b(x)) if a(x)/b(x) tends to zero as

x tends to infinity. We also write for non-negative

b(x), a(x) = O(b(x)) (or a(x) ≪ b(x)) if there is a

constant K such that |a(x)| ≤ Kb(x) for all x.

Let us look at the main term. A quick calcula-

tion shows that it is(

2k(2ℓ + 1)

(k + 2ℓ + 1)(ℓ + 1)log D − log x

)

× (log D)k+2ℓ

(k + 2ℓ)!

(

2ℓ

ℓ

)

Sx.

We need to choose D so that the term in brackets

is positive. Let D = xα. The term in brackets is

positive provided

2k(2ℓ + 1)

(k + 2ℓ + 1)(ℓ + 1)α − 1 > 0.

That is, we need

α >(k + 2ℓ + 1)(ℓ + 1)

2k(2ℓ + 1)=

1

4

(

1 +2ℓ + 1

k

) (

1 +1

2ℓ + 1

)

.

From this, we see that if k and ℓ are chosen to

be sufficiently large and ℓ/k is sufficiently small,

the quantity on the right side is asymptotic to 1/4.

Thus, if we can choose α > 1/4 then we can find

choices of k and ℓ for which the main term is

positive.

The error term is easily recognised to be re-

lated to the Bombieri–Vinogradov theorem which

shows that for any α < 1/4, the error is negli-

gible. So we seem to be at an impasse. How-

ever, a well-known conjecture of Elliott and

Halbertsam [12] predicts that the error is negli-

gible for any α < 1/2. This is where things stood

in 2005 after the appearance of the paper [4].

The new contribution of Zhang is that in the

sums T∗1 and T∗2 (which are actually defined as

terms involving the Mobius function and g(d)),

he notes that terms with divisors d having a large

prime divisor are relatively small. So if we let P

be the product of primes less than a small power

of x and impose the condition that d|P in the

Bombieri–Vinogradov theorem then he is able to

establish the following:

Theorem 2. For 1 ≤ i ≤ k, we have∑

d<D2,d|P

∑

c∈Ci(d)

|∆(θ; d, c)| ≪ x

logA x,

for any A > 0 and D = xα with α = 1/4 + 1/1168.

This theorem is the new innovation. Zhang

admits that his choice of k may not be optimal and

that the optimal value of k is “an open problem

that will not be discussed in this paper”.

After the appearance of Zhang’s paper, several

blogs have discussed improvements, the most

notable being Tao’s blog [14] and another blog

[15], where (as of July 10, 2013), k in Zhang’s

theorem has been reduced to 1466 and the gap

between consecutive primes is now at most 12,006

infinitely often. These are encouraging develop-

ments and perhaps we are well on our way to

resolving the twin prime conjecture in the fore-

seeable future.



3. A Closer Look at S1 and S2

The analysis of S1 and S2 follows closely the

treatment in [4] but with a small change. Zhang

[1] observes that it is convenient to introduce the

condition d|P with P being the product of primes

less than x with = 1/1168. With this under-

standing, the terms S1 and S2 are easily handled

by direct expansion of the square. Indeed, the first

term for S1 is

q≤Dq|P

r≤Dr|P

µ(q)µ(r)g(q)g(q)

n∼x[q,r]|P(n)

1.

Following Zhang, let 1(q) be the number of so-

lutions of the congruence P(n) ≡ 0 (mod q) for q

squarefree and zero otherwise. By the Chinese re-

mainder theorem, this is a multiplicative function

and we have 1(p) = k if p is coprime to

1≤i<j≤k

|hi − hj|

and in general, 1(p) ≤ k. Thus, the innermost sum

is

x1([q, r])

[q, r]+O(1([q, r])),

where the implied constant is bounded by unity.

The main term of S1 is

x

q≤Dq|P

r≤Dr|P

µ(q)µ(r)g(q)g(r)([q, r])

[q, r]+O(D2+ǫ),

for any ǫ > 0 since ([q, r]) ≤ kω([q,r]), where

ω(n) denotes the number of distinct prime factors

of n. Elementary number theory shows that this

function is O(Dǫ) for q, r ≤ D and any ǫ > 0.

We let d0 = (q, r) and write q = d0d1, r = d0d2

with (d1, d2) = 1. The sum S1 now becomes

T1x +O(D2+ǫ),

where

T1 =

d0 |P

d1 |P

d2 |P

µ(d1)µ(d2)1(d0d1d2)

d0d1d2g(d0d1)g(d0d2) .

The point is that the same sum without the

restriction di|P for i = 0, 1, 2 has already been

studied in [4] and the initial section of Zhang’s

paper is devoted to showing that (essentially)

the same asymptotic formula of [4] (namely the

formula for T∗1 given above) still holds with the

extra condition d|P. (More precisely, what is de-

rived is an upper bound for T1 which is within

e−1200 of T∗1.)

To derive a lower bound for S2, we have (after

a minor change of variables)

S2 =

k

i=1

n∼x

θ(n)λ(n − hi)2.

We expand the square, interchange summation

and obtain

k

i=1

q|P

r|Pµ(q)µ(r)g(q)g(r)

n∼x[q,r]|P(n−hi )

θ(n).

To handle the innermost sum, we observe that the

condition

P(n − hi) ≡ 0(mod d) (n, d) = 1

is equivalent to n ≡ c (mod d) for some c ∈ Ci(d).

For d = p, a prime, this number is the number of

distinct residue classes (mod p) occupied by the

set hi−hj : hi hj(mod p) which is νp(H )−1. Thus,

defining a multiplicative function (supported only

on squarefree values of d) 2(d) by setting 2(p) =

νp(H ) − 1 and extending it multiplicatively, we

obtain (using notation introduced earlier), the in-

nermost sum as

c∈Ci([q,r])

n∼xn≡c( mod [q,r])

θ(n) =2([q, r])φ([q, r])

n∼x

θ(n)

+

c∈Ci([q,r])

∆(θ; [q, r], c).

Now it is an elementary exercise (see for example,

[2]) to show that the number of pairs q, r such

that [q, r] = d is given by the divisor function τ3(d)

which is the number of ways of writing d as a

product of three positive integers. Thus, we can

simplify this to

n∼x

θ(n)λ(n − hi)2= T2

n∼x

θ(n) +O(Ei),

where

T2 =

q|P

r|P

µ(q)g(q)µ(r)g(r)

φ([q, r])2([q, r])

and

Ei =

d<D2,d|P

τ3(d)2(d)

c∈Ci(d)

|∆(θ, d, c)|.

The error term is estimated using Theorem 2.

Indeed, by the Cauchy–Schwarz inequality

Ei ≪

d<D2

c∈Ci(d)

τ23(d)2

2(d)|∆(θ; d, c)|

1/2

×

d<D2,d|P

c∈Ci(d)

|∆(θ; d, c)|

1/2

.



On the first factor, we use the trivial estimate

|∆(θ; d, c)| ≪ x

d+ 1

and see (by elementary number theory) that its

contribution is at most a power of a logarithm.

For the second factor, we use Theorem 2 to save

the few powers of logarithm. Thus,

S2 = kT2x +O(x(log x)−A).

As before, we can rewrite T2 as

T2 =

∑

d0 |P

∑

d1 |P

∑

d2 |P

µ(d1d2)2(d0d1d2)

φ(d0d1d2)g(d0d1)g(d0d2).

Again, this sum without the restriction di|P i =

0, 1, 2 was treated in [4] and shown to have the

asymptotic behaviour given by T∗2. Zhang shows

that T2 does not differ much from T∗2 (more pre-

cisely, that it is within a factor of e−1181.579 of T∗2).

Thus,

S2 − (log 3x)S1 ≥ ωSx(log D)k+2ℓ+1+ o(x(log x)k+2ℓ+1),

where

ω =1

(k + 2ℓ)!

(

2ℓ

ℓ

) (

2(2ℓ + 1)k

(ℓ + 1)(k + 2ℓ + 1)−

1

α

)

nearly. For α = 1/4 + 1/1168, it is easily verified

that ω > 0.

This calculation already shows that if we have

the Elliott–Halberstam conjecture, then for some

k0 and any admissible k0-tuple H , the set n +h : h ∈ H contains at least two primes for in-

finitely many values of n. (Tao has labelled this as

DHL[k0, 2].) Farkas, Pintz and Revesz [16] made

this relationship a bit more precise as follows.

Suppose we have for any A > 0,∑

d<Q

max(a,d)=1

|E(x, d, a)| ≪ x

logA x,

with Q = xθ. We call this the modified Elliott–

Halberstam conjecture EH[θ]. Let jn denote the

first positive zero of the Bessel function (of the

first kind) Jn(x) given by the power series

∞∑

j=0

( − 1) j

22j+nj!(n + j)!x2j+n.

Then we may take any k0 ≥ 2 which satisfies the

inequalityj2k0−2

k0(k0 − 1)< 2θ

and for this k0 we have DHL[k0, 2]. The left-hand

side is greater than 1 and tends to 1 as k0 tends

to infinity.

4. Variations of Bombieri–Vinogradov

Theorem and Extensions

Since we are unable to prove EH[θ] for any θ >

1/2, we look for some suitable modification. Based

on the works of Motohashi, Pintz and Zhang,

Tao [14] makes the following conjecture which he

labels as MPZ[, δ]: let H be a fixed k0-tuple (not

necessarily admissible) with k0 ≥ 2. Fix w and set

W to be the product of the primes less than w.

Let b mod W be a coprime residue class and put

I = (w, xδ). Let SI be the set of squarefree numbers

all of whose prime factors lie in I. Put

∆b,W(Λ; q, a) :=∑

n∼x,n≡a( mod q)n≡b( mod W)

Λ(n)

− 1

φ(q)

∑

n∼x,n≡b( mod W)

Λ(n)

and C(q) is the set of zeros (mod q) of the polyno-

mial P(n). Then the conjecture MPZ[, δ] is that∑

q<x12+

q∈SI

∑

a∈C(q)

|∆b,W(Λ; q, a)| ≪ x

logA x

for any fixed A > 0. Zhang proved that MPZ[,]

holds for any 0 < < 1/1168. Apparently,

Zhang’s argument can be extended to show that

MPZ[, δ] is true provided

207 + 43δ <1

4.

The relationship of the MPZ conjecture to the

DHL conjecture is given by (see [14]) the follow-

ing result. Let 0 < < 1/4 and 0 < δ < 1/4 + .

Let k0 ≥ 2 be an integer which satisfies

1 + 4 >j2k0−2

k0(k0 − 1)(1 + κ),

where

κ :=∑

1≤n< 1+42δ

(

1 − 2nδ

1 + 4

)k0/2 n∏

j=1

(

1 + 3k0 log(

1 +1

j

))

.

Then MPZ[, δ] implies DHL[k0, 2]. It is the fine

tuning of this theorem along with other observa-

tions (regarding admissible sets) that have led to

the numerical improvements in Zhang’s theorem.

Thus, to prove MPZ[, δ], we may restrict our

moduli to be in the range (x1/2−ǫ , x1/2+2) since the

initial range (1, x1/2−ǫ) can be treated using the

classical Bombieri–Vinogradov theorem. Also, it

is not difficult to see that θ can be replaced by the

von Mangoldt function Λ since the contribution



from prime powers (squares and higher) can be

shown to be negligible.

An important idea in all proofs of Bombieri–

Vinogradov theorem is to decompose the von

Mangoldt function into sums of “short sums”. To

be precise, let us define the Dirichlet convolution

of two arithmetic functions f , g to be

( f ∗ g)(n) :=∑

d|n

f (d)g(n/d).

Let L(n) = log n, 1(n) = 1 for all n and set δ(n) = 1

if n = 1 and zero otherwise. Then,

Λ = µ ∗ L and δ = µ ∗ 1.

If we write f ∗n to denote the n-fold Dirichlet

convolution, then

Λ = µ∗10 ∗ 1∗9 ∗ L

is a fact utilised by Zhang (in his Lemma 6) to

decompose the von Mangoldt function into “short

sums”. Let x∗ > (2x)1/10 and write µ = µ≤x∗ + µ>x∗ ,

where in the first term, µ is restricted to [1, x∗] and

in the second, to the range > x∗. Clearly

µ∗10>x∗ ∗ 1∗9 ∗ L = 0,

since n ∼ x cannot be factored as a product of

10 terms each larger than x∗. Thus, writing µ>x∗ =

µ − µ≤x∗ and using the binomial formula we see

easily that

Λ =

10∑

j=1

( −1) j−1

(

10

j

)

µ∗j≤x∗ ∗ 1∗( j−1) ∗ L

which is an identity of Heath-Brown (but the idea

of decomposing arithmetic functions in this way

goes back to Linnik).

One can also use the formal identity

−ζ′(s)

ζ(s)= − ζ′(s)

1 + (ζ(s) − 1)

= ζ′(s)(−1 + (ζ(s) − 1) − (ζ(s) − 1)2+ · · · ).

This allows one to write the von Mangoldt func-

tion as a sum of divisor functions and in this

way one reduces the study of primes in arith-

metic progressions to the study of divisor sums

in arithmetic progressions.

In any case, one uses this decomposition of Λ

in the treatment of d in the range [x1/2−ǫ , x1/2+2].The decomposition leads to three kinds of sums

(called Type I, II and III in the literature, not

to be confused with the types occurring in the

Vaughan method). The first type involves convo-

lutions α ∗ β, where β is supported on the interval

[x3/8+8, x1/2−4] which forces the argument of α to

be in [x1/2+4, x5/8−8]. Type II sums again involve

convolutions of the form α ∗ β, but with β now

supported on [x1/2−4, x1/2] so that α is supported

on [x1/2, x1/2+4], and Type III are the remaining

types.

In 1976, Motohashi [17] derived a general in-

duction principle to derive theorems of Bombieri–

Vinogradov type for a wide class of arithmetical

functions. Much of the treatment of these types

of sums follows earlier work of Bombieri, Fried-

lander and Iwaniec [5] and one needs to verify

that the estimates are still valid with the extra

condition d|P. The point to note is that in the

range under consideration, namely d > x1/2−ǫ ,

the condition that d|P means we can factor d

as d = rq with r lying in a suitable interval.

This factorization turns out to be crucial in the

estimates. Thus, “smoothness” of d is essential in

this part of the argument.

Another noteworthy point involves Zhang’s

estimation of type III sums. His analysis leads

to the question of estimating hyper-Kloosterman

sums for which Bombieri and Birch have given

estimates using Deligne’s work on the Weil con-

jectures. Therefore, this work on the twin prime

problem is very much a 21st century theorem!

References

[1] Y. Zhang, Bounded gaps between primes, Annalsof Math., 2013.

[2] M. Ram Murty, Problems in Analytic NumberTheory, 2nd edn. (Springer, 2008).

[3] H. Davenport, Multiplicative Number Theory, 3rdedn. (Springer, 2000).

[4] D. Goldston, J. Pintz and C. Y. Yildirim, Primes inTuples, I, Annals of Math. 170 (2009) 819–862.

[5] E. Bombieri, J. Friedlander and H. Iwaniec, Primesin arithmetic progressions to large moduli, ActaMath. 156 (1986) 203–251.

[6] E. Bombieri, J. Friedlander and H. Iwaniec, Primesin arithmetic progressions to large moduli II, Math.Annalen 277 (1987) 361–393.

[7] E. Bombieri, J. Friedlander and H. Iwaniec, Primesin arithmetic progressions to large moduli III, J.Amer. Math. Soc. 2 (1989) 215–224.

[8] G. H. Hardy and J. E. Littlewood, Some problemsof Partitio Numerorum III: on the expression of anumber as a sum of primes, Acta Math. 44 (1923)1–70.

[9] G. H. Hardy and E. M. Wright, An Introduction tothe Theory of Numbers, 6th edn. (Oxford UniversityPress, 2008).

[10] H. G. Gadiyar and R. Padma, Ramanujan-Fourierseries, the Wiener-Khintchine formula and the dis-tribution of prime pairs, Phys. A. 269(2–4) (1999)503–510.

[11] B. Bagchi, A promising approach to the twin primeproblem, Resonance 8(3) (2003) 26–31.



[12] P. D. T. A. Elliott and H. Halberstam, A conjecturein number theory, symp. Math. 4 (1968) 59–72.

[13] P. Dusart, Autour de la fonction qui compte lenombre de nombres premiers, Ph.D. thesis, Uni-versite de Limoges, 1998.

[14] T. Tao’s, blog:terrytao.wordpress.com/tag/yoichi-motohashi/

[15] michaelnielsen.org/polymath1/index.php?title =Bounded\ gaps\ between\ primes

[16] B. Farkas, J. Pintz and S. Revesz, On the optimalweight function in the Goldston-Pintz-Yildirimmethod for finding small gaps between consecu-tive primes, to appear.

[17] Y. Motohashi, An induction principle for the gen-eralization of Bombieri’s prime number theorem,Proc. Japan Acad. 52(6) (1976) 273–275.

M Ram Murty Queen’s University, [email protected]

M Ram Murty, a Canadian mathematician, is currently Queen's Research Chair in Mathematics and Philosophy at the Queen's University in Canada. He is also an adjunct professor at several institutions in India (TIFR in Mumbai, IMSc in Chennai and HRI in Allahabad.) He also teaches Indian philosophy at Queen's University and has recently published a book titled Indian Philosophy and has writtenmany popular monographs for students of mathematics.

Reproduced from Resonance of Indian Academy of Sciences



Discrepancy, Graphs, and theKadison–Singer Problem

N Srivastava

Discrepancy theory seeks to understand how well

a continuous object can be approximated by a

discrete one, with respect to some measure of

uniformity. For instance, a celebrated result due to

Spencer says that given any set family S1, . . . , Sn ⊂[n], it is possible to colour the elements of [n] Red

and Blue in a manner that:

∀Si ||Si ∩ R| − |Si|2| ≤ 3

√n,

where R ⊂ [n] denotes the set of red elements.

In other words, it is possible to partition [n] into

two subsets so that this partition is very close

to balanced on each one of the test sets Si. Note

that a “continuous” partition which splits each

element exactly in half will be exactly balanced

on each Si; the content of Spencer’s theorem is

that we can get very close to this ideal situation

with an actual, discrete partition which respects

the wholeness of each element.

Spencer’s theorem and its variants have had

applications in approximation algorithms, numer-

ical integration, and many other areas. In this

post I will describe a new discrepancy theorem [1]

due to Adam Marcus, Dan Spielman, and myself,

which also seems to have many applications. The

theorem is about “uniformly” partitioning sets of

vectors in Rn and says the following:

Theorem 1. (implied by Corollary 1.3 in [1])

Given vectors v1, . . . , vm ∈ Rn satisfying vi2 ≤ α and

m∑

i=1

vi, x2 = 1 ∀x = 1, (1)

there exists a partition T1 ∪ T2 = [m] satisfying∣

∣

∣

∣

∣

∣

∣

∣

∑

i∈Tj

vi, x2 − 1

2

∣

∣

∣

∣

∣

∣

∣

∣

≤ 5√α ∀x = 1.

Thus, instead of being nearly balanced with re-

spect to a finite set family as in Spencer’s setting,

we require our partition of v1, . . . , vm to be nearly

balanced with respect to the infinite set of test

vectors x = 1. In this context, “nearly balanced”

means that about half of the quadratic form

(“energy”) of the v1, . . . , vm in direction x comes

from T1 (and the rest, which must also be about

half, comes from T2). We will henceforth refer

to the maximum deviation from perfect balance

(i.e. 1/2) over all x as the discrepancy of a partition.

Note that every partition has discrepancy at most

1/2, so the guarantee of the theorem is nontrivial

whenever 5√α < 1/2.

This type of theorem was conjectured to hold

by Nik Weaver [2], with any constant strictly less

than 1/2 (independent of m and n) in place of

5√α. The reason he was interested in it is that

he showed it implies a positive solution to the

so-called Kadison–Singer (KS) problem, a central

question in operator theory which had been open

since 1959. KS was itself motivated by a basic

question about the mathematical foundations of

quantum mechanics — check out the blog soul-

physics [3] for an intuitive description of its

physical significance. If you want to know exactly

what the statement of KS is and how it can be

reduced to finite-dimensional vector discrepancy

statements similar to Theorem 1, I highly rec-

ommend the accessible and self-contained survey

article written recently by Nick Harvey [4].

In the rest of the post I will try to demystify

what Theorem 1 is about, say a bit about the

proof, and describe a simple application to graph

theory.

1. What the Theorem Says

Let’s examine how restrictive the hypotheses of

Theorem 1 are. To see that some bound on the

norms of the vi is necessary for the conclusion of

the theorem to hold, consider an example where

one vector has large norm, say v12 = 3/4. In any

partition of v1, . . . , vm, one of the sets, say T1, will

contain v1. If we now examine the quadratic form

in the direction x = v1/v1, we see that∑

i∈T1

vi, x2 ≥ v12 = 3/4,

so this partition has discrepancy at least 1/4.

The problem is that v1 by itself accounts for

Discrepancy, Graphs, and theKadison–Singer Problem

N Srivastava



significantly more than half of the quadratic form

in direction x, and there is no way to get closer

to half without splitting the vector.

Another instructive example is the one-

dimensional instance v1, . . . , vm ∈ R1, with v2i=

1/m = α for all i and m odd. Here, the larger

side of any partition must have

i∈Tjvi, e12 =

i∈Tjv2

i≥ 1/2 + α/2, leading to a discrepancy of

at least α/2.

In general, the above examples show that the

presence of large vectors is an obstruction to the

existence of a low discrepancy partition. Theorem

1 shows that this is the only obstruction, and

if all the vectors have sufficiently small norm

then an appropriately low discrepancy partition

must exist. It is worth mentioning that by a

more sophisticated example than the ones above,

Weaver has shown that the O(√α) dependence in

Theorem 1 cannot be improved.

Let us now consider the “isotropy” condition

(1). This may seem like a very strong requirement

at first, but it is in fact best viewed as a normali-

sation condition. To see why, let us first write the

theorem using matrix notation. It says that given

vectors v1, . . . , vm ∈ Rn with vi2 ≤ α and

m

i=1

vivTi = I,

there is a partition T1 ∪ T2 = [m] satisfying

1

2− 5√α

I

i∈Tj

vivTi

1

2+ 5√α

I,

where A B means that

xTAx ≤ xTBx ∀x ∈ Rn,

or equivalently that B−A is positive semidefinite.

Now suppose I am given some arbitrary vec-

tors w1, . . . , wm ∈ Rn, which are not necessar-

ily isotropic. Assume that the span of the wi

is Rn (otherwise, change the basis and write

them as vectors in some lower-dimensional Rk).

This implies that the positive semidefinite matrix

W :=m

i=1 wiwTi

is invertible, and therefore has

a negative square root W−1/2. Now consider the

“normalised” vectors

vi =W−1/2wi, i = 1, . . . , m

and observe that

m

i=1

vivTi =W−1/2

m

i=1

wiwTi

W−1/2= I,

so these vectors are isotropic. The normalised

vectors have norms

vi2 = W−1/2wi2.

To better grasp what these norms mean, we can

write:

W−1/2wi2 = supx0

x, W−1/2wi2

xTx( ∗ )

= supy=W1/2x0

W1/2y, W−1/2wi2

yTWy

= supy0

y, wi2

iy, wi2.

Thus, the norms vi2 measure the maximum frac-

tion of the quadratic form of W that a single vector

wi can be responsible for — exactly the critical

quantity in the example at the beginning of this

section.

These numbers are sometimes called “leverage

scores” in numerical linear algebra and statistics.

As long as the leverage scores are bounded by α,

we can apply Theorem 1 to v1, . . . , vm to obtain a

partition satisfying

1

2− 5√α

I

i∈Tj

vivTi = W−1/2

i∈Tj

wiwTi

W−1/2

1

2+ 5√α

I.

We now appeal to the fact that A B iff MAM MBM, for any invertible M (this amounts to a

simple change of variables similar to what we did

in (*)). Multiplying by W1/2 on both sides, we find

that the partition T1 ∪ T2 guaranteed by Theorem

1 satisfies:

1

2− 5√α

m

i=1

wiwTi

i∈Tj

wiwTi

1

2+ 5√α

m

i=1

wiwTi

. (2)

Thus, we have the following restatement of

Theorem 1:

Theorem 2. Given any vectors w1, . . . , wm ∈ Rn, there

is a partition T1 ∪ T2 = [m] such that (2) holds with

α = maxi wTi(m

i=1 wiwTi)+wi.

Note that we have used the pseudoinverse

instead of the usual inverse to handle the case

where the vectors do not span Rn.



For those who do not like to think about sums

of rank one matrices (I know you’re out there),

Theorem 2 may be restated very concretely as:

Theorem 3. Any matrix Bm×n whose rows wTi

have

leverage scores wTi(BTB)+wi bounded by α can be

partitioned into two row submatrices B1 and B2 so

that for all x ∈ Rn:

(1/2 − 5√α)Bx2 ≤ Bjx2 ≤ (1/2 + 5

√α)Bx2.

The reason this theorem is powerful is that lots

of diverse objects can be encoded as quadratic

forms of matrices. We will see one such applica-

tion later in the post.

2. Matrix Chernoff Bounds and

Interlacing Polynomials

Let me quickly say a bit about the proof of

Theorem 1. One reasonable way to try to find a

good partition T1 ∪ T2 is randomly, and indeed

this strategy is successful to a certain extent. The

tool that we use to analyse a random partition

is the so-called “Matrix Chernoff Bound”, de-

veloped and refined by Lust-Piquard, Rudelson,

Ahlswede-Winter, Tropp, and others. The variant

that is most convenient for our application is the

following:

Theorem 4. (Theorem 4.1 in [5])

Given symmetric matrices A1 . . . , Am ∈ Rn×n and

independent random Bernoulli signs ǫ1, . . . , ǫm, we

have

P

m

i=1

ǫiAi

≥ t

≤ 2n · exp

− t2

2m

i=1 A2i

.

Applying the theorem to Ai = vivTi

and taking

T1 = i : ǫi = +1 yields Theorem 1 with a

discrepancy of O(

α log n), which is nontrivial

when α ≤ O(1/ log n). This bound is interesting

and useful in some settings, but it is not sufficient

to prove the Kadison–Singer conjecture (which

requires a uniform bound as n → ∞), or for the

application in the next section. It may be seen

as analogous to the discrepancy of O(

n log n)

achieved by a random colouring of a set family

S1, . . . , Sn ⊂ [n], which is easily analysed using the

usual Chernoff bound and a union bound.

In order to remove the logarithmic factor

and obtain Theorem 1, we prove the following

stronger but less general inequality, which con-

trols the deviation of a sum of independent rank-

one matrices at a constant rather than logarithmic

scale, but only with nonzero (rather than high)

probability:

Theorem 5. (Theorem 1.2 in [1])

If ǫ > 0 and v1, . . . , vm are independent random vectors

in Rn with finite support such that

m

i=1

EvivTi = I,

and

Evi2 ≤ α

for all i, then

P

m

i=1

vivTi

≤ (1 +√α)2

> 0.

The conclusion of the theorem is equivalent to

the following existence statement: there is a point

ω ∈ Ω in the probability space implicitly defined

by the vis such that

i≤m

vi(ω)vi(ω)T

≤ (1 +√α)2.

To prove the theorem, we begin by considering

for every ω the univariate polynomial

P[ω](x) := det

xI −

i≤m

vi(ω)vi(ω)T

.

The roots of P[ω] are real since it is the charac-

teristic polynomial of a symmetric matrix, and in

particular the largest root is equal to the spectral

norm of

i≤m vi(ω)vi(ω)T.

The proof now proceeds in two steps. First, we

show that there must exist an ω such that

λmax(P[ω]) ≤ λmax(EP), (3)

where λmax denotes the largest root of a poly-

nomial. This type of statement may be seen as

a generalisation of the probabilistic method to

polynomial-valued random variables, and was

introduced in the paper [6], where we used it to

show the existence of bipartite Ramanujan graphs

of every degree. Note that (3) does not hold for

general polynomial-valued random variables —

in general, the roots of a sum of polynomials

do not have much to do with the roots of the

individual polynomials. The reason it holds in this

particular case is that the P[ω] are generated by

sums of rank-one matrices (which by Cauchy’s

theorem produce interlacing characteristic poly-

nomials) and form what we call an “interlacing

family”.



The second step is to upper bound the roots

of the expected polynomial µ(x) := EP(x). It turns

out that the right way to do this is to write µ(x)

as a linear transformation of a certain m-variate

polynomial Q(z1, . . . , zm), and show that Q does

not have any roots in a certain region of Rm.

This is achieved by a new multivariate general-

isation of the “barrier function” argument used

in [7] to construct spectral sparsifiers of graphs.

The multivariate barrier argument relies heavily

on the theory of real stable polynomials, which

are a multivariate generalisation of real-rooted

polynomials.

Rather than giving any further details, I en-

courage you to read the paper. The proof is not

difficult to follow, and from what I have heard

quite “readable”.

3. Partitioning a Graph into Sparsifiers

One very fruitful setting in which to apply The-

orem 2 is that of Laplacian matrices of graphs.

Recall that for an undirected graph G = (V, E) on

n vertices, the Laplacian is the n × n symmetric

matrix defined by:

LG =

∑

ij∈Ebijb

Tij ,

where bij := (ei − ej) is the incidence vector of the

edge ij. The Laplacian quadratic form

xTLGx =∑

ij∈E(x(i) − x(j))2

encodes a lot of useful information about a graph.

For instance, it is easy to check that given any cut

S ⊂ V, the quadratic form xTSLGxS of the indicator

vector xS(i) = 1i∈S is equal to the number of

edges between S and S. Thus, the values of xTLGx

completely determine the cut structure of G. (We

mention in passing that the extremisers of the

quadratic form are eigenvalues and are related to

various other properties of G — this is the subject

of spectral graph theory.)

Now consider G = Kn, the complete graph on

n vertices, which has Laplacian

LKn=

∑

ij

bijbTij .

An elementary calculation reveals that the lever-

age scores in this graph are all very small:

bTij L+

Knbij =

2

n.

This is a good time to mention that the leverage

scores of the incidence vectors bij in any graph G

have a natural interpretation — they are simply

the effective resistances of the edges ij when the

graph is viewed as an electrical network (this

happens because inverting LG is equivalent to

computing an electrical flow, and the quantity

xTL+G

x is equal to the energy dissipated by the

flow.) In any case, for the complete graph, all of

the edges have effective resistances equal to 2/n,

so we may apply Theorem 2 with α = 2/n to

conclude that there is a partition of the edges into

two sets, T1 and T2, each satisfying

(

1/2 −O(1/√

n))

LKn∑

ij∈Tk

bijbTij

(

1/2 +O(1/√

n))

LKn. (4)

Now observe that each sum over Tk is the Lapla-

cian LGkof a subgraph Gk of Kn. By recalling the

connection to cuts, this implies that Kn can be par-

titioned into two subgraphs, G1 and G2, each of

which approximates its cuts up to a 1/2±O(1/√

n)

factor.

This seems like a cute result, but we can go a

lot further. As long as the effective resistances of

edges in G1 and G2 are sufficiently small, we can

apply Theorem 2 again to each of them to obtain

four subgraphs. And then again to obtain eight

subgraphs, and so on.

How long can we keep doing this? The an-

swer depends on how fast the effective resistances

grow as we keep partitioning the graph. The fol-

lowing simple calculation reveals that they grow

geometrically at a favourable rate. Initially, all of

the effective resistances are equal to ℓ0 = 2/n. After

one partition, the maximum effective resistance of

an edge in Gk is at most

ℓ1 := maxij∈Gk

bTij L+

Gkbij ≤ (1/2 −O(1/

√n))−1bijL

+

Knbij

= (1/2 −O(1/√

n))−1 · (2/n).

In general, after i levels of partitioning, we have

the inequalities:

2 exp (O(√

ℓi−1))ℓi−1 ≥ (1/2 −O(√

ℓi−1))−1ℓi−1

≥ ℓi≥ (1/2 +O(

√

ℓi−1))−1ℓi−1

≥ (3/2)ℓi−1,

as long as ℓi−1 is bounded by some sufficiently

small absolute constant δ. Applying these inequal-



ities iteratively we find that after t levels:

ℓt ≤ 2t exp

O

t−1

i=0

ℓi

ℓ0

≤ 2t · exp

O

t−1

i=0

(2/3)t−1−iℓt−1

· (2/n)

≤ exp (O(√δ)) · 2t(2/n),

and the inequalities are valid as long as we main-

tain that ℓt−1 ≤ δ. Taking binary logs, we find that

these conditions are satisfied as long as

O(√δ) + t + log (2/n) ≤ log (δ),

which means we can continue the recursion for

t = log n − 1 + log (δ) −O(√δ) = log n −O(1)

levels. This yields a partition of Kn into O(n) sub-

graphs, each of which is an O(1)-factor spectral

approximation of (1/2t)Kn, in the sense of (4). This

latter approximation property implies that each

of the graphs must have constant degree (by con-

sidering that the degree cuts must approximate

those of (1/2t)Kn) and constant spectral gap; thus

we have shown that Kn can be partitioned into

O(n) constant degree expander graphs.

The real punchline, however, is that we did

not use anything special about the structure of

Kn other than the fact that its effective resistances

are bounded by O(1/n). In fact, the above proof

works exactly the same way on any graph on n

vertices with m edges, whose effective resistances

are bounded by O(n/m) — for such a graph, the

same calculations reveal that we can recursively

partition the graph for log (m/n) − O(1) levels,

while maintaining a constant factor approxima-

tion! Note that the total effective resistance of any

unweighted graph on n vertices is n − 1, so the

boundedness condition is just saying that every

effective resistance is at most a constant times the

average over all m edges.

For instance, the effective resistances of all

edges in the hypercube Qn on N = 2n vertices

are very close to 1/2n = 1/2 log N. Thus, repeat-

edly applying Theorem 2 implies that it can be

partitioned into O( log N) constant degree sub-

graphs, each of which is an O(1)-factor spectral

approximation of 1/ log N · Qn. In fact, this type

of conclusion holds for any edge-transitive graph,

in which symmetry implies that each edge has

exactly the same effective resistance.

The above result may be seen as a gener-

alisation of the theorem of Frieze and Molloy

[9], which says that up to a certain extent, any

sufficiently good expander graph may be parti-

tioned into sparser expander graphs. It may also

be seen as an unweighted version of the spectral

sparsification theorem of Batson, Spielman, and

myself [7], which says that every graph has a

weighted O(1)-factor spectral approximation with

O(n) edges. The recursive partitioning argument

that we have used is quite natural and appears to

have been observed a number of times in various

contexts; see for instance paper of Rudelson [10],

as well as the very recent work of Harvey and

Olver [11].

4. Conclusion and Open Questions

Theorem 1 essentially shows that under the

mildest possible conditions, a quadratic form/

sum of outer products can be “split in two” while

preserving its spectral properties. Since graphs

can be encoded as quadratic forms/outer prod-

ucts, the theorem implies that they also can be

“split into two” while preserving some proper-

ties. However, a lot of other objects can also be

encoded this way. For instance, applying The-

orem 1 to a submatrix of a Discrete Fourier

Transform (it also holds over Cn) or Hadamard

matrix yields a strengthening of the “uncertainty

principle” for Fourier matrices, which says that a

signal cannot be localised both in the time domain

and the frequency domain; see paper of Casazza

and Weber [12] for details. This strengthening

has implications in signal processing, and its

infinite-dimensional analogue is useful in analytic

number theory. For a thorough survey of the

consequences of the Kadison–Singer conjecture

and Theorem 1 in many diverse areas, check

out [13].

To conclude, let me point out that the cur-

rent proof of Theorem 1 is not algorithmic, since

it involves reasoning about polynomials which

are in general #P-hard to compute. Finding a

polynomial-time algorithm which delivers the

low-discrepancy partition promised by the theo-

rem is likely to yield further insights into the tech-

niques used to prove it as well as more connec-

tions to other areas — just as the beautiful work of

Moser-Tardos [14], Bansal [15], and Lovett-Meka

[16] has done for the Lovasz Local Lemma and

Spencer’s theorem. It would also be nice to see

if the methods used here can also be used to



recover known results in discrepancy theory, such

as Spencer’s theorem itself.

Acknowledgements

Thanks to Nick Harvey, Daniel Spielman, and

Nisheeth Vishnoi for helpful suggestions, com-

ments, and corrections during the preparation of

this article. Special thanks to my coauthors Adam

Marcus and Daniel Spielman of Yale University.

References

[1] A. Marcus, D. A. Spielman and N. Srivas-tava, Interlacing families II: Mixed characteris-tic polynomials and the Kadison–Singer problem,arXiv:1306.3969 (2013).

[2] N. Weaver, The Kadison–Singer problem in dis-crepancy theory, Discrete Mathematics 278 (2004)227–239.

[3] B. Roberts, Philosophy and physics in the Kadison–Singer conjecture, http://www.soulphysics.org/2013/06/philosophy-and-physics-in-the-kadison-singer-conjecture/

[4] N. J. A. Harvey, An introduction to the Kadison–Singer problem and the paving conjecture (2013).

[5] J. A. Tropp, User-friendly tail bounds for sums ofrandom matrices, arXiv:1004.4389 (2011).

[6] A. Marcus, D. A. Spielman and N. Srivastava,Interlacing families I: Bipartite Ramanujan graphsof all degrees, arXiv:1304.4132 (2013).

[7] J. Batson, D. A. Spielman and N. Srivastava, Twice-Ramanujan sparsifiers, arXiv:0808.0163 (2009).

[8] D. G. Wagner, Multivariate stable polynomials:theory and applications, arXiv:0911.3569 (2009).

[9] A. M. Frieze and M. Molloy, Splitting an expandergraph, J. Algorithms 33(1) (1999) 166–172.

[10] M. Rudelson, Almost orthogonal submatrices ofan orthogonal matrix, arXiv:math/9606213 (1996).

[11] N. J. A. Harvey and N. Olver, Pipage rounding,pessimistic estimators and matrix concentration,arXiv:1307.2274 (2013).

[12] P. G. Casazza and E. Weber, The Kadison–Singerproblem and the uncertainty principle, Proc. Amer.Math. Soc. 136(12) (2008) 4235–4243.

[13] P. G. Casazza, M. Fickus, J. C. Tremain and E. We-ber, The Kadison–Singer problem in mathematicsand engineering: a detailed account, in D. Han,P. E. T. Jorgensen and D. R. Larson, eds. Contem-porary Mathematics, Vol. 414 (2006), pp. 299–356.

[14] R. A. Moser and G. Tardos, A constructive proof ofthe general Lovasz Local Lemma, arXiv:0903.0544(2009).

[15] N. Bansal, Constructive algorithms for discrep-ancy minimization, arXiv:1002.2259 (2010).

[16] S. Lovett and R. Meka, Constructive discrep-ancy minimization by walking on the edges,arXiv:1203.5747 (2012).

Nikhil Srivastava Microsoft Research, Bangalore, India

[email protected]

Nikhil Srivastava graduated in Mathematics and Computer Science from Union College, Schenectady, NY in June 2005. In May 2010 he obtained PhD from Yale University in Computer Science with the dissertation “Spectral Sparsification and Restricted Invertibility". He did his postdoc at Princeton, MSRI (Berkeley) and IAS (Princeton). Currently he is with Microsoft Research, Bangalore, India. His current research interests are theoretical computer science, linear algebra, random matrices, and convex geometry.



Journalist in Residence (JIR) Programme in Mathematics in Japan

Koji Fujiwara

1. What is JIR?

We have lots of benefits from science and technology, and the modern society cannot continue without that. Even some of the very abstract theories in mathematics and physics find application in the daily life. For example, theory of elliptic curves is used for cryptog-raphy and GPS needs general relativity to correctly work. Some of them are directly related to our safety and health. Genetic engineering is becoming more and more common. We have to worry about the radiation problem after the incident in Fukushima and lots of researches are going on but opinions differ even among specialists such as physicists, statisticians and doctors. Advanced medical technologies raise ethical issues for us to discuss. “Big science” such as space science, accelerators, genome projects and super computers spend lots of money (tax) and not only researchers but also many other people are involved. Science and technology are not something we can just use, but we may want to know about that enough to form our own opinions.

So, we need good science writers. But it is not so easy to produce them because one has to be a good writer, and at the same time he/she needs to know advanced science and technology to write about the cutting edge research. But as far as I know there are nearly no programmes of science writings in Japanese universi-ties. That is the reason why I started the programme “Journalist in Residence” (JIR). I wanted to make a small change from mathematics. By this programme, journalists and writers, who already have lots of expe-rience in writing, stay at mathematics departments hosting them for a few weeks. They talk to mathemati-cians, visitors, students, administrators and librarians, and also attend conferences and seminars. Since they are away from their own jobs, each department pays for accommodations, a small per diem and an office. They are not obliged to write for the department or the programme. It is simply an opportunity for them to stay, or “reside”, at a department of mathematics, explore and

get to know about mathematics and mathematicians. I am also hoping that having journalists around in the department will create an interaction between the journalists and our students, and that some of them might get interested in science writing.

The idea of JIR is not my original one. MSRI in Berkeley, California ran a similar programme from 1998 to 2005. The difference is that their programme had people staying for one semester. As far as I know, our JIR is the first such programme in Japan in any discipline.

I started the programme 4 years ago. I talked to Professor Takashi Tsuboi at the University of Tokyo, who was the president of the Mathematical Society of Japan (MSJ) at that moment. He encouraged me and suggested to start the programme right away. We had a press interview about the launch of the programme and the applications to the programme are handled by MSJ since then. So far more than 10 departments of mathematics, institutions and research groups related to mathematics, have joined the programme, and more than 20 people have attended the programme. Typically each person stays for a week or two at one or two places. There is a lot of variety in the background of the participating journalists, science writers, photog-raphers, science magazine editors, cartoonist, TV programme directors, and science translators. Some of the host departments have grants from “Global centre of excellence” programme in mathematics by Japanese Society of promotion of Science (JSPS) and JIR is a part of the projects they run by that grant.

2. Mathematics in the Japanese Society

People in Japan have a strong interest in mathematics. For example, “The Housekeeper and the Professor”, a popular novel by Yoko Ogawa about a mathematician who only has a short memory after a car accident, was made into a film and a TV drama and it was a big success. Sudoku puzzles got many fans in Japan before it spreads to other countries. We have a few



monthly mathematics magazines for non mathemati-cians and you can find them at any big bookstores in the town. Typical readers are high school teachers of mathematics, undergraduate students interested in mathematics, and ordinary people who have an interest in mathematics as a hobby. I heard that many retired people buy the magazines regularly too. Most of the articles in those magazines are written by math-ematicians and some of them are pretty advanced, for example, on complex analysis, group theory, algebraic topology and mathematics finance, etc. There are quite a few “popular science” books and many of them are on mathematics and physics.

On the other hand, mathematics is not one of the most popular subjects as majors at universities. It is slowly getting less popular than 30 years ago, when I was a high school student. The situation is better than Physics. I heard that only 20–30% of high school students learn Physics these days in Japan. Nearly all of the students majoring in mathematics at Kyoto Univer-sity are men. When I was a student, best students tend to major in Law or Medicine. But probably students’ interest is also changing, at least regarding Law majors, and they are more interested in business, internet tech-nology and interdisciplinary studies, although Medical schools are still most popular among good students.

Recently, the Japanese government is trying to attract more young people to Science and Engineering, in particular more female students. It seems that they started thinking that science and technology is a key to boost the Japanese economy (also remember that IMF published a report “Can women save Japan?” last year). They encourage universities and professors to organise activities for public: many universities have “open campus” days and high school students visit laboratories or attend talks. Professors visit nearby schools and explain their research. I have done that several times and it was a fun for me too. They also funded a few universities for five years to run a course for science writing. As far as I know those are the first such programmes in Japan.

3. Record of JIR 2010–2013

List of 13 host institutions:

Tohoku University (Mathe-matics; AIMR), the University of Tokyo (Mathematical sciences, Lab of Aihara for mathematics, life sciences and

informatics), Tokyo Institute of Technology (Math-ematics and computer science), Meiji University (Math-ematics), Keio University (Mathematics), Institute of Statistical Mathematics, Riken Brain Science Institute (Lab of Amari), Nagoya University (Mathematics), Kyoto University (Mathematics; RIMS), Kyushu University (Mathematics).

List of 20 participants from journalists:

2010: Masahito Kasuga, Director of science programme for NHK (Japan Broadcasting Corporation); Seiji Hasegawa, Senior science reporter for Yomiuri Shinbun newspaper; Eiichi Asami, Science reporter for Kyodo Tsushin press; Akemi Satoda, Reporter for Chugoku Shinbun newspaper; Yoshiko Miwa, Writer; Yoshitaka Arafune, Writer; Yuka Kamiya, Writer; Hideaki Takamori, Science and technology writer.

2011: Akemi Satoda, Yoshiko Miwa, Masahito Kasuga, Yoshitaka Arafune, Seiji Hasegawa, Satoshi Tomita (Science book editor for Edit).

2012: Kunie Suzuki, Book editor for Keiso Shobo; Hoshi Tominaga, Translator for popular science books; Naoyuki Uchimura, Science writer; Aya Furuta, Chief editor for Nikkei Science magazine; Seiji Hasegawa; Tetsujiro Kamei, Editor of books in mathematics; Hiroaki Kono, Photographer and photojournalist; Masahito Kasuga; Hayano Kobayashi, Science cartoonist; Yoshiko Miwa; Kenneth Chang, Science reporter for New York Times.

2013: Shigeyuki Koide, Science writer, President of Japanese Association of Science and Technology Journalists; Tetsujiro Kamei; Hiroaki Kono; Akemi Satoda; Tamiko Nakamura, Lawyer; Kazuyuki Harada, Reporter for Yomiuri Shinbun.

Photo exhibition at Kyoto University in March 2013, Photographer Hiroaki Kono (left) and Science editor Tetsujiro Kamei (right)



Some comments are in order. Out of 20 participants, 15 of them have studied science or engineering in undergraduate or graduate schools. This statistics can be misleading. Among writers and journalists in Japan, only a small portion of them, maybe less than 20%, have a science background in university education. Among science writers, maybe more than half of them have a science back-ground. Yomiuri Shinbun is one of the biggest newspaper companies in Japan, which sells nearly 10 millions copies every day. The science section (independent from medical section) has 20 reporters or so, which is one of the largest in the world. Seiji Hasegawa is the chief of the section. Masahito Kasuga made a 90 minutes documentary programme for NHK on the solution of the Poincaré conjecture (before he attended the programme). Hoshi Tominaga translated more than 10 popular books in mathematics from English into Japanese, including “The Mathematician’s Brain” by D Ruelle and “The Music of the Primes” by M Sautoy.

I work for the department of mathematics of Kyoto University. Our department and RIMS (Research insti-tute for mathematical sciences) hosted 7 participants in 2012. One new challenge was that the programme had the first oversea participant. Kenneth Chang, a science writer for New York Times, spent two weeks. After the programme he says “My two weeks as a journalist-in-residence at the Kyoto University were certainly the most intellectually intensive vacation I’ve ever had, and it was a lot of fun, too. Hopefully, it will also lead me to write better newspaper articles about mathematics than I would have otherwise.”

4. Workshops and Events Related to JIR

There are some activities and events related to the programme. Professor Takashi Tsuboi at the University of Tokyo organised three workshops for the participants and the host professors of the JIR programme to share experiences and ideas to each other. I have attended it two times and it has been very useful and enjoyable.

The MSJ have semi-annual meetings for its members. The MSJ has more than 5000 members, and many of them attend the meetings. The last one took place at Kyoto University in March 2013. Taking advantage of being at the host university, I organised a panel discussion and an exhibition on JIR. We got 9 panelists from the programme and more than 100 people came

to listen. The discussion lasted for 90 minutes. In the exhibition, we presented more than 150 photos by Hiroaki Kono, cartoons by Hayano Kobayashi, and popular books in mathematics translated by Hoshi Tominaga. We had more than 300 people dropping by during the two days.

Panel discussion held at Kyoto University in March 2013

I record some opinions from programme partici-pants at the panel discussion: “After I attend the programme, I had a chance to write about the papers by Professor Shinichi Mochizuki on the ABC conjecture. I got lots of help from the professors I met through the programme”. “I’m translating popular books in mathematics from English. I majored in Mathematics for my undergraduate study but I need more knowledge in mathematics for my work. Talking to mathemati-cians and attending research seminars in mathematics has been very helpful.” “I studied mathematics in my undergraduate and became a newspaper reporter. Mathematical or logical thinking is very important for good writing. I’m most interested in the interface between mathematics and society.” “The most impor-tant aspect of the programme is that it is not seeking for a return in a short time.” “I made a TV programme on the Poincaré conjecture. BBC had made a programme on the Fermat last theorem, which was highly appreci-ated internationally. That programme focuses on people including Andrew Wiles, but I wanted my programme to be not only about people but also about mathematics itself. After I attended the programme, I feel I can make more programmes on mathematics.” “UK has a long and good tradition for communicating science to public, for example, Royal institution Christmas lectures and Simonyi professorship at University of Oxford. It is very important to have a lot of diversity in supporting core research.”

Opinions by host professors: “When I first heard about the programme, I could not have a clear idea on what it is like. We have already been doing some events to communicate mathematics to public, but after hosting JIR, the difference is that we get a feedback



from the participants and know what we look like to them.” “There is a huge gap between mathematicians and general public, and it is not easy to fill the gap, but that makes it more interesting and challenging. We really appreciate the programme participants who try to do that, and what’s important for mathemati-cians is to welcome them and show the ‘real thing’ in mathematics.”

5. Summary and Future Directions

The programme has been well received both by the host institutions and the participants. Most mathematicians are very enthusiastic to talk about their research for hours. I heard from the participants that some are easier to understand than others and I am curious to know what makes the difference. There might be a hint for us to learn for better communication. In general, it is still true that research of mathematics is so abstract that listening to them for a few hours is in many times simply not enough for the journalists and the writers to digest the contents. As I wrote, many of our participants have a science background from university study and lots of experience of science writing. Some of them suggested after the programme that it might be helpful if a crash course of the summary of university level mathematics (for example, manifolds, homology, set theory, groups, basic number theory, complex analysis and functional analysis, etc.) is available before they start the programme. That could be useful to fill the gap between their experience and knowledge and the research mathematics.

There have been quite a few articles on the pro-gramme by the participants in a newspaper, magazines in mathematics and newsletters of the host institutions. Some of the articles in the newspapers on recent major

achievement in mathematics, for example, on the ABC conjecture and the twin prime conjecture, are written by our programme participants. I believe our programme is increasing the supporters of mathematics.

I am going to continue the programme for some more years in the same style. I also want to try a few new things. One is that to make the programme more international, having more foreign participants and sending some of the programme participants to visit foreign institutes of mathematics. Another is to have more students involved in the programme. In the long run it would be very important to have science writers who have a strong education in Science. Also I feel it is time to communicate our experience and ideas to mathematicians, researchers in other fields and general public who are interested in mathematics.

A major part of the programme in the first three years has been supported by the GCOE programme by JSPS, but it is over. Since this year the host institutions are using their own fund. It is important for me to find a new funding. The programme will be partly supported for two years by Suuri Kagaku Shinkoukai, a foundation to promote mathematical science whose president is Professor Heisuke Hironaka (a Fields medalist).

Acknowledgements

I would like to thank the Mathematical Society of Japan, Professor Takashi Tsuboi, the host institutions and professors in charge of the programme, JSPS, the programme participants and mathematicians and other people, who were always willing to talk to them. I also thank Professor Noriko Hirata-Kohno for reading this article carefully.

Translated from Sugaku Tushin, Vol. 17 (4) (2013)

Koji FujiwaraKyoto University, Japan

Koji Fujiwara is a mathematician. He received a PhD from University of Tokyo in 1993 and did a postdoctoral research at MSRI in Berkeley. He has held posi-tions at Keio University, Tohoku University and has been a professor at Kyoto University since 2012.

He received a Geometry Prize from MSJ in 2005 for his work in geometric group theory, and a Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology in 2013 for the JIR programme.

Gonit Sora: The Two Year JourneyPankaj Jyoti Mahanta and Manjil P. Saikia*

1

Gonit Sora: The Two Year JourneyPankaj Jyoti Mahanta and Manjil P. Saikia∗

Gonit Sora (http://gonitsora.com) is a multilingualwebsite devoted to publishing articles related tomathematics for the students of North Eastern India.The website completed two years on April 20, 2013.This article discusses the website, its goals and futureobjectives.

1. Introduction

The seed of the idea of a magazine devoted tostudents in Assam of India appealed to the firstauthor (PJM), but due to various financial and ad-ministrative troubles it could not germinate prop-erly. It was then that the two of us got togetherand decided to form an online magazine to caterto the students. In that way it would not be restric-tive to a particular geographic location and canhave both flexibility and greater reach. Thus onApril 21, 2011 Gonit Sora (http://gonitsora.com)was launched with a few articles in English andAssamese and with just a team of two. Nowafter a span of two years, we have a very goodand hardworking team of enthusiastic studentsand teachers and we post almost 10 articles ona variety of topics each month. At the time ofwriting the total number of articles published inthe website is about 292.

To properly introduce the website, Gonit Sorais a multilingual website devoted to publishinggood and original articles related to mathematicsin general. But we are not restrictive in the articleselection and almost everything that is connectedwith mathematics gets featured on the website.Many famous mathematicians have given inter-views for the website and we also provide careercounselling through our interactive comments onthe website from time to time. Thus, Gonit Sora isnot restrictive in its approach, and the fact that theteam consists of students and lovers of mathemat-ics have the added advantage of us being dynamicin our approach and open to experimentation.The enormous amount of support that we receiveevery month (more than 400,000 hits) only makesour goals and commitment stronger.

∗Corresponding author.

2. Goals and Activities

From the time of its inception there has been afixed set of goals for the website which can besurmised below

i. To cater to the student community byposting relevant articles in all branches ofmathematics,

ii. To focus on the human side of the subjectwhich is almost always lost in the traditionalclassroom approach to teaching,

iii. Create an online repository of mathematicalarticles and facts, which can be accessed freeof cost by anyone willing to do so,

iv. Digitise the regional mathematical content inIndia in a form that is suitable for the web,

v. Organise workshops and outreach activitiesfor school students to make them see thebeauty and joy of doing mathematics, and

vi. To create a platform for students and teachersalike to discuss ideas.

In this regard, we have come a long way sincewe started out. Below we mention a few of theactivities that we are engaged in

i. Posting articles every week on a topic relatedto mathematics,

ii. Posting interviews with mathematicians likeBruce C Berndt, Terence Tao, S R S Varadhan,R Sujatha, etc. to motivate the study of thesubject in the young students,

iii. Digitising the Assamese texts in mathematicswhose copyrights are either in the publicdomain or expired,

iv. Collaborated with the Assam Academy ofMathematics to digitise their enormous math-ematical content in terms of articles andbooks,

v. Organising and facilitating workshops forOlympiad outreach activities for the schoolstudents in the North Eastern part of India,and

vi. Answering queries posted on the website forthe students, teachers and parents regardingmathematics, its study and problems.



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3. Collaborations

For the achievement of our goals we have alsocollaborated with various organisations from timeto time. This two way collaboration is plannedso that both the parties can mutually benefitfrom one another. Till now we have the followingcollaborations:

i. Assam Academy of Mathematics (AAM):To digitise their entire collection of booksand articles published in Assamese. Till nowwe have digitised 3 books and many arti-cles published by the AAM in their biannualpublication, Ganit Bikash. We have also col-laborated with AAM to make their in housemathematics journal, Journal of the AssamAcademy of Mathematics (ISSN 2229-3884)available online, and it will be up on ourwebsite very soon.

ii. Xobdo.org: To make a glossary of math-ematical terms in the Assamese language.Xobdo.org is an online dictionary and theyhave shared with us their database for thispurpose.

iii. Asia Pacific Mathematics Newsletter: Topublish the articles of the newsletter in theweb so that it can be better accessed bythe students of the North-Eastern region ofIndia.

iv. Friends of Assam and Seven Sisters (FASS):To organise various workshops, seminars, etcwith the help of FASS in various places ofAssam.

v. Mathematics of Planet Earth 2013 (MPE): Topopularise the efforts of MPE in India, wehave been a magazine partner of MPE sincelast year.

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3. Collaborations

For the achievement of our goals we have alsocollaborated with various organisations from timeto time. This two way collaboration is plannedso that both the parties can mutually benefitfrom one another. Till now we have the followingcollaborations:

i. Assam Academy of Mathematics (AAM):To digitise their entire collection of booksand articles published in Assamese. Till nowwe have digitised 3 books and many articlespublished by the AAM in their biannual pub-lication, Ganit Bikash.

ii. Xobdo.org: To make a glossary of math-ematical terms in the Assamese language.Xobdo.org is an online dictionary and theyhave shared with us their database for thispurpose.

iii. Asia Pacific Mathematics Newsletter: Topublish the articles of the newsletter in theweb so that it can be better accessed bythe students of the North-Eastern region ofIndia.

iv. Friends of Assam and Seven Sisters (FASS):To organise various workshops, seminars, etcwith the help of FASS in various places ofAssam.

v. Mathematics of Planet Earth 2013 (MPE): Topopularise the efforts of MPE in India, wehave been a magazine partner of MPE sincelast year.

In the future we are working on collaborationswith various other organisations and individualsso that we can serve the young students and loversof mathematics in a better way.



Pankaj Jyoti Mahanta Department of Mathematics, Gauhati University, Assam, [email protected]

Pankaj Jyoti Mahanta is a graduate student at the Department of Mathematics, Gauhati University, India. He is the co-founder and editor of the Assamese section of Gonit Sora. His research interests are in algebraic graph theory.

Manjil P Saikia Department of Mathematical Sciences, Tezpur University, Assam, India

[email protected]

Manjil P Saikia is a final year undergraduate student at the Department of Math-ematical Sciences, Tezpur University, India. He is the co-founder and editor of the english section of Gonit Sora.

3

In the future we are working on collaborationswith various other organisations and individualsso that we can serve the young students and loversof mathematics in a better way.

4. Future Objectives

Although we are two years old but still there arelots of things that we are yet to do. The futureonly holds enormous opportunities for us and wewould strive hard to make the achievement of ourgoals a success. In the coming days we plan ondoing the following

i. Create a forum for the discussion and delib-eration of mathematical ideas,

ii. Create a mathematical chronological data-base,

iii. Expand to other languages like Bengali andHindi,

iv. Organise workshops on specific topics ofmathematics,

v. Create an offline presence in terms of printedmaterials, and

vi. Create a database of mathematical notes forcollege and university students.

5. Conclusion

It has been noticed by us and we have even beeninformed by several of the readers of how much

it has made an impact in the way they view math-ematics. In the comments of the website, studentsfrom all over India ask questions to career re-lated things and get prompt and correct responsesfrom our experts. This has enabled many studentsacross India to make a good and timely careerchoice. We have been posting the admission testsof various institutes and organisations in Indiaand many students have been benefited by these.The articles in the website cater to a wide range ofmathematical topics and hence it has also enabledschool and college teachers to go beyond theirclassroom teaching and add excitement and enjoy-ment to the subject they teach. With encouragingcomments and messages that we receive almosteveryday we have been very happy to learn thatour humble efforts have helped at least a fewstudents of the country and maybe encourage afew others to take up mathematics as their careerchoice.

Acknowledgements

The authors would like to thank all the teammembers and the contributors of the website overthe last two years and its readers for the support.They would specially like to thank the supportand encouragement of Professor Sujatha Ramdoraitowards Gonit Sora and also for her encourage-ment in writing this article.



Book Reviews


Book Reviews

Secular Mathematics in Sacred Precincts

Sujatha Ramdorai

Sacred Mathematics: Japanese Temple Geometry

Fukagawa Hidetoshi and Tony RothmanPrinceton University Press, 2008, 392 ppISBN: 9780691127453

Imagine this…. The Muromachi period in Japan (1338–1573) was a period of cultural development (the Noh plays, the tea ceremony…), and extensive trade with Southeast Asia. Apocryphal though it might be, the story goes that one could hardly find in all of Japan, a person capable of carrying out the art of division! This period was followed by confrontations of the daimyos (warlords) culminating in the battle of Sekigahara (1600), which saw the establishment of the Tokugawa Shogunate. The famous daimyo, Toyotomi Hideyoshi (1537–1598) had already begun to develop a serious mistrust of the Christian (mainly Portuguese) missionaries. The Tokugawa Shogun, Ieyasu followed up on Hideyoshi’s resolve, and in 1614 outlawed the practice of Christianity. From then, until the forceful opening up of Japan by Commodore Perry in the middle of the nineteenth century, Japan followed the policy of “Sakoku” or a “closed country”. In the three millennia when the Tokugawa shogunate held sway, there was a period of relative peace and a renaissance,

referred to as Genroku. It was also in the mid-to-late seventeenth century that mathematics flourished — the main arenas being temple shrines, the subjects largely being restricted to geometry and the participants being a cross-section of the general population!

What survives today as a striking testimony to this are the “Sangaku”, which are wooden tablets painted with geometrical figures and were then displayed in Shinto shrines and Buddhist temples. Each tablet encapsulates a theorem or a problem in geometry. These were posed as challenges to experts, and the participants in this unique form of mathematical chal-lenge, saw this whole exercise partly as dedication to Divinity, for helping them to see the path to solutions and progress in their mathematical knowledge. Though there are parallels to the mathematical exchanges in Europe at around the same period (remember Fermat and his letters…), there are key differences. For one, these challenges and their solutions were played out across Japan in various temples and shrines. Second, the participants seem to have constituted larger sections of the general public — there are lovely woodblock images of people (including women and children) huddled together (Plate 4: Sangaku of the Sozume shrine). Importantly, there is also the aesthetic aspect — the Sangaku tablets are beautiful, typifying many attributes of Japanese art.

The book Sacred Mathematics: Japanese Temple Geometry is a delightful book which is aimed at both mathematics experts and the non-experts. The authors Fukagawa and Rothman have strived hard to balance the task of delving in detail at some of the Sangaku problems along with complete solutions, while simul-taneously keeping the text accessible to an interested reader. Fukagawa, a tireless devotee of the Sangaku has spent his life studying them, recording them, and writing about them. Rothman, a theoretical cosmolo-gist, was fascinated when he first saw Fukagawa’s book with Dan Pedoe on Sangaku and saw the value in bringing this beautiful and rich part of traditional

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Japanese mathematics to a broader international audience. The two of them never met but collaborated extensively by way of e-mail exchanges and letters to bring out this delightful book. What makes this whole endeavour even more remarkable is the absence of a common conversational language between them — Rothman does not speak Japanese and Fukagawa is not conversationally fluent in English.

The book is a fascinating source of nuggets from a bygone era — by way of Japanese history, art and mathematics. It has endless possibilities for a curious and interested mind, both that of students and teachers. What role does culture play in shaping math-ematical thought? In what ways did the Sakoku contribute to this blossoming of high level geom-etry with the inter-esting component of secular public participation within sacred spaces? The book deals also with other fascinating stories related to Sangaku, for instance the travel diaries of a Sangaku enthusiast and itinerant mathematician, Yamaguchi Kanzan, during 1817–1828. His diary entries provide a charming view of the mores and feelings that mathematics evoked at that time among the public, both ordinary and the

Sangaku from the Sozume shrine

Yamaguchi Kanzan Diary 6. Takeda’s Maximum Problem

“intellectual” class. Needless to say, an added bonus are the visual images of the Sangaku and other related Japanese prints, etc., which are a virtual visual treat. The book is already making waves in the west, especially amongst educators who see the possibility of adding other interesting dimensions to classroom teaching by choosing problems and discussing them, etc. While the strength of Japanese mathematics in the 20th century and at present is well-known, this book offers more than a glimpse of a little known part of mathematics in the Japanese past. It is a book that is bound to delight and fascinate a broad section of interested readers.

Professors Fukagawa and Rothman have kindly agreed to an e-interview which appears along with this article. I would like to sincerely thank Florian Sprung for help with translation and coordinating the interview with Fukagawa.



Interview with Hidetoshi FukagawaSujatha Ramdorai

Hidetoshi Fukagawa

Sujatha Ramdorai: Tell us a little about yourself.

Hidetoshi Fukagawa: I was born in Kitakyushu city, Fukuoka prefecture in 1943, and graduated in 1967 from the Mathematics Department in Yamaguchi University. I served as a high school teacher of math-ematics in Aichi Prefecture during 1967–2004, having taught at six high schools. I married my wife Miyako in 1972 and obtained my PhD in Mathematics Educa-tion from the Bulgaria Academy of Sciences in 1996. I retired as a high school teacher in 2004, and since then have been teaching courses on “Mathematics and Math-ematics Education” at several universities, part of the time. Currently, I give lectures at Daidou University and Kogakkan University. In my free time, I enjoy growing vegetables in the fields. I have published several books and articles related to mathematics, especially Sangaku, and they are listed below chronologically.

[1989] With Dan Pedoe, Japanese Temple Geometry Problems: Sangaku (Winnipeg University, CBRC, Canada).

[1991] Japan Geometric — How Many Problems Can You Solve, in Japanese (Morikita Shuppan Publication).

[1994] Japanese Mathematics (two volumes), in Japa-nese (Morikita Shuppan Publication).

[1998] Sangaku and Japanese Mathematics, in Japanese (Morikita Shuppan Publication).

[2002] With John F Rigby, Traditional Japanese Mathematics Problems of the 18th and 19th Centuries (SCT-publishing, Singapore).

[2002] Translation. Robert Geretshlager, Geometric Origami, translated by Fukagawa Hidetoshi into Japa-nese (Morikita Shuppan Publication).

[2005] Supervised in “Big Sangaku Exhibition” held at the Nagoya City Science Museum, sponsored by Asahi Shinbun Company.

[2008] With Tony Rothman, Sacred Mathematics (Princeton University Press).

[2011] With Kitaoka Yoshiyuki and Kawamura Tsukasa, Fundamental Calculus for Engineering, university text, in Japanese (Gakujyutsu Syuppan).

[2013] Elementary Mathematics, in Japanese (Kogakkan University Press).

SR: How did you first hear of the Sangaku?

HF: Being a math teacher, I looked for materials by examining the history of mathematics, so that students could have interest in mathematics. In Japan, at that time, mathematics during the Edo period was specific to that period and had no worth for high school, and so no one had been studying it. Its content is very low and unavailable for high-school mathematics, in general. Only Greek mathematics, or Abel or Galois story were investigated by all math teachers without looking at the mathematical content. Mathematical contents of



western mathematics history are too professional for high school students, and they were difficult.

When I served as a teacher at first in Handa high school in Aichi Prefecture, I met a linguist teacher Kunihiko Sakakibara who was a prominent linguist. One day, he brought a dirty old book of Japanese mathematics to me, saying, “It’s Edo period math book and I don’t know the content, can you decode it?” It was the first Edo period math book for me. I had never seen authentic Edo period math books until then. I said to him. “It is generally believed that mathematics during Edo period had totally useless, low level content. So don’t expect too much”, and began the translation work. I had studied Chinese, just as studying Latin is for anyone interested in history of the Western world. I finished the translation of the book six months later and I was very much surprised.

Although they didn’t know western mathematics, mathematicians during the Edo period used “Partial derivative” or “Power series”. I was startled and so started to study traditional Japanese mathematics. There were many Japanese mathematics books. In my study, I found a word, “Wooden tablet on which Japa-nese mathematics problems recorded” in some book. What is a wooden plank with mathematical problems? Then I found a board kept unnoticed to any modern mathematicians. There was a wooden plank in existence in Aichi prefecture on which mathematics problems were written during the Edo period. I was surprised and investigated, and found that local historians had reported about it. They found the content difficult for them, because they were not mathematicians, and the plank was recorded as a mere cultural property. Some Sangaku survived in Mie and Aichi prefectures, as mere cultural properties, are preserved. This was the start of my love for Sangaku.

SR: Have you tried using the Sangaku problems and method of solving them in the classroom?

HF: Most Sangaku problems were introduced only as a cultural asset and were difficult for high school students. The high school attached to Aichi educational College was my third school. One day, I was going to Nagasaki for the school excursion with my students. Before departure, I had translated Sangaku problems of Nagasaki Suwa Shrine into modern language and handed the problems to my class students. On the day before they set out for travel, somehow during my lunch break I went to my classroom and found five or six students debating about Suwa shrine Sangaku

problems. From this time, I was convinced that easy Sangaku problems are best for students. But Japanese high school students are busy in everyday classes, and they have no extra time to study Sangaku. I once was a lecturer at the Education Centre for Aichi Prefecture’s high school teachers, and introduced the importance of Sangaku, from 1980 to 1992. Now, I am talking on Sangaku in my lecture at Nagoya University and some other Universities in mathematics education course.

SR: You can obviously mix this with history, culture, and politics. Just as in the introductory portions of your book. Have you tried this form of mixing the problems with story-telling in the class? What are the reactions of the students?

HF: Traditional Japanese mathematics is based on Chinese mathematics and is independent from Western mathematics. In 17th century, Japan was exposed to the danger of the invasion from the West. Finding out that other Asian Nations were invaded by the West, the Tokugawa Government prohibited other countries that had traded with Japan from intervening in domestic matters. The Tokugawa government was sensitive to and restricted the invasion of particularly religious or scientific information. In the 17th and 18th centuries, in Japan, science and culture took roots on their own. This is Edo culture and we give too much appreciation to it, that is, traditional Japanese culture. The culture includes mathematics too. The culture developed, because the Tokugawa Government avoided war, aimed at agricultural growth, to be a rich country. People lived in not so poor but rich environment, and so the culture developed. In high school, I have been speaking, “Peace developed culture and peace is so important”. Sangaku is a product of popular culture. I always emphasised this in the classroom. There were a lot of people who enjoyed mathematics during the Edo period.

SR: Are there other allusions to Sangaku in Japanese texts or folklore?

HF: Studies of mathematics during the Edo period were done as cultural property only and not in the view of mathematics. In a Japanese history textbook there was only one line about it. The Sangaku hadn’t touched everyone. Historians couldn’t understand the high mathematical level of the Sangaku. Sangaku was reported as material left from history and worthless for mathematics education. I focused on studying Sangaku, analysed the contents of mathematical research, but



it was a heresy, and has been ignored by historians. However, I noted its contents, and continued to study their style. Mr Haruki Abe, who was a reporter of Asahi news company, became interested in my research. He introduced Sangaku that I studied in the Asahi newspaper. Researchers studied the materials that were left, panicked and began examining the Sangaku since then. The historians then wrote about Sangaku in the history textbooks of high school in Japan.

Sangaku didn’t appear in any Japan high school history textbooks until 40 years ago, but is now described in Japan history textbooks. However, the mathematical content of Sangaku is very difficult to introduce.

SR: Is there any evidence that the Japanese were aware of Mathematical knowledge from other civilisations around the world at that time?

HF: Western science, translated into Chinese, was imported to Japan during the Edo period. Calendar was important for the Tokugawa government and the knowledge of the Western calendar was coming into Japan. Especially the calculator Abacus or “Soroban” (just as the modern PC was imported from China), and they used it on many occasions of everyday life. Abacus training rooms were opened in many regions of Japan in the Edo period.

During the 17th–19th centuries in Japan, many small schools teaching reading and writing were opened. Village classrooms sprouted up throughout the country to teach reading, writing and arithmetic, or three “R”s. The classroom was called “Jyuku” or “Terakoya”, and played a particularly important role for increasing literacy rate and pushing up the general level of education of the common people.

Schools were run even privately, and the size varied widely from 10 to 1,000 students. Poor samurais, priests and any intelligentsia could become a teacher of the school easily, and could get some money. These schools were private, not public. Therefore, many people were strong in calculation, reading and writing. At some Jyuku, advanced mathematics was studied, and people who loved math studied there. In such schools, mathematics was just really fun in ordinary life. In some provinces where there were mathematics lovers, the wooden tablets, on which geometry problems or the land surveying results were written, were hung in the shrine, and thanked God. Thus many elementary schools proliferated in 18th and 19th centuries of Japan. Number of cram schools in the Edo period was

more than 80,000. (Refer to http://library.u-gakugei. ac.jp.)

The literacy rate in Japan at that time was so high and said to be more than 70%. During the 18th and 19th centuries, it is said that the literacy rate in London was about 20%, and in Paris, 10%. However, in Edo period, it was 70–86%. It was easy to run such schools, even in the home garden. Samurais who lost their jobs and some intellectuals easily ran such schools. The Government thought that the influence of literacy was also useful in letting people know laws, so did not put restrictions on such schools. Mathematicians of the Edo era were good at computation of geometric problems. Greek mathematics depended on logic, but Japanese mathematics used complex calculations. Logical thinking was not born in Japan. But compu-tational geometric problems thrived and left behind great material.

SR: Tell us a little about your experience in collabo-rating with Rothman for the book.

HF: Rothman and I have never met each other until now. However, we published the book. Mathemati-cians who joined Sangaku tour and asked me to be the guide were surprised that we as co-authors have not seen each other. I started to research Sangaku when I was a high school teacher. But nobody recognised my work. During the Edo period, mathematicians studied hard geometric problems and most of Sangaku problems were on geometry. They used computational geometry without logic. Geometric logic was not used in Japan. Until 40 years ago, Sangaku mathematics had been ignored, that is, Sangaku was a forgotten world. All mathematicians in Japan at that time thought the mathematics during the Edo period had no value. But plenty of problems, from the view of a high school math teacher, are suitable for high school students.

I wanted to introduce this forgotten mathematics to the world and so acted. I guess it was 1984; my first job was buying a book on how to write in English. I have never written an English letter until then. My favourite language was only Japanese (this is a joke). If I hadn’t come across Sangaku, then I wouldn’t have needed to study English. I studied how to write English letters for the first time at the age of 42. I sent letters, in which Sangaku geometric theorems were written, to ten foreign mathematicians who had interest in history and geometry all over the world. But nobody sent me any reply. These were letters I wrote to foreign countries for the first time. Sangaku inspired me towards such



behaviour because I was mad about Sangaku. Two months later, my wife shouted, an air mail arrived from abroad. I received a letter from abroad for the first time. The letter was from Dan Pedoe (1910–1998) of the University of Minnesota. He was impressed by my letter, “Sangaku is a wonderful world, so we two will research it”. In 1988, I know that Dan Pedoe struggled in publishing the Sangaku. When he introduced the theorem on an ellipse of Sangaku in his lecture in Australia, one participant sent another solution to me. Dan Pedoe consulted about publishing “Sangaku” with Australian Mathematical Society. The answer to this was Ralph Stanton of the University of Winnipeg in Canada. Japanese Temple Geometry: Sangaku was published by CBRC, Winnipeg in 1989, thanks to him. This book contains interesting geometry problems. It is my first book, dedicated to Australian Mathematical Society.

The book was read by many people. Thanks to this book, Sangaku was introduced to the world for the first time. Tony Rothman especially had many answers and asked questions about this book. The interaction with Rothman is the longest one. He solved many problems. And I helped him write his article in Scientific American in 1998. This article was organised by Tony about 5 years ago. From then on, Tony and I continued to discuss on Sangaku problems over a long period. There happened more interesting things. Tony moved to Princeton University, deepened the acquaintance with the eminent physicist Freeman Dyson. Freeman Dyson was a student, to whom Dan Pedoe had taught geometry in London. So Dyson cooperated with me after Dan Pedoe requested him to help me. In 1994, I bought a fax machine. The first fax mail was not from any Japanese but from Princeton University, Freeman Dyson’s recommendation to my new book in Japan. Collaboration between Freeman Dyson, Tony Rothman and myself enabled Sacred Mathematics to be issued from Princeton University in 2008. Tony Rothman drew all of about 300 figures, rewrote my manuscript and changed the sequential order of the contents. He did most of the work. My English is still not good and I am learning English from my English teacher Mr Takeshi Taniguchi, my friend. Even now, my English is still not so good.

SR: How have the Japanese received your book? I think there was a recent Japanese movie on Yamaguchi Kanzan and the Sangaku. Was it related to your work in any way?

HF: After my book Japanese Temple Geometry Problems:

Sangaku with Dan Pedoe was published in Canada, I thought it would be easy for me to publish the Japanese version since I originally wrote the manuscript in Japanese. However, it was not easy to find a publisher in Japan. I wasn’t so famous then. However, Mr Setsuo Tanaka, staff of Morikita Shuppan, publisher in Tokyo, was intrigued by my manuscript. In 1991, I managed to publish the Japanese version of my book, Japanese Temple Geometry Problems with Morikita publisher. It is said in Japan, that a mathematics book is a success if 3,000 copies are sold. The book I translated sold more than 12,000 copies. One reader who was in hospital sent me a letter, in which he wrote “I have a lot of time to solve many interesting problems in the book. Many thanks for your book”. I was the first person to introduce Sangaku to the world as mathematics. In 2008, Japanese version of Fukagawa Hidetoshi and Tony Rothman’s Sacred Mathematics by Princeton University was published by the same publisher Morikita Shuppan. After this book, historians got interested in the study of Sangaku. A movie “Tenchi Mei Satsu” featuring the strategist of Edo period was made in 2012. I was not involved in this film. I have not seen this movie. In this movie, Yamaguchi Kanzan has nothing to do with story of this film. Yamaguchi’s diary has not yet been published in modern Japanese language.

SR: How has the world outside reacted to your extraor-dinary findings [Research]?

HF: The late Professor Shiko Iwata, prominent geom-eter in Japan, knew that the mathematical contents of Sangaku were very good. Iwata, his friend Isao Naoi and I had been studying and analysing traditional Japanese Mathematics very enthusiastically. I thought about studying English, to introduce Sangaku abroad. I sent a letter to ten geometricians of the world, in which beautiful Sangaku theorems were written. Only Dan Pedoe gave me a reply. He was a friend of Leo Sauv (1921–1987), a world renowned geometrician who edited at that time Canada’s geometric problem solving journal Crux Mathematicorum. Dan Pedoe advised me to contribute the Sangaku problems to Crux Mathemati-corum of Canada. Leo Sauv edited the Sangaku problem and put the problem 995 in the December 1984 issue. This is the first time that Sangaku was introduced to the larger world. I thereafter provided many problems with this magazine, Crux Mathematicorum. I have received letters from people in many countries who read the magazine. Of course, I introduced Sangaku problems to mathematics magazines in Japan prior to



this, but nobody had been interested in the Sangaku world. The book published by Winnipeg University with the help of Dan Pedoe in 1989, Japanese Temple Geometry was decisive. Pedoe wrote most of the texts since I was not good at English. He was a prominent geometer and wrote Sangaku problems as “problems of Euclid”. Pedoe has spread Sangaku to all over the world. A modern Greek complained to me in his letter, “There is no Geometry other than in Greece”. After some years, he came to love Sangaku.

SR: What is the oldest Sangaku that you have come across?

HF: There are 900 Sangaku tablets remaining and the oldest Sangaku was hung in 1683 at Hoshinomiya shrine of Tochigi Prefecture. The surface of this plate was burnt, and cannot be decrypted. But before it was burnt, local junior students had already made a replica, we can see its content. Because we were unable to carry the earliest Sangaku, we carried the replicas when the national Sangaku exhibition was held in Nagoya. I supervised and exhibited it in 2005 at the Nagoya City Science Museum. The replica of the earliest Sangaku is a board 180 cm wide and 90 cm in height. There is actually in the Edo era (1603–1867), 54 years ago before the earliest surviving Sangaku, a recording of an even older Sangaku hung in the shrine of Fukushima Prefecture after 1657. After the Sangaku exhibition in Nagoya, five more tablets were found in Toyama Prefec-ture. When I held the Sangaku national exhibition, a local historian became interested in the Sangaku and found one new Sangaku. However, in the catastrophic earthquake disaster in the Northeast Japan in 2011, we lost two or three tablets in Fukushima prefecture. Recently in modern children’s events, they make small Sangakus freely, in which modern school mathematics, not traditional ones, is written. But they have nothing to do with traditional Japanese Mathematics.

SR: You are clearly passionate about this. What future plans do you have in this regard?

HF: Two weeks ago, I solved problems of a Sangaku tablet dedicated in 1841 at Tashiro shrine in Yoro-Cho of Gifu prefecture, which I visited and gave the analysis to the priest, since nobody had been able to analyse the content of the Sangaku by then. Five problems written on the tablet were so interesting. Three of them were submitted by twelve, thirteen, and eleven year old boys respectively. Two other problems were so difficult to

solve that it took me one month to solve the problems. I wanted to show the five problems to undergraduate mathematics students. Sangaku problems often interest people. For example, a geometric problem among birds and flowers, depicted on the ceiling grid in the temple in Nagano prefecture was so nice and I submitted it to the Crux Mathematicorum. Now the temple no longer exists.

A British geometrician visited Japan several years ago, and he wanted me to see his solution to the problem and came to my home in Gifu, since he was so excited to find it after some struggles. He found the best answer to this problem. We just met in my home, and I have never been acquainted with him before that. In fact his solution was so good. His name is John F Rigby and his solution is introduced in [2]. Thanks to his invitation, I was given a chance to demonstrate the Sangaku to the teachers of high school who graduated from the University of Wales in 2004.

In 2012, the idea of giving some Sangaku tours to the people from other countries was proposed to me. In March 2012, a Swiss mathematician, Professor Emmanuelle Gracchi, and in April, Carsten Cramon of Denmark with 20 people visited me. In July, American mathematician David Clark of Randolph-Macon college, in August, a student Ian Johnston of Boston University, and in September, Rosalie Hosking from New Zealand visited Ogaki Sangaku. Currently I am preparing for a visit of 20 Singapore high school students in August 2013. They are going to visit Sangakus at Atsuta shrine in Nagoya city and Ogaki. Since languages are different, they won’t know its contents. One visitor, Professor Peter Wong of Bates College in the US, with more than 20 years of acquaint-ance, knows the content of Sangaku. I was surprised when I met him for the first time, by his understanding of the content of the Sangaku. However, he couldn’t understand or speak Japanese. Generally people don’t know the contents of Sangaku and so I would like to translate it, and introduce it to the world. Sangaku is a great material for mathematics education. In September this year, I will visit two universities — Valladorid and Sevilla of Spain, and will give a talk on Sangaku.

SR: Your own personal favourite problem and solution among the Sangakus.

HF: Circles and triangles and rectangles are geometric tools in traditional Japanese mathematics. Let me introduce an interesting simple problem. An equilateral triangle ABE has sides of length 10 units and, an outside



square ABCD has side length 10 units. The problem is to find the radius of the circle that passes through the three points E, C, and D. This is not a Sangaku problem but quoted from the book published in 1877. The other problem has not been solved yet and is recorded in Yamaguchi’s diary, which is a Sangaku problem. It was described as “problem not solved yet” in his diary. I think it’s pretty hard. I have not been able to solve it. Two externally touching circles of radii a and b lie on the straight line L. Describe a square inscribed in the space bounded by two circles and the line. The side of square x varies. Find the minimum and maximum of x in terms of a and b. I think it’s pretty hard.

In 1994, in some conference of Bulgaria, an aged mathematician who sat in the front row at the Confer-ence in Bulgaria asked me a question. Are there unre-solved problems in the Sangaku world? Since I had not studied the diary of Yamaguchi at that time, I couldn’t answer him. His name was Paul Erdos (1913–1996).

SR: Has this taught you something about traditional schooling or learning in Japan?

HF: Sangaku problems are difficult for high school students and I didn’t teach them at my high school. I introduced Sangaku problems in “Mathematics magazines for high school students” in Japan. Other work of mine on Sangaku was to introduce Sangaku

to high school math teachers of Aichi prefecture in the workshop during 1980–1992. Currently I am teaching university students of the department of mathematics at Nagoya University, from 1990 till now. Moreover, I have introduced the Sangaku in mathematics education at several universities.

From 1987, in Bulgaria, I provided Sangaku prob-lems on the cover every month for teenage magazines in Bulgarian Education of Mathematics and Informatics until 1992. In the 1987 issue, a student of Bulgaria high school came up with a wonderful solution to a Sangaku problem. This project was run by geometrician Jordan Tavob of Bulgaria Academy of Science.

In 2005, I organised “The National Sangaku exhibi-tion” at Nagoya City Science Museum and exhibited one hundred Sangakus, carrying them to Nagoya by truck. The leading newspaper Asahi Shimbun spent a huge amount of money. Mr Abe Haruki from Asahi Shimbun proposed this exhibition. This large scale exhibition touched many people.

SR: When you compare the solutions of some of the geometric problems and solutions, is there anything strikingly different in the way of approaching a problem in this culture as opposed to say, the Greeks and the geometry developed by the Greeks? Or later in other European countries?

HF: “Wasan”, traditional Japanese Mathematics, developed based on the Chinese mathematics. Sangaku world is a part of “Wasan”. Computation is the subject there. Contrary to this, Greek mathematical or Western geometry has evolved from logic as the subject. For example, when a triangle was given, Feuer Bach circle has the relation passing through three midpoints of the sides of triangle and nine points of the triangle in western geometry. Wasan mathematicians calculated the radius of the circle touching three circles in terms of three sides. The aims of western mathematics and Japanese mathematics are the relations and calculations respectively. Complex calculation is the main aim of Wasan and Sangaku.

See [1, p. 111]. In [3, Chapter 6, p. 232], you can find factoring a fourth degree equation into two second degree equations. Few Sangaku theorems on the ellipses are found in Western mathematics. See [1, pp. 50–68].

Sangaku problems introduced in [3, pp. 212–216] were calculated redundantly. Immediately after publica-tion in the United States, a good short solution appeared in the article in the USA. After long calculations on circles or spheres contacting problems, Japanese



mathematicians then got a clean result. But it can be gained easily by the modern inversion technique. In 1937, in the west “six ball chain theorems” was published by Nobel prize winner Fredric Soddy, but the same theorem had already been used in Sangaku about 100 years before. Also we find the same analysis diagrams, “Descartes circle theorem” in complete works of Descartes, but it is seen in the old book already used. See [3, p. 286].

SR: Thank you for this wonderful interview, it has been a pleasure interacting with you.

References

[1] H. Fukagawa and D. Pedoe, Japanese Temple Geom-etry Problems: Sangaku (CBRC, Winnipeg University, 1989).

[2] H. Fukagawa and John F. Rigby, Traditional Japanese Mathematics Problems of the 18th and 19th Centuries (SCT-publishing, Singapore, 2002).

[3] H. Fukagawa and T. Rothman, Sacred Mathematics (Princeton University Press, 2008).

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

R Sujatha University of British Columbia, [email protected]



Sujatha Ramdorai: Tell us a little about yourself.

Tony Rothman: I’m a theoretical physicist who has specialised in general relativity and cosmology. Most of my research has concerned the very early universe and black holes. I am just finishing a six-year appointment in the physics department at Princeton University and will be teaching at The College of New Jersey in the fall. I’ve also done a fair amount of writing for the general public (sometimes I hesitate to call it “popular”). Quite recently I published my tenth book, Firebird, which is a novel set in a fusion-research laboratory. I think it is unusual in that it isn’t science fiction, but an attempt to base a novel on real science. To the best of my abili-ties the science is totally accurate and, unfortunately, the politics too. I’ve also just drafted a play about the famous sixteenth-century Cardano–Tartaglia feud over the cubic equation. It’s been fun, but difficult. One question has been how “accurate” to make it. Much of what is written about it in the semi-popular literature is nothing more than fairy tales. Several recent books have Tartaglia causing Cardano’s arrest for heresy — 13 years after Tartaglia died! At any rate, it’s something that I needed to get done.

Interview with Tony RothmanSujatha Ramdorai

Tony Rothman

SR: What appealed to you in the Sangaku story and Hidetoshi’s work that you decided to collaborate on the book?

TR: While in high school my favourite math subject was certainly geometry. I think mathematicians have either algebraic imaginations or geometric imaginations. I don’t consider myself a terribly creative mathemati-cian — like most physicists I use mathematics to solve problems — but my own imagination is certainly geometric. I suspect this is one reason I fell in love with relativity, which is a very geometric subject. My contact with Sangaku came about during a very specific space-time event. One day, as I recall, in winter 1989–1990, I stopped by Freeman Dyson’s office at the Institute for Advanced Study in Princeton. We were probably just planning to have lunch. As soon as Freeman raised his hand to say hello, he said, “Take a look at this,” and handed me the Sangaku-problem book Hidetoshi had just published with Dan Pedoe, who had been Free-man’s math teacher long ago in England. I had abso-lutely no idea of what “Sangaku” or “temple geometry” meant. As I leafed through the book with dropped jaw, Freeman stood there laughing. I found the problems visually striking, quite different from anything I had seen in school — they even looked Japanese. But the main impression was how damn difficult they were. For all my love of geometry, I quickly realised to my embarrassment that I hadn’t the faintest idea of how to solve most of them. The fact that they were found in temples and had evidently been largely created by farmers and peasants was an additional embarrassment, not to mention extremely intriguing. I bought a copy of the book for myself, worked on some of the problems and eventually contacted Hidetoshi about a possible Scientific American article, which I wrote with his assistance. The article sat at the magazine for three years before it was published — even though I had been an editor there. When it finally appeared, it proved fairly influential — I think it was the first major piece in the West about Sangaku — and it helped make temple geometry part of the world heritage of mathematics.



So I am happy about that. I hadn’t initially intended to write an entire book about temple geometry. I prefer to write fiction, actually, but it has become almost impossible to get fiction published. And so, around 2005, when all my fiction projects had collapsed, I contacted Princeton University Press about doing a book on Sangaku and the editor there, Vickie Kearn, quickly agreed (literally within about twenty minutes, although it was actually the second time I approached them; a previous editor had expected me to pay for it!) I did all this without even telling Hidetoshi, but he was quite glad to hear the news.

SR: One of the things that strikes the reader — and which you comment yourself — is the aesthetic side of the Sangaku. What are your thoughts on this.

TR: As I said, I found the problems quite beautiful — miniature Japanese works of art. Like most scientists, I suspect, I am drawn to “clean” artwork — I am always struck by how many of my colleagues have collections of African art, and I do as well. Japanese art certainly fits the bill. In fact, I think the Japanese are incapable of creating anything ugly. I was also struck by the asymmetry in many of the problems, compared to the Greek-inspired problems we all face in high school. From Daisetz Suzuki’s books on Zen, it seems that asymmetry is a characteristic feature of Japanese art. So I suspect that the whole aesthetic of Sangaku evolved from the Japanese artistic aesthetic. I’m certain that many of the problems evolved from everyday situa-tions and objects — like fans, which are really sectors of circles, and origami designs. The tablets themselves are also beautiful, brightly coloured, and in one case, surrounded by a striking dragon frame.

SR: Can you tell us more about the whole collaborative process?

TR: It wasn’t easy. To this day, Hidetoshi and I have never met. I don’t speak any Japanese and his English, although it’s improved over the years, is far from his native language. The whole thing was done by email. Over the two years we worked on it, I’d guess we exchanged about a thousand emails. Luckily, mathematical terminology is limited and, usually, well defined, but sometimes we would exchange ten emails just to clarify one sentence. Hidetoshi is the expert on Sangaku; my role was basically editorial. He would send me the raw material and I would check it for errors and rewrite the problem statements into

respectable English. The intro chapters I wrote pretty much from scratch. Also, I wanted the book to appeal to non-mathematicians, so I tried to avoid technical terms when possible, even when they might have made things clearer to geometers. We had some organisational issues as well. Hidetoshi wanted to organise the book by tablet, but this resulted in very easy problems being placed side by side with nearly impossible problems, and I felt that this would discourage a lot of readers, not to mention make presentation of solutions extremely difficult. So I reordered everything, placing easy problems first and harder problems later. Most of the solutions were either traditional or Hidetoshi’s, but I also contributed a few and did all the line drawings, mainly because Hidetoshi’s drawing software wasn’t compatible with anything I had. The whole thing ended up being a gigantic jigsaw puzzle. From a design perspective, it was certainly the most complicated book I’ve worked on. The Princeton University Press art director, Dimitri Karetnikov, was very helpful in this regard.

SR: Has working on this project led you to explore other areas of “Japanese Science” or other forms of Japanese knowledge or culture, especially from that period or earlier?

TR: I am not a scholar of Japanese culture — and don’t speak Japanese — so I haven’t plunged far into related areas, but I am intrigued by certain aspects of Japanese mathematical history, which seem to me not well understood. For instance, the feudal Japanese mathematicians didn’t know calculus — at least what we regard as calculus — and we don’t know anything about how they handled differentiation. Yet some Sangaku problems seem to require differential calculus for their solution. It is a mystery to me how the Japanese solved them. Also, there is a whole field known as “Rangaku”, literally “Dutch Learning”, which concerns foreign knowledge that seeped into Japan during the period of national isolation through the Dutch trading post on Deshima island. There seems to be quite a debate among scholars about just what the Japanese knew of foreign science and when they knew it, but the Wikipedia article on Rangaku, for example, isn’t very satisfactory. I would be interested in learning more about Japanese knowledge of foreign developments in mathematics. Finally, my Scientific American article and the book seem to have given people the impression that everybody in Edo-period Japan was creating Sangaku. It is difficult to estimate the number of original tablets, but even if there were



50,000, that would only be about 150 a year over three centuries, and that is surely an upper limit. Since many of the problems on different Sangaku are duplicates, I suspect that we have most of the problems that were created — only several thousand. So it may not have been such a widespread cultural phenomenon. One or two other Sangaku investigators have written to me about such matters and perhaps they should all get together and try to sort them out.

SR: The book is well publicised in the West. What have the reactions been to what one might call a “Coffee Table” book on mathematics?

TR: It was my intent from the start to create exactly the first coffee-table math book; I even called it that and I guess it has been received as such, although I don’t know of too many people who bought it just to look at the pictures. (Given the available resources, Princeton University Press did a good job. The book would have been even more beautiful if Abrams had published it, but it would have cost $100.) Most of the feedback I’ve gotten has been from mathematics faculty members at various universities who are planning a trip to Japan and would like to see a Sangaku in the flesh. I pass them on to Hidetoshi, who knows where they all are. (I should say that most of the original Sangaku have been removed from the temples and are either in museums or in temple storehouses, where you need prior permission to view them.) One interesting outcome is that an artist in Santa Fe, Jean Constant, has based a whole series of his and his students’ works on Sangaku. They’re quite striking. A furniture maker has also created a “sangaku” line. I’m always glad when science or math inspires artists, even if their creations are metaphorical. Nevertheless, in this case most of my mail has come from mathematics people.

SR: Tell us a little about your experience in this whole transcultural, mathematical journey that straddles two civilisations.

TR: I think I’ve already given some idea about that. In general I believe in culture shock — it keeps you on your toes. Certainly, to interact with someone from a different culture whom you’ve never met — especially by email — takes a lot of patience. The whole situation is a minefield for misunderstanding, and sometimes I think Hidetoshi and I blew each other up. When I taught in Korea a few years ago and would hang out with the students, the long silences made me uncomfortable,

until they told me that silence was admired in their culture. Luckily, mathematics itself is universal. The problems were basically Euclidean geometry problems, and although the Japanese often attacked them with methods that wouldn’t have occurred to me, I was nevertheless able to understand what they were doing. I do feel that I wasn’t the ideal person to collaborate with on the book. A mathematician fluent in Japanese and versed in Japanese history would have been a better choice. My only qualification was that I stepped up to the plate.

SR: When did you actually first see a Sangaku in reality?

TR: Believe it or not, I never have. I’ve travelled widely around the world, and have lived for many years abroad, but for some reason have never been to Japan. As I just said, I wasn’t the ideal person to do this book. I hope someday to get there and then Hidetoshi will show me some.

SR: Did you notice anything different in the way the problems were posed and answered, compared to your own training in the West?

TR: Sure. The repeated, intricate use of the Pythagorean theorem was really ingenious, if at times cumber-some. It’s amazing how much you can do with just the Pythagorean theorem. One eye-opener was the Japa-nese way of dealing with ellipses, which is quite different from ours. The Japanese mathematicians viewed an ellipse as a slice through a right circular cylinder, not as a conic section. A circle inscribed in the ellipse was the projection of a sphere in the cylinder onto the slice. They could then use the Pythagorean theorem to connect the various important lengths involved. This “3-D” approach allows you to solve some really difficult problems, which I never would have been able to do using the usual equation for an ellipse. In fact, you don’t even need the usual equation for an ellipse.

I did find some of the problems ill-posed. Hidetoshi tells me this is a feature of traditional Japanese math-ematics. For instance, take problem 7.12 in the book, which is an unsolved problem in which you are asked to find the radius of three identical circles, two of which are inscribed in an ellipse, which is itself inscribed in a right triangle along with the third circle. It wasn’t at all clear to me at first that there even was an analytic solution. Recently Jesu Alvarez Lobo from Spain has sent me his solution. I haven’t worked through it,



but it seems to be a tour-de-force, over thirty pages (arXiv:1110.1299). He does find an analytic, closed solution for an isosceles right triangle, but for the general case he can only get an implicit solution. Some of the traditional solutions are from another galaxy. We are often taught to draw auxiliary lines in high school geometry courses to solve problems. In at least one Sangaku problem (6.3), the author of the solution introduces an entire auxiliary circle, which at first seems to have nothing to do with the problem whatsoever. I doubt I’d ever have thought of that solution. And again, it wasn’t entirely obvious to me that there even was one. Lobo showed that the solution exists only for a particular base angle of the isoceles triangle involved in the problem. Also, many of the solutions, especially by Yoshida Tameyuki, assume rather sophisticated lemmas or other steps, which aren’t stated. I don’t know whether Yoshida just assumed everyone knew them or what, but I doubt I’d ever present a proof with so many important details missing. One thing I learnt, is that to solve these intricate Sangaku problems, you have to make a really good drawing, not just a sketch. And in proving things about triangles you should never draw a 45-degree line.

SR: There were algebraic, arithmetic as well as geometric problems that were posed, though geometry seems to have been the most popular. Some of the problems, as you observe in the book have appeared in other guises in other cultures. Why do you think Geometry was more popular?

TR: Many problems, both algebraic and geometric, pop up in different cultures, just as most scientific discoveries are made multiple times. I don’t know whether the duplication of the math problems was due to cross-fertilisation by “word of mouth” over the centuries, or whether they cropped up independently. Certainly every time I do something in physics, no matter how obscure it seems, somebody else always claims to have done it first! If geometry problems have been more popular, it must be because of the visual appeal, and in some sense geometry is easier than algebra. Even if you are algebraically challenged, as I often am, you can often solve problems geometrically, and many of the basic geometric theorems regarding angles and so forth are pretty self-evident, so you don’t really have to prove them before solving a problem. In writing this play about Tartaglia and Cardano, I was looking at the Tartaglia–Cardano solution to the depressed cubic equation. They did this before modern

algebraic notation existed and so you might think it really hard. But to find the cubic formula is actually really easy if you think geometrically and remember that a cubic equation must give the volume of a cube. If you slice up the cube as those fellows did, the cubic formula falls out almost immediately. It’s a good lesson. Nowadays we have algebratised geometry to such an extent that we’ve often make things more complicated than they really are.

SR: “Sacred Math”, “Temple Geometry”.... In the West it would almost be anachronistic to juxtapose science and the spiritual in this manner, yet this appears natural in the East. Especially the thought of the problems and solutions being offerings to the divine! What are your thoughts on this....

TR: The idea that mathematical tablets were presented as religious offerings is very appealing to me, but of course, the Buddhist idea of God, or the divine, is much more abstract than Western ideas. Some readers of our book have suggested that our use of the word “God” in the translation of some of the tablet inscriptions may not be accurate. Unfortunately, since I don’t know Japanese, I am unable to say. Russians often speak of “lighting a candle to God”, whether they are talking about creating a work of art or solving a scientific problem. That’s more or less how I feel about it, although in my case “God” may be even vaguer than it is for the average Buddhist. I think, though, that Sangaku served several purposes. Since hanging tablets in temples and shrines was a long-established tradition in Japan before the advent of Sangaku, one can’t rule out the possibility that many people were just doing it for “fun”, or maybe with about as much religious fervour as most Americans celebrate Christmas. Some tablets were apparently created by classes at small schools, called Jyuku, and almost certainly these were hung in the temples as advertisements for the school. In any case, since the Sangaku almost always contain an answer, but rarely the solution, they were pretty clearly issued as challenges to other “worshippers”.

SR: Any lessons you have learnt or any other related thoughts you might want to share?

TR: It’s become clear to me that geometry education has declined considerably, at least in the US. To write Sacred Mathematics, I consulted a number of textbooks that are currently used in high schools, but they were totally inadequate to solve most Sangaku problems. To write



the chapter on inversion, I needed to go back to texts that were literally a century old, e.g. Clement Durrell’s geometry. Inversion simply isn’t taught anymore, except in some advanced college math courses. And it’s not even that hard!

SR: Thanks very much for taking the time for the interview.

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

R Sujatha University of British Columbia, [email protected]



Problem Corner 3.4Ivan Guo

1

Problem Corner 3.4Ivan Guo

Welcome to Problem Corner 3.4. If yousolve any of these problems, please sendyour solutions to [email protected] by

30 November 2013. A book prize will be awarded tothe person with the best submission. The solutionswill be posted in a future Problem Corner.

Problem 1 — Distinct Sets

Let a ≥ 2 be a positive integer. Prove that ifi1, i2, . . . , ik and j1, j2, . . . , jl are different sets ofpositive integers, then we must have

(ai1+ 1)(ai2

+ 1) · · · (aik+ 1)

(aj1+ 1)(aj2

+ 1) · · · (ajl+ 1).

Problem 2 — Colouring Game

Alice and Bob play the following game on an m×n grid. Each player, on their turn, must choosetwo uncoloured squares with a common side andthen colour them in. Alice goes first. A player whocannot move loses.

(a) Who has a winning strategy if m = 2012 andn = 2012?

(b) Who has a winning strategy if m = 2012 andn = 2013?

Problem 3 — Circular Calls

A group of friends talk on the phone every day sothat each pair of them talk to each other exactlyonce. On one particular day, each one of themcalled up at least one other person.

Is it necessarily true that there will be threefriends such that the first called the second, thesecond called the third and the third called thefirst?

Problem Corner 3.3 Solutions

A prize is awarded to Minh Can for his submissionin Problem Corner 3.3. Congratulations!

Problem 1 — Simultaneous Equations

Find all solutions to the following system ofequations

x(y + z + 1) = y2+ z2 − 5, (1)

y(z + x + 1) = z2+ x2 − 5, (2)

z(x + y + 1) = x2+ y2 − 5, (3)

where x, y and z are all integers.Solution: Suppose that x, y and z are not all

equal. Without the loss of generality, say x y.Subtracting (2) from (1), we arrive at the followingequation,

xz + x − yz − y = y2 − x2

⇐⇒ (x + y + z + 1)(x − y) = 0.

Since x y, this implies that x + y + z = −1.Substituting back into (1), we have

x2+ y2+ z2= 5.

Since x2, y2 and z2 are perfect squares, the onlypossibility is for them to be 0, 1 and 4 in some

order. Since x + y + z = −1, we must have(x, y, z) = (0, 1,−2) or some permutations of them.It can be easily checked that they are indeedsolutions.

Now suppose that all three variables are equal,or x = y = z. Then (1) quickly simplifies to x = y =z = −5. This solution also clearly works.

To summarise, the full set of solutions aregiven by:

(x, y, z) = (0, 1,−2), (0,−2, 1), (1, 0,−2), (1,−2, 0),

(−2, 0, 1), (−2, 1, 0), (−5,−5,−5).

Problem 2 — Icosahedral Planet

Two aliens are situated on opposite vertices of asmall planet shaped like a regular icosahedron,whose edge length is one mile. Due to technolog-ical restrictions, the aliens may only travel alongthe surface of the planet.

What is the shortest length one alien musttravel in order to visit the other?

Solution: Denote the positions of the aliens,two opposite vertices of the icosahedron, by A andB. We shall present the shortest path between Aand B using the net of the icosahedron. See thefollowing diagram.



Ivan [email protected]

Ivan Guo is with the School of Mathematics and Statistics, University of Sydney.

2

A A A A A

B B B B B

Note that both A and B appear five times inthe diagram because every vertex is adjacent tofive triangles.

From the diagram, it is clear that the shortestpath between A and B is indicated by the straightdotted line. Its length x can be calculated usingthe cosine rule,

x =√

12+ 22 − 2 × 1 × 2 × cos 120 =

√7.

Hence the required answer is√

7 miles.

Problem 3 — Football Competition

In a national football league, there are n teamscompeting in a round robin competition. Everypair of teams plays each other exactly once duringthe season. In the country, there are n − 1 footballstadiums available for the competition.

For which n is it possible to run the competi-tion, so that no team plays in the same stadiummore than once?

Solution: The case of n = 1 holds trivially, asno matches will be played. Now consider the caseof n ≥ 2. In particular, we will prove that it ispossible to run the competition if and only if n iseven.

First suppose that n is an odd integer greaterthan 1. Since each team plays in n−1 matches andthere are only n− 1 stadiums available, each teammust play in each stadium exactly once. But since

every match involves two teams, each stadiummust host exactly n/2 matches. This is not possiblesince n is odd.

Now we show that the conditions can besatisfied when n is even. Denote the teamsby T∗, T0, T1, . . . , Tn−2 and the stadiums byS0, S1, . . . , Sn−2. Organise the competition asfollows:

• The match between Ti and Tj are played inthe stadium Si+j, where the indices are takenin modulo n − 1.

• The match between T∗ and Ti are played inthe stadium S2i, where the indices are takenin modulo n − 1.

It suffices to check that no team plays twomatches in the same stadium. We will argue viacontradictions. Note that all of the following con-gruences are taken in modulo n − 1.

• If Ti played against Tj and Tk in the samestadium, then

i + j ≡ i + k =⇒ j ≡ k,

which is a contradiction.• If Ti played against Tj and T∗ in the same

stadium, then

i + j ≡ 2i =⇒ j ≡ i,

which is a contradiction.• If T∗ played against Tj and Tk in the same

stadium, then (since n − 1 is odd)

2j ≡ 2k =⇒ j ≡ k,

which is a contradiction.

So in all cases, no team has played more thanonce in the same stadium. This completes theconstruction.

Therefore it is possible to run the competitionif and only if n = 1 or n is even.



Michio Jimbo and Tetsuji Miwa Awarded the Dannie Heineman Prize

for Mathematical PhysicsYoshihiro Takeyama

In March 2013, the Dannie Heineman Prize for Math-ematical Physics was awarded to Professor Michio Jimbo (Rikkyo University, Japan) and Professor Tetsuji Miwa (Kyoto University, Japan), for profound developments in integrable systems and their correlation functions in statistical mechanics and quantum field theory. Their works make use of quantum groups, algebraic analysis and deformation theory. I am sure that many researchers in the field of integrable systems recognise that their contributions are really essential, including the theory of holonomic quantum fields studied with Professor Mikio Sato, transformation groups for soliton equations and correlation functions of solvable lattice models.

Their textbook Algebraic Analysis of Solvable Lattice Models (published by the AMS in 1995), which is widely known to mathematicians and physicists, is a special book for me. When I was an undergraduate student, Professor Jimbo gave a series of lectures on solvable lattice models. One day, I visited his office and asked several questions about his lectures. After answering, he showed me the textbook and said to me “if you intend to make earnest efforts on this subject, I present this book to you.” I was very delighted to receive a book on mathematics from a mathematician. This encourage-ment led me to decide to become a mathematician.

Professor Miwa was my supervisor when I was a graduate student. He is a very active mathematician. We had a weekly seminar on F Smirnov’s book Form Factors in Completely Integrable Models of Quantum Field Theory (published by World Scientific in 1992). Every time he followed precisely the calculations in the book, much more than I did. One day he said “I was exhausted by meetings yesterday, so I did calcula-tions to recover myself.” This showed to me what a mathematician is.

After I received my PhD degree, I studied with Professor Jimbo and Professor Miwa on form factors and related topics in the representation theory. It was a happy period for me. I am convinced that many researchers who studied with them have the same impression during the joint works. In 2009 and 2011

we held workshops dedicated to the 60th birthdays of Professor Miwa and Professor Jimbo, respectively. During the whole workshops, the speakers and partici-pants close to them gave warm reminiscences.

As above, I owe what I am today to my teachers Professor Jimbo and Professor Miwa. I would like to sincerely congratulate them on their winning the Dannie Heineman Prize.

Translated from Sugaku Tushin, Vol. 18 (1) (2013)

Michio JimboCurrent affiliation: College of Natural Science, Rikkyo University. PhD from Kyoto University.

Research Career: Research Associate at RIMS, Kyoto University. Professor at Kyoto University and the University of Tokyo until 2008.

Tetsuji Miwa Current affiliation: Professor Emeritus at Kyoto University. PhD from University of Tokyo.

Research Career: Associate Professor at RIMS, Kyoto University. Professor at RIMS, Kyoto University until 2013.

Yoshihiro Takeyama is an asso-ciate professor at University of Tsukuba since 2011.

He got a PhD from Kyoto University in 2002. His research interest includes representation theory, difference equations,

special functions and combinatorics arising from quantum integrable systems.

News in Asia Pacific RegionNews from Australia

Royal Medal for Rodney Baxter

Rodney Baxter FRS, Emeritus Professor at the Math-ematical Sciences Institute at ANU, has been awarded the Royal Society’s 2013 Royal Medal for “his remark-able exact solutions of fundamental models in statistical mechanics”.

King George IV founded the Royal Medals in 1825. Each year now, three medals are awarded for the most important contributions in the physical, biological and applied sciences, by citizens or residents of Common-wealth countries and the Irish Republic. Also known as the Queen’s Medals, they are awarded annually by the Sovereign on the recommendation of the Council of the Royal Society. The three medals are of silver gilt and are accompanied by a gift of £5000.

The list of former recipients speaks for itself. Amongst them: Andrew Wiles, Simon Donaldson, Roger Penrose, Abdus Salam, Francis Crick, Michael Atiyah, Subrahmanyan Chandrasekhar, Paul Dirac, Lord Rayleigh, JJ Sylvester, Arthur Cayley, Michael Faraday, George Boole and John Herschel.

Exactly solved models play an important role in equilib-rium statistical mechanics, particularly their behaviour near a critical point or phase transition, as this is where previous approximate theories can fail dramatically.

Professor Baxter is single-handedly responsible for solving exactly an impressive collection of two-dimensional lattice models, by generalising the Bethe

ansatz method. In particular, the Hard Hexagon Model helps to explain accurately how helium is absorbed into graphite.

He remains active, despite having officially retired from ANU in 2003 after almost 35 years of service. As he said to the ANU Reporter, he was very pleased to receive the news, which he almost mistook for junk mail:

“The news came in the form of a letter from the Royal Society and when I saw it on my desk I just put it in my pocket thinking ‘oh, it’s just another circulation’. So I was carrying it around for a couple of hours before I actually read it.”

The Awards presentation will take place in November, at the Royal Society headquarters in London, where he was admitted as a Fellow in 1982.

Australian Mathematical Sciences Student Conference

The second Australian Mathematical Sciences Student Conference (AMSSC) was held at the Australian National University (ANU) from July 15 to 17. The aim of the conference was to provide a relaxed environ-ment in which graduate students of the mathematical sciences, from all over Australia, had a chance to meet and share their work, and to provide a platform for possible future collaboration.

The event attracted 75 student participants from across the country, with attendees from as far as Perth, Adelaide, Toowoomba and Hobart. The 61 student presentations covered a broad range of topics, from invariants of supermanifolds to the effect of climatic



and oceanographic variables on penguin survival. The organisers were impressed with the volume of material that included original research. While most of the attendees were PhD students, there were 20 honours and masters students at the conference, many of whom also presented talks.

Guest speakers were Associate Professor Mary Myer-scough (University of Sydney), who gave a presentation of her work in modelling the behaviour of social insects; Professor Mathai Varghese (University of Adelaide) who talked about index theory and his work developing fractional index theory; and Dr Marty Ross (Math-ematical Nomad) who gave an entertaining exposition on the art of communicating mathematics. In addition, as part of the 2013 year of the Mathematics of Planet Earth, a public lecture was delivered on the Monday evening by Dr Steve Roberts (ANU). Steve described the mathematical modelling of floods and tsunami waves, and at the same time gave insights into his experiences as a leading developer of the hydrodynamic modelling software ANUGA.

Recently, a Women in Mathematics group was founded, as part of the AustMS, to promote gender equality in the mathematical sciences. On the Tuesday afternoon of the conference, an informal gathering between members of the group and conference participants was held. About 20–25 people attended; the overall sentiment was that the discussion had been fruitful and interesting.

At the end of the conference, three participants were awarded prizes for presenting excellent talks. One of the prizes was dedicated to the best talk from the special stream “Mathematics of Planet Earth”, and the other two prizes were awarded to the best talks from the remaining participants. Billie Ganendran (ADFA) was awarded the Mathematics of Planet Earth prize for her talk entitled “Effect of climate and oceanographic variables on survival of Little Penguins in South-Eastern Australia”, while Matthew Tam (University of Newcastle) and Daniel Mansfield (UNSW) were awarded the remaining prizes for their respective talks “Douglas–Rachford for Combinatorial Optimisation” and “Non-singular dynamics and average return time”. Each of the award winners received a prize of $250, sponsored by the Modelling and Simulation Society of Australia and New Zealand.

News from China

The 10th Feng Kang Prize for Scientific Computing

The 10th Feng Kang Prize for Scientific Computing has been awarded to Dr Huazhong Tang from the School of Mathematical Sciences of Peking University, and Dr Weizhu Bao from the Department of Math-ematics of National University of Singapore. They received the prize for their significant contributions in numerical analysis for Bose–Einstein condensation and computation of Schrodinger solutions; and studies on the mechanism of shock capturing schemes and construction of high resolution schemes for hyperbolic conservation laws.

Huazhong Tang graduated from the mathematics depart-ment of Peking University in 1990. Currently he is a professor at the Department of Computing Science and Engineering in the School of Mathematical Sciences, Peking University. His research areas include numerical methods for hyperbolic conservation laws, computation of Hamilton–Jacobi equation, computational fluid dynamics, adaptive mesh method, large-scale scientific and engineering problems computation, and compu-tational physics.

Weizhu Bao obtained his PhD from Tsinghua University in 1995, and did his postdoc at the Imperial College London in 1996–1997. He has worked in Tsinghua University, Georgia Institute of Technology, Univer-sity of Wisconsin-Madison and National University of Singapore. Currently he is a professor at the Department of mathematics, National University of Singapore.

Professor Bao’s research interests include Bose–Einstein condensation, computational fluid dynamics, compu-tational quantum physics and chemistry, hyperbolic conservation laws, multiscale modelling, simulation and applications, quantised vortices in superfluidity and superconductivity, numerical methods for problems

Weizhu Bao

Huazhong Tang



in unbounded domains, finite element method for some nonlinear problems, numerical analysis and scientific computing, and computational and applied mathematics in general.

The Feng Kang Prize is dedicated to the memory of the late Professor Feng Kang, the founder and pioneer of Chinese computational mathematics. He was a member of Chinese Academy of Sciences, a professor and the founding director of the Computing Centre of the Chinese Academy of Sciences. His work on sympletic methods was awarded the First Prize of National Natural Science Award of China.

The award ceremony will be held on October 19, 2013 at the General Assembly of Computational Mathematics of Chinese Universities, Changsha, Hunan Province.

59th World Statistics Congress Held in Hong Kong

(From left) The Deputy Secretary for Financial Services and the Treasury (Financial Services), Mr Eddie Cheung; the Deputy Commissioner for Census and Statistics, Mr Leslie Tang; the Executive Director of Hong Kong Tourism Board, Mr Anthony Lau; the Permanent Secretary for Financial Services and the Treasury (Financial Services), Miss Au King-chi; Professor K C Chan; the Commissioner of the National Bureau of Statistics of China, Mr Ma Jiantang; the Commissioner for Census and Statistics, Mrs Lily Ou-yang; the President of the ISI, Professor Jae Chang Lee and his wife; and Mrs Nair and the President-elect of the ISI, Professor Vijay Nair; pictured after the opening ceremony.

The 59th World Statistics Congress (WSC) of the Inter-national Statistical Institute (ISI) 2013 was held this year in Hong Kong during August 25–30. It brought together around 2500 statistical experts and practitioners from around the world.

In addition to the usual sessions dedicated to the advances in statistical theory and applications, several sessions were dedicated to celebrating the International Year of Statistics. This included a special presentation by Ron Wasserstein [executive director of the American Statistical Association], who explained that 2013 was chosen as the Year of Statistics because it coincides with many statistical milestones such as the 250th anniversary of Bayes’ theorem. He spoke about the

aims of the campaign — to celebrate the discipline and those involved by highlighting its importance across the world, thus improving the perception and statistical literacy of the general public.

Participating nations had so far celebrated the Inter-national Year of Statistics in a variety of ways, ranging from decorative banners proclaiming the celebratory occasion to Spanish statisticians embarking on bicycle road trips in order to help improve statistical literacy in the local community. More exciting activities are planned for the remaining four months of the year by participating countries.

WSC 2013 also marked the launch of the Karl Pearson Prize, an award recognising a contemporary research contribution that has profound influence on statistical theory, methodology, practice and applications. Peter McCullagh, together with the late John Nelder, were made the first recipients of the prize for their seminal monograph on “Generalised Linear Models” (1983).

As well as accepting the prize, Peter McCullagh also presented a humorous lecture titled, “Statistical issues in modern scientific research”, which demonstrated the invalidity of statistical results presented in a recent published scientific article. This highlighted the need for statisticians to work with scientific researchers from the beginning of their proposed experiment, rather than an afterthought when analysis needs to be performed. Many of the other presentations emphasised a problem with the perception of statistics: that it is a toolbox only to be used for analysis.

Another aim of the International Year of Statistics is to improve perception and awareness of statistics in the world among young people. In light of this, Wednesday, August 28 was designated Youth Theme Day with a variety of activities to showcase the research and opportunities available to young statisticians. Activities included a designated postgraduate students’ session in which the statistical societies of the UK, Spain, South Africa, Korea, Japan and Taiwan were represented by a nominated postgraduate from their country to showcase their research.

A special career development session was also organ-ised by Byeong Uk Park which included talks by Robert Rodriquez (head of R&D at SAS Institute and former president of the American Statistical Association), Jef Teugels (professor at Catholic University of Louvain),



Jing Shyr (a statistical consultant at IBM) and Patrick Poon (professor at Hong Kong University). Talks covered the future opportunities available to upcoming statisticians (particularly with the big data boom and advances in computing power and affordability); the additional “soft skills” that are necessary along with existing statistical skills to be successful statisticians; and the need to “go back to the basics”, occasionally in expanding one’s statistical skill set and checking whether one’s statistical analysis is appropriate.

An interesting presentation also took place on the potential differences between the term “statistician” and the relatively new terms “data scientist” and “business analyst”. All three require a certain degree of statistical skills, although often with different purposes in mind. It was generally agreed that “statisticians” tend to be more pessimistic and conservative with the presentation of their results, “data scientists” often have superior computing skills, and “business analysts” have a specific objective in mind. One final fundamental distinguishing factor between “statisticians” and the other two entities is that they always contribute to the community by sharing their research whether it be through publications or presentations at conferences.

The keynote presentation of the congress was given by Kaushik Basu, chief economist at the World Bank. The presentation, “World Bank goals on eliminating extreme poverty and boosting shared prosperity: Implications for data and policy” highlighted the World Bank’s goals and why it was necessary for all nations of the world and their banks to co-operate and collaborate in achieving this goal. The final remark was how statisticians could get involved in achieving this goal by their existing statistical research and by actively collaborating with the World Bank.

In addition to working hard, delegates were treated to sumptuous banquets, traditional and modern Chinese lion dances, martial arts and spectacular views of Victoria Harbour as part of their social programme.

Detailed information of the 59th WSC is available on its website (www.isi2013.hk/en/index.php).

Courtesy Report by Christopher Nam on 10 September 2013, posted in Features

China Top the 2013 International Mathematical Olympiad

Chinese team photo with the volunteers

The 54th International Mathematics Olympiad (IMO 2013) was held in Santa Marta, Colombia from July 18 to 28, 2013. 527 students from 97 countries and regions participated in the competition. The Chinese team scored 208 points to win the first place, with 5 gold medals and 1 silver medal. The overall top scorer was Liu Yutao (Shanghai High School) who obtained 41 points. China and Korea tied for gold medals.

Members of the Chinese team are as follows:

Liu Yutao (41 points) gold medal Zhang Lingfu (38 points) gold medal Liu Xiao (35 points) gold medalLiao Yuxuan (33 points) gold medal Gu Chao (31 points) gold medal Rao Jiading (30 points) silver medal

2013 IMO top 10 teams and their scores are

1. China (208)2. Korea (204)3. United States (190)4. Russia (187)5. North Korea (184)6. Singapore (182)7. Vietnam (180)8. Taiwan (176)9. United Kingdom (171) 10. Iran (168)

Cut-off points for medals are: Gold: 31, Silver: 24 and Bronze: 15.



News from India

UK-India Initiative in Applied Mathematics Announced

RCUK India facilitated a successful UK-India meeting in July 2012, following which the UK’s Engineering and Physical Sciences Research Council (EPSRC) and India’s Department of Science and Technology (DST) have now launched a jointly funded programme for organising 12–14 workshops in Applied Mathematics in the next two years.

These workshops will take place between April 2014 and April 2016, and will focus on the commonalities between the UK and India and also explore new devel-opments in Applied Mathematics research.

This jointly funded programme in Applied Math-ematics further strengthens and complements the research partnership built between the UK and India in the last five years.

In November 2013, RCUK India completes five years of its successful research partnership with India. This EPSRC-DST initiative is one out of the many mutu-ally benefitting research programmes that illustrate UK-India research partnership, which has grown from less than £1 million to over £100 million since 2008.

Proposals submitted under this initiative should be submitted at one of the following deadlines: October 11, 2013 and July 31, 2014.

Country coordinators:

In UK — ICMS

In India — Professor Dinesh Singh, Vice Chancellor, University of Delhi

For more details see http://www.icms.org.uk/proposals.php.

Indian Researcher Helps Prove Kadison–Singer Conjecture*

On June 18, Adam Marcus and Daniel A Spielman of Yale University, along with Nikhil Srivastava of Microsoft Research India, announced a proof of the Kadison–Singer conjecture, a question about the mathematical foundations of quantum mechanics. Ten days later, they posted, on Cornell University’s arXiv

open-access e-prints site, a manuscript titled Interlacing Families II: Mixed Characteristic Polynomials and the Kadison–Singer Problem.

Thousands of academic papers are published every year, and this one’s title wouldn’t necessarily earn it much attention beyond a niche audience … except for the fact that the text divulged a proof of a mathematical conjecture more than half a century old — and the ramifications could be broad and significant.

The Kadison–Singer conjec-ture was first offered in 1959 by mathematicians Richard Kadison and Isadore Singer. In a summary of the achievement, the website Soul Physics says, “… this conjecture is equiva-lent to a remarkable number of open problems in other fields … [and] has important consequences for the foundations of physics!”

That description will get no argument from Ravi Kannan, principal researcher in the Algorithms Research Group at Microsoft Research India.

“Nikhil Srivastava and his co-authors have settled an important, 54-year-old problem in mathematics,” Kannan says. “They gave an elegant proof of a conjecture that has implications for many areas of mathematics, computer science, and quantum physics.”

Srivastava offers a layman’s explanation of what he, Marcus, and Spielman have achieved.

“We proved a very fundamental and general statement about quadratic polynomials that was conjectured by [mathematician] Nik Weaver and that, he showed, implies Kadison–Singer. The proof is based on a new technique we developed, which we call the ‘method of interlacing families of polynomials’.”

The proof — for a more technical, extended discussion, see Srivastava’s post on the Windows on Theory blog — elicited the most basic of emotions from Srivastava when he got a chance to contemplate what he and his colleagues had wrought.

“My main reaction was awe at how beautiful the final proof was,” he recalls. “I actually started laughing when

Nikhil Srivastava



I realised that it worked. It fit together so beautifully and sensibly you knew it was the ‘right’ proof and not something ad hoc. It combined bits of ideas that we had generated from all over the five years we spent working on this.”

“It has clear implications for the foundations of quantum physics,” he says. “This is something Paul Dirac mistakenly thought was obvious, and Kadison and Singer and many other experts thought this was probably false.”

“It implies that it is possible to ‘approximate’ a broad class of networks by networks with very few edges, which should have impact in combinatorics and algo-rithms. Finally, it is equivalent to several conjectures in signal processing and applied mathematics that seem to have practical use.” Courtesy of

Inside Microsoft Research, July 16, 2013

*For more detail on the results of Marcus, Spielman and Srivas-tava, see page 15 of this issue.

Four Indian Americans Win Top Science and Maths Awards

Four Indian American professors are among the 13 mathematicians, theoretical physicists and theoretical computer scientists who have won 2013 Simons Inves-tigators awards.

Currently working at Stanford University, Harvard, Massachusetts Institute of Technology and Pennsyl-vania University, they will each receive $100,000 a year for five years for their long-term research with the possibility of renewal for five additional years.

The awards are given by nonprofit New York-based Simons Foundation, incorporated in 1994 by Jim and Marilyn Simons with a mission to advance the frontiers of research in mathematics and the basic sciences.

Among the four mathematicians who won Simons grants is Stanford professor of mathematics Kannan Soundararajan, “one of the world’s leaders in analytic number theory and related areas”, the Simons Founda-tion said.

“His work is focused on understanding the zeros and value distribution of L-functions, and on analysing the behaviour of multiplicative functions.”

The India-born professor represented India at the International Mathematical Olympiad in 1991, where he won a silver medal. A Sloan Foundation Fellow, he has an undergraduate degree from the University of Michigan and a PhD from Princeton.

Two of three awards in computer science went to Indian Americans. They are Rajeev Alur, Zisman Family Professor in the Department of Computer and Informa-tion Science at the University of Pennsylvania; and Salil P Vadhan, Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University.

Alur is a top researcher in formal modelling and algorithmic analysis of computer systems, the Simons Foundation said.

“A number of automata and logics introduced by him have now become standard models with great impact on both the theory and practice of verification.”

Alur has BS and PhD degrees in computer science from IIT-Kanpur and Stanford University, respectively.

Vadhan, the Simons Foundation said, has “produced a series of original and influential papers on compu-tational complexity and cryptography. He uses complexity-theoretic methods and perspectives to delineate the border between the possible and impos-sible in cryptography and data privacy.”

Vadhan has a PhD in applied mathematics from MIT, a certificate of advanced study in mathematics from Churchill College at Cambridge University and AB in mathematics and computer science from Harvard University.

Senthil Todadri, a professor of physics at MIT and Distinguished Research Chair at the Perimeter Institute of Physics, was one of six Simons grant winners in that discipline.

“Senthil Todadri’s work with Fisher on Z2 topological order in models of spin liquid states provided key insights and initiated the systematic investigation of gauge structures in many-body systems, now a vital subfield of condensed matter physics,” the foundation said.

Todadri has his PhD from Yale and an undergraduate degree from IIT-Kanpur.

Courtesy of Daily News, July 27, 2013



Indian Women and Mathematics

The Symposium “Indian Women and Mathematics” (IWM2013) was organised at Indian Institute of Science Education and Research at Pune, India, during July 26–28, 2013.

This was a follow-up of IWM-2012 held at Institute of Mathematical Sciences, Chennai, India, during January 8–10, 2012. This was the first meeting organised in India to facilitate interaction between women math-ematicians with an active research programme, college teachers from around the country and graduate and undergraduate students. The goal was to attract more women into mathematics and the lectures were kept at a very accessible level. The response was encouraging, and the National Board of Higher Mathematics, India, offered to support this venture. This prompted the organisers, Professors Vyjayanthi Chari (University of California, Riverside, USA) and Jaya NN Iyer (IMSc, Chennai) to apply for funding to continue the activities in a more systematic way.

The Symposium was attended by around 100 women college and university teachers, in addition to young women at various stages in academics. The focus of this meeting was to introduce new mathematics and also enable the participants to showcase their knowledge. This was facilitated by having two mini-courses; on mathematical biology and non-commutative algebras. Both are emerging and largely unexplored areas in mathematics. The plenary talks focused on different aspects of mathematics; study of groups via analysis and geometry, enumeration problems, nonlinear analysis and other areas. The young researchers and contrib-uted talks by participants were delivered and were received with enthusiasm and attention. The poster presentations also attracted attention and interest. The participants and invited specialists had ample time and opportunity to have informal discussions and interac-tion. The mathematics department and the Director at IISER, Pune, also gave their whole-hearted support and helped to host the event. The cultural activities included a music concert by renowned vocalists and instrumentalists in Indian Carnatic music, and a short movie was also presented.

The meeting concluded with a session on feedback from the participants. The concern voiced was to give expo-sure and bring the teachers in the forefront in advancing their knowledge base and skills in mathematics. This

will filter down to improving the education in under-graduate levels in the country, especially at college and universities in smaller towns. To this effect, a Women’s Teachers Training programme is planned at Mumbai University, Mumbai, during December 23–28, 2013. We hope to have two more meetings in 2014. The Symposium concluded with a note of thanks by the Convener, Professors Rama Mishra (IISER, Pune) and Shantha Bhushan (FLAME Institute, Pune).

Reported by Jaya NN Iyer(Institute of Mathematical Sciences, Chennai, India)

News from Japan

MSJ Seasonal Institute 2014 “Hyperbolic Geometry and Geometric Group Theory”

The 7th MSJ-SI (Mathematical Society of Japan, Seasonal Institute) entitled “Hyperbolic Geometry and Geometric Group Theory” will take place in the University of Tokyo from July 30 to August 5 in 2014. This is an international conference focusing on recent progresses in hyperbolic geometry and geometric group theory. There will be four survey talks and a dozen of research talks by internationally renowned specialists in this field.

The web page of the conference is:http://www.is.titech.ac.jp/msjsi2014/.

The invited speakers include:Martin Bridson (University of Oxford)Kenneth Bromberg (Utah University)Yoshitaka Kida (Kyoto University)Sang-hyun Kim (KAIST)Yair Minsky (Yale University)Narutaka Ozawa (Kyoto University)Athanase Papadopoulos (Université de Strasbourg)Michah Sageev (Technion)Karren Vogtmann (Cornell University)

The conference is open to all researchers, and especially graduate students and young researchers are very welcome to participate.

The 2013 MSJ Autumn Prize

The 2013 MSJ Autumn Prize was awarded to Masato TSUJII, Professor at Faculty of Mathematics, Kyushu



University. Masato TSUJII is recognised for his outstanding contributions to “Functional analytic methods in ergodic theory of differentiable dynamical systems”. The Spring Prize and the Autumn Prize are the most prestigious prizes awarded by the MSJ to its members. The Autumn Prize is awarded without age restriction to people who have made exceptional contributions in their fields of research.

The 2013 MSJ Takebe Katahiro Prizes

The 2013 MSJ Takebe Katahiro Prize and the 2013 Takebe Katahiro Prize for encouragement of young researchers were awarded to the following members of MSJ.

MSJ Takebe Katahiro Prize

Benoît COLLINS (Tohoku University) Free probability and its applications

Takehiko YASUDA (Osaka University) Motivic Integration and singularities

Kentaro NAGAO (Nagoya University) Donaldson–Thomas theory and cluster algebras

MSJ Takebe Katahiro Prize for Encouragement

Nao HAMAMUKI (The University of Tokyo) Analysis on Hamilton–Jacobi equations with its appli-cations to crystal growth phenomena

Hiromu TANAKA (Kyoto University) Minimal model theory in positive characteristic

Hajime KANEKO (Nihon University) Diophantine approximation of algebraic numbers and a conjecture of Emile Borel

Yoh TANIMOTO (The University of Tokyo) Operator algebraic methods in two-dimentional quantum field theory

Hisashi KASUYA (Tokyo Institute of Technology) Topology and geometry of solvmanifolds

Kenta OZEKI (National Institute of Informatics and JST-ERATO) Hamiltonicity of graphs

In celebration of its 50th anniversary, the MSJ estab-lished the above-mentioned prizes named after Katahiro Takebe (1644–1739) — a prominent math-ematician in Japan who was a disciple of Seki Takakazu and was noted for his creation of charts for the values of trigonometric functions. The Takebe Prize is set up

for young researchers who have obtained outstanding results, and the Encouragement Prize is intended for young mathematicians who are deemed to have begun promising careers in research by obtaining significant results.

The MSJ Spring Meeting 2014

The MSJ Spring Meeting 2014 will be organised in Gakushuin University in Toyko during the period March 15–18, 2014. The Chairs of the Organising Committee and the Executive Committee are Dr Matsumoto, Yukio and Dr Kawasaki, Tetsuro at Gakushuin University, respectively. The official webpage of the meeting is http://mathsoc.jp/meeting/gakushuin14mar/.

The 2013 MSJ Geometry Prize

The 2013 MSJ Geometry Prizes were awarded to Toshitake KOHNO, Professor at the Univer-sity of Tokyo, and Katsutoshi YAMANOI, Associate Professor at the Tokyo Institute of Tech-nology.

The award to T Kohno was given for his fundamental and outstanding contribution to geometric representation theory for quantum groups.

The award to K Yamanoi was given for his final solution of the Gol’dberg–Mues conjecture in Nevanlinna theory.

MSJ Takebe Prizes Awardees

K Yamanoi

T Kohno



News from Korea

Korea Ranks 2nd in the 54th International Math-ematical Olympiad (IMO)

Korea ranks 2nd in the 54th IMO, with 5 gold medals and 1 silver medal scoring a total of 204 points. The IMO is the world championship mathematics competi-tion for high school students and is held annually in a different country. This year, the IMO was held in Santa Marta, Colombia during July 18–28 with 528 participants from 97 countries.

JongHae Keum Inaugurated as President of Korea Institute for Advanced Study (KIAS)

Professor JongHae Keum (KIAS) was inaugurated as the 6th presi-dent of KIAS on September 5, 2013. He will lead KIAS for 3 years until September 2016. KIAS is an open institute of dynamic scientific interactions with three schools — mathematics, physics, and computational sciences.

Scientists from all over the world visit KIAS for collaborative research, sabbatical leave, and other research activities organised by the Institute. KIAS also hosts numerous conferences, seminars, workshops, and seasonal schools. Furthermore, the faculty and research bodies of the Institute are composed of diverse nation-ality, and competitive programs are developed by the world’s most recognised scholars and scientists. Given this global environment, KIAS welcomes interactions with academic communities and research organisations around the world. For more information, visit http://www.kias.re.kr/.

2012 SCI Impact Factors of the Journal of KMS and the Bulletin of KMS

* Eigenfactor™ Score(EF): A measure of the overall value provided by all of the articles published in a given journal in a year.

2013 Korea Best Scientist Award

Professor Park Jongil of the Department of Mathematical Sciences of Seoul National University (SNU) has been awarded the Korea Science Award in the field of Math-ematics. The Korea Science Award is given out to scholars of the natural sciences with outstanding research outcomes by the Ministry of Education, Science and Technology and the National Research Foundation of Korea every year. Professor Park is known for his leading research in topology of 4-manifolds.

Park has been a professor of topology at SNU since 2004. He also taught at Konkuk University, and the University of California, Irvine. He is the third math-ematician to receive the award since the award was established in 2003.

“I am honoured to have had my efforts acknowledged by not only the mathematics field but also the science and technology field,” Park said. “I feel lucky to have received this award as a pure mathematician, among many excellent scientists.”

The science and technology award is granted to scien-tists who have contributed to the nation’s scientific development by reporting and researching new findings and developing new technologies. So far 30 scientists have had the honour of winning the award.

JongHae Keum



The award ceremony was held in Busan on July 5. Each winner received a presidential award and 270 million won.

News from Mongolia

2013 CIMPA-UNESCO-MONGOLIA Research School on Partial Differential Equations in Mechanics

Participants of the CIMPA-UNESCO Research School

The CIMPA-UNESCO Research School “Partial Differential Equations in Mechanics” was held during July 15–26, 2013 at the Mongolian University of Science and Technology, Ulaanbaatar. The research school was organised by Professor Doina Cioranescu of the CNRS Laboratoire J L Lions, University Paris VI, France and Professor Sarantuya Tsedendamba, Professor in Differential Equations of the School of Mathematics of the Mongolian University of Science and Technology (MUST).

The main focus of the school was on some of the recent advances on mathematical analysis and numerical computations related to the partial differential equa-tions in fluid mechanics for engineering science. This subject has attracted particular interest from the engineering faculties and students of the Mongolian Universities and overseas participants from China, Egypt and Philippines.

The opening speech was addressed by the President of the Mongolian University of Science and Technology Prof Dr Ochirbat Baatar.

The courses were taught by prominent experts in their respective field of research. The list of lecturers and their topics were: Doina Cioranescu (CNRS Laboratoire J L Lions, University Paris VI, France): Fluid Flows through Porous Media, Hans-Dieter Alber (University of Technology Darmstadt, Germany): Theory and Numerical Simulation of Phase Transformations in Solids, Alain Damlamian (Université Paris-Est Val

de Marne, France and Vice President of the CIMPA): Periodic Homogenisation of Elastic Media with Contact on Oscillating Interfaces, Gantumur Tsogtgerel (McGill University, Canada): A Gentle Introduction to the Regularity Theory of the Navier-Stokes Equa-tions, Thomas Mikosch (University of Copenhagen, Denmark): Introduction to Poisson Random Measures and Poisson Integrals, Christian Wieners (Karlsruhe Institute of Technology, Germany): Numerical Approximation of Elasto-Plasticity, Rolf Jeltsch (ETH Zuerich, Switzerland): Finite Volume Schemes for Conservation Laws and Andrey L Piatnitski (Narvik University College, Norway): Homogenisation of Singular Structures and Measures.

Professor Alain Damlamian (Vice President of the CIMPA)

Professor Thomas Mikosch (University of Copenhagen Denmark)

Professor Hans-Dieter Alber (TU Darmstadt Germany)



The school was attended by about 30 participants from Mongolian University of Science and Tech-nology, National University of Mongolia, Institute of Technology in Erdenet, University of Khovd and 4 overseas students from College of Physics Science and Technology, Hebei University and College of Science, China University of Petroleum, Beijing China, Department of Mathematics of the College of Arts and Sciences of the Caraga State University, Philippines and Mathematics Department of the Faculty of Science of the Sohag University, Egypt.

The scientific objectives of the school have been fully achieved. The courses were of high quality, starting from a basic introduction and ending with recent advances in the fields of the Navier-Stokes equations, numerical simulation of phase transformation in solids, Poisson integral and finite volume schemes for conser-vation laws. Uncertainty quantification has recently emerged as a major field in applied mathematics and this school was fortunate to be a venue for introducing this active area of research. The school also provided an opportunity for local and overseas graduate students to establish networking among themselves and with researchers from abroad.

Main sponsors of this meeting were CIMPA, IMU, TU Darmstadt, TU Karlsruhe, University of Copenhagen, McGill University, and Mongolian University of Science and Technology.

Sarantuya TsedendambaChair of the Local Organising Committee

Mongolian University of Science and TechnologyP O Box 13/625

Ulaanbaatar 15160, Mongolia

News from New Zealand

John C Butcher Honoured

In the Queen’s Birthday Honours list, John Butcher was awarded the Officer of the New Zealand Order of Merit (ONZM), for “services to mathematics”. At most 80 ONZM awards can be made each year in all fields of human activity. The Wiki-pedia page tells us that ONZM John Charles Butcher

is awarded “for those persons who in any field of endeavour, have rendered meritorious service to the Crown and nation or who have become distinguished by their eminence, talents, contributions or other merits”.

John Butcher, Emeritus Professor at the University of Auckland specialises in numerical methods for the solution of ordinary differential equations. Butcher works on multistage methods for initial value problems, such as Runge–Kutta and general linear methods. The Butcher group is named after him.

Einstein Medal for Roy Kerr

Roy Kerr, the first New Zealander to be awarded the Einstein Medal, is reflected in a framed photo-graph he owns of the famous physicist

University of Canterbury Emeritus Professor Roy Kerr headed to Europe in May to become the first New Zealander to receive the Einstein Medal from the Albert Einstein Society in Switzerland. The award ceremony was held at the University of Bern on May 28.

Roy discovered a specific solution to Einstein’s field equations which describes a structure now termed a Kerr black hole. The Kerr Solution has been pivotal in understanding the most violent and energetic phenomena in the Universe.

The Einstein Medal is awarded annually by the Einstein Society “to deserving individuals for outstanding scien-tific findings, works, or publications related to Albert Einstein”. The medal was first awarded to Stephen Hawking in 1979 and, since then, many distinguished scientists have received the medal including six Nobel laureates.



Memorial Meeting for Charles Pearce (1940–2013)

On June 17, Graeme Wake was privileged to be invited to present a talk at the Charles Pearce Memorial symposium at the University of Adelaide. Professor Pearce was one of NZ’s much-loved and distinguished mathematicians, and he is pictured on the concluding slide of Graeme’s talk.

Nearly 100 people from many countries came to honour this occasion for one of NZ’s famous mathematical sons, who served for over 30 years at the University of Adelaide, and was one of their senior mathematical professors at the time of his tragic death, as a result of a motor accident, in June 2012. Graeme Wake, three years his junior, was a contemporary of Charles at Victoria University of Wellington in the early 1960s. They became close friends working together both on probabilistic modelling and in the formative years of the two country grouping ANZIAM (Australia and New Zealand Industrial and Applied Mathematics) even before 1993, when it was first formed as we now know it. Charles was the founding editor of the ANZIAM Journal and served in this role for nearly 20 years. Such was Charles’ dedication to trans-Tasman activities he was one of the very few Australasians to become a Fellow of both the NZ and Australian Mathematical Societies. Charles was a NZer with both Maori and Pakeha ancestry and spent considerable time tracing the 800 year-old long Polynesian migration to the land, and was indeed on such another such quest at the time of his untimely death in Westland in June 2012.

Report by Graeme Wake

Graeme Wake at Charles Pearce memorial — Charles pictured on slide

News from Philippines

CIMPA-ICTP Research School on Algebraic Curves over Finite Fields

The CIMPA-ICTP Research School on Algebraic Curves over Finite Fields and Applications was held in Manila, Philippines, bringing together 67 math-ematicians and graduate students from 15 countries (including 10 lecturers) in a two-week workshop consisting of lectures/discussions and computation sessions on algebraic curves.

One main feature of this school was the large number of participants from overseas. There were 37 participants outside Philippines, coming from India (8), Indonesia (7), Cambodia (4), Nepal (4), Iran (3), Italy (2), Thai-land (2), France (1), Malaysia (1), Nigeria (1), Pakistan (1), Turkey (1), USA (1), and Vietnam (1). On top of that, there were 20 participants from the Philippines. Among these participants eight were female, though more women were selected to participate but they did not turn up. The ten lecturers (including one woman) were from Italy (4), USA (2), France (2), Spain (1), and Netherlands (1).

The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school covered theoretical, computational and applied aspects of the topic and thus is useful to a broad range of students and young math-ematicians interested in algebra and its applications.

The CIMPA-ICTP research school developed the subject almost from scratch, beginning from introductory classes on finite fields and algebraic curves. We covered aspects of the theory of elliptic curves over finite fields as well as the application of the Riemann–Roch theorem

Participants of CIMP-ICTP Research School



to the zeta function of an algebraic curve over a finite field (including the Stepanov–Bombieri–Schmidt proof of the Riemann hypothesis). Applications also figured prominently with sessions on elliptic curve cryptog-raphy, coding theory and computational examples using Pari GP and Sage. Moreover the school also covered the explicit construction of elliptic curves over finite fields with group of points of large prime order (as needed by cryptographic applications) via complex multiplication.

The School was held at the Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines. The main sponsors of this research school were CIMPA and ICTP.

News from Taiwan

2013 Hsu Chen-Jung Lectures

Professor Richard Melvin Schoen, the Bass Professor of Humanities and Sciences at Stanford University, and the 2013 Hsu Chen-Jung Chair Professor, will give a Hsu Chen-Jung lecture series in the Institute of Mathematics, Academia Sinica, during the first week of December 2013. The Hsu Chen-Jung Chair, dedicated to the memory of Professor Hsu, is sponsored by the Mathematical Society of Republic of China and the Institute of Mathematics, Academia Sinica.

International Conference of Chinese Mathematicians 2013 in Taipei

The Sixth International Congress of Chinese Math-ematicians (ICCM) was held from July 14 to 19, 2013 in Taipei. The ICCM is a triennial event that brings together Chinese and overseas mathematicians to discuss the latest research developments in pure and applied mathematics and statistics. The opening ceremony was held on July 14 in the Big Hall of the Grand Hotel. During the great opening the prestigious Morningside Awards were conferred upon math-ematicians for their outstanding contributions. The awardees were selected by an international panel of eminent mathematicians. This year’s panel members are Professors Richard Borcherds (UC Berkeley), John Coates (Cambridge), Simon Donaldson (Impe-rial College London), Bjorn Enquist (Austin), Gerd Faltings (MPI), James Glimm (Stony Brook), Dorian Goldfeld (Columbia), Benedict Gross (Harvard), Victor Guillemin (MIT), Yuri Manin (MPI/Northwestern),

Stanley Osher (UCLA), and Shing-Tung Yao (Harvard). The following are the award winners of this year’s ICCM Morningside Awards: The Morningside Special Achievement Award in Mathematics was bestowed upon Yitang Zhang (University of New Hampshire). Xuhua He (University of Science and Technology) and Ye Tian (Chinese Academy of Sciences) both received the Morningside Gold Medal in Mathematics, and Xianfeng David Gu (State University of New York at Stony Brook) the Morningside Gold Medal in Applied Mathematics. Chieh-Yu Chang (National Tsinghua University), Xiaoqing Li (State University of New York at Buffalo), Hao Xu (Harvard University), and Tai-Peng Tsai (University of British Columbia) received the Morningside Silver Medal. Jean-Pierre Serre (College de France) received the ICM International Cooperation Award, while Si-Chen Lee (National Taiwan University) and Bong Lian (Brandeis University) both received the Chern Prize. Chengbiao Pan (China Agricultural University/Peking University) was awarded the Morn-ingside Mentor Award in Mathematics.

Following the Grand Opening three public symposia were held in the Grand Hotel in the afternoon of July 14. The first symposium is entitled “Unlocking our future: how government policies can foster funda-mental science development” with panelists Way Kuo

From left to right: President Kuo, President Wu, Dr Chen, President Wong

Honoured guests together with the 2013 Morningside Award



(President, City University of Hong Kong), Chi-Huey Wong (President, Academia Sinica), and Yan-Hwa Wu Lee (President, National Chiao-Tung University), and moderator Gerald L Chan (Morningside Foundation). The second and third symposia are public lectures entitled “The Art of Bridge Building” and “Juggling Mathematics and Magic” given by C L Liu (National Tsing-Hua University) and Ronald Graham (University of California San Diego), respectively. The 2013 New World Mathematics Awards were presented in the evening to young mathematician of Chinese descents whose have made outstanding contributions in their fields in their PhD theses.

The scientific program started on July 15 with Professor Jean-Pierre Serre’s general audience lecture entitled “Historical remarks on cohomology”, which, as the title indicates, gives a survey of the development of the notion of cohomology. Among the many other high-lights of this year’s ICCM lectures was also Professor Yitang Zhang’s plenary lecture on July 16 explaining his celebrated proof of a weak version of the famous twin prime conjecture based on his paper “Bounded gaps between primes” which will appear in the Annals of Mathematics. On April 17, 2013 Professor Zhang made an announcement that there are infinitely many pairs of consecutive prime numbers with a gap at most 70 million between them. His proof is the first to establish the existence of a finite bound, thus resolving a weak form of the twin prime conjecture, which claims that there are infinitely many pairs of consecutive primes with a gap of size 2. Professor Zhang was invited to present his work at Harvard University on May 13, and an article in the journal Nature reporting on his work appeared on May 14, 2013. Professor Zhang was a Master’s degree student of Professor Chengbiao Pan at Peking University. He obtained his PhD degree in math-ematics from Purdue University under the supervision

Yitang Zhang and Shing-Tung Yau (Photo provided by TIMS)

of Professor Tzuong-Tsieng Moh in December 1991. After graduation, Professor Zhang had a hard time finding an academic position. In 1999 he managed to find a position at the University of New Hampshire, where he currently holds the position of a lecturer.

Further information on this event can be found at http://iccm.tims.ntu.edu.tw/. A photo gallery is avail-able at http://w3.math.sinica.edu.tw/iccm2013/day01/day01.html.

News from Vietnam

I. Upcoming Events

1. Mini-workshop “Differential Equations and Applications”

Time: October 18, 2013Venue: VIASM, Hanoi

The aim of this workshop is to give discussions on some recent aspects and developments in the field of differential equations and their applications in Physics, Population Dynamics, Control Theory, etc. The work-shop consists of eight 45-minutes invited lectures given by experts in the field.

Invited Speakers: Nguyen Ngoc Doanh (HUST), Dinh Nho Hao (IM-VAST), Nguyen Thieu Huy (HUST), Tran Dinh Ke (HNUE) , Vu Hoang Linh (HUS-VNU), Phan Thanh Nam (Qui Nhon Univ), Le Quang Nam (IM-VAST), Do Duc Thuan (HUST).

The mini-workshop website: http://viasm.edu.vn/activities/dea2013/?lang=en.

2. International Conference on Commutative Algebra and Its Interaction to Algebraic Geom-etry and Combinatorics

Time: December 16–20, 2013Venue: Institute of Mathematics, Hanoi

The aim of the conference is to present recent develop-ments in Commutative Algebra and its interaction in Algebraic Geometry and Combinatorics. There will also be discussion on how to promote mathematics in Vietnam.

Conference website: http://vie.math.ac.vn/CA-2013/



3. Workshop on Birational Geometry and Stability of Moduli Stacks and Spaces of Curves

Time: January 5–26 and February 9–March 1, 2014 Venue: VIASM, Hanoi

We intend for the participants to shape the scientific agenda of the workshop once at VIASM, but we anticipate areas of activity will include log minimal model programmes and the associated Modularity Conjecture, GIT quotients with respect to linearisations of fixed degree, techniques for constructing weakly proper moduli stacks, bounds for ample and effective cones and connections to holomorphic differentials and Teichmüller dynamics, applications of Bridge-land stability to related birational questions, and the clarification of empirically observed relations between these problems. Both the organisation and the goals of the workshop will be unconventional, with the hope of creating mathematical opportunities not duplicated by other meetings with these themes.

We have three main goals:

1. Introduce the Vietnamese mathematical community to the themes of the workshop through mini-courses of 2–4 lectures given by participants that progress from basic notions to more specialised ones.

2. Introduce the participants to Vietnam, its people and scientific heritage, and initiate the development of longer term scientific connections between them and the Vietnamese mathematical community.

3. Facilitate intensive collaboration between partici-pants on problems arising from their current research, and provide a sequel for the 2012 AIM workshop log minimal model programme for moduli spaces.

Conference website: http://viasm.edu.vn/20130807/hdkh/moduli2014/

II. Past Events

1. SEAMS School “Algebraic curves”

The SEAMS School “Algebraic curves” took place at VIASM Lecture Hall from July 8 to 19, 2013. This school provided basic materials on Commutative Algebra and on Algebraic Curves. The organisers of the SEAMS School included Professor Ngo Bao Chau

(Chicago and VIASM, Director), Dr Doan Trung Cuong (Institute of Mathematics, Hanoi), Professor Le Tuan Hoa (VIASM) and Dr Nguyen Chu Gia Vuong (Institute of Mathematics Hanoi). Lecturers included Professors Ngo Bao Chau, Nguyen Tu Cuong (Institute of Mathematics, Hanoi) and Phung Ho Hai (Institute of Mathematics, Hanoi).

Nguyen Tu Cuong (Institute of Mathematics, Hanoi) gave the first lecture at SEAMS School

There are 33 students, including 6 foreign students from the Philippines, Malaysia and Indonesia. The students were selected and introduced by the Southeast Asian Mathematical Society (SEAMS). Among Viet-namese students, there were also PhD students from US universities such as Harvard, Michigan. SEAMS School students were sponsored by VIASM and Centre International de Mathématiques Pures et Appliquées (CIMPA).

Students of the SEAMS School

For more detail about the school, visit: http://viasm.edu.vn/activities/school_ac2013/?lang=en

2. Pan Asian Number Theory Conference 2013

The 2013 Pan Asian Number Theory Conference (PANT) opened at VIASM B4 Lecture Hall on July 22. The conference lasted until July 26, 2013.



The aim of the annual Pan Asian Number Theory (PANT) Conferences is to encourage research in Number Theory in Asia, and especially to stimulate collaborations among young asian number theorists. Previous PANT Conferences have been held in Pohang, Korea (2009), Kyoto, Japan (2010), Beijing, China (2011), and Pune, India (2012).

This year, the PANT Conference have 62 participants, among them are 49 foreigners. There are 22 math-ematicians presenting their reports at the conference, including many famous mathematicians in the world. According to Professor John Henry Coates (Cambridge, UK), there were more participants to this conference than any other PANT conference before, and more importantly, there were more young mathematicians.

The programme committee included Professors Ngo Bao Chau, John Henry Coates, Wee Teck Gan and Tamotsu Ikeda, etc.

The lectures at the first session of this PANT were by Professors Freydoon Shahidi and Shunsuke Yamana titled “Some arithmetic consequences of Eisenstein series” and “L-functions and theta cor-respondence”, respectively.

Freydoon Shahidi giving his lecture

During the conference, the participants had a city tour and opportunities to watch water puppet show, visit Halong Bay at the weekend after closing the conference.

For more information about the activity, please visit: http://viasm.edu.vn/activities/pant2013/?lang=en

3. VIASM Annual Meeting 2013

VIASM Annual Meeting is a regular activity of Vietnam Institute for Advance Study in Mathematics, to be organised once a year following the example of

Bourbaki seminar. This year it was held at VIASM during July 20–21, 2013.

In each annual meeting, VIASM invites highly reputed mathematicians to deliver lecturers on central topics of contemporary mathematics. The lecturers provide the audience with most interested problems in their research fields, main ideas and main results (and generally not on their own work). The reports are to be written by the time of the meeting and will be published in a special issue of Acta Mathematica Vietnamica.

The mathematicians invited this year are: John Coates (Cambridge, UK), Du’o’ng HÔng Phong (Columbia, USA), Takeshi Saito (Tokyo, Japan), Vasudevan Srinivas (Tata Institute, India), Gan Wee Teck (National Univer-sity of Singapore).

John Coates giving his lecture on congruent numbers

The first lecture of this annual meeting was given by Professor Duong Hong Phong titled “Non-linear heat flows in complex geometry”. In the next sessions, participants also enjoyed the lectures of Professor Vansudevan Srinivas about “The Tate Conjecture for K3 surfaces”, Professor Takeshi Saito about “The weight-monodromy conjecture and perfectoid spaces”, Professor Gan Wee Teck about “Recent progress on the Gross-Prasad Conjecture”, and Professor John Coates about “Congruent numbers”.

This year, the annual meeting attracted 50 participants, among them there were 12 foreigners or Vietnamese people currently working abroad.

For more information about the meeting, please visit: http://viasm.edu.vn/activities/am2013/?lang=en

4. The 8th Vietnamese Mathematical Conference

The 8th Vietnamese Mathematical Conference was held



from August 10 to 14, 2013 at University of Information Officers, Nha Trang, Khanh Hoa.

This is the largest national mathematical conference in Vietnam as it is organised every 5 years. Since 1974, the conference has been an opportunity for Vietnamese mathematicians to talk about their work in research, teaching and applying mathematics. This is also the forum to discuss the contemporary issues of mathematical development of Vietnam. From this year, the conference was also an activity of Vietnam National Programme for the Development of Mathematics from 2010 to 2020.

The opening ceremony of the 8th Vietnamese Mathematical Conference

This year, there were over 700 participants in this year’s conference, divided into eight parallel sessions: Algebra–Geometry–Topology, Mathematical Analysis, Differential and Partial Differential Equations, Discrete Mathematics and Mathematical Informatics, Optimi-sation and Scientific Computation, Probability and Mathematical Statistics, Applied Mathematics, Educa-tion and Mathematical History. The conference consists of 5 plenary lectures/talks, 45 session lectures/talks and over 250 short communications at parallel sessions.

The 7th Vietnamese National Congress of Mathemati-cians was also held at the same time.

5. Vietnam Develops Maths Thinktank

The conference for 2 year performance review of Vietnam Institute for Advanced Study in Mathematics (VIASM) took place at VIASM on August 24, 2013.

The conference welcomed the presence of many researchers who were working or had worked at VIASM, reputed Vietnamese mathematicians, and representa-tives of ministries such as Ministry of Education and Training, Ministry of Science and Technology, etc.

Minister of Science and Technology Nguyen Quan at the conference

After 2 years of official operations, VIASM had success-fully created a special academic environment where scientists and university lecturers conceive new ideas and train rising talents in mathematics.

Also addressing the event, Minister of Science and Technology Nguyen Quan assured that, as a part of the National Programme for the Development of Math-ematics from 2010 to 2020, VIASM was contributing towards a better future for maths in Vietnam. He said his ministry would prioritise the development of five science-technology fields, including maths research.

Over its past two years, VIASM had attracted 137 researchers, including 40 foreign and overseas Viet-namese mathematicians. 21 papers had been published in prestigious foreign maths magazines and 69 other papers were under the form of preprints (all these work had been fully or partially done during the time the researchers worked at VIASM). The Institute also held 17 short-term training courses.

Moreover, the Institute organised eight international conferences and workshops, notably the France-Vietnam Joint Maths Conference in the central city of Hue (August 2012) with 450 participants and the 8th National Mathematical Conference in the southern city of Nha Trang (August 2013), with some 700 delegates taking part.

Furthermore, VIASM also actively assists the Managing Board of the National Programme for the Develop-ment of Mathematics from 2010 to 2020 to implement the programme activities such as awarding excellent research work, granting scholarships to excellent high school and college students in mathematics, etc.



Conference CALENDAR


Conference CALENDAR

Conferences in Asia Pacific Region

OCTOBER 2013

1 – 4 Oct 2013 New Zealand Association of Mathematics Teachers 13th Biennial ConferenceWellington, New Zealand http://nzamt13.org.nz/

1 – 5 Oct 2013 II International Seminar: Nonlinear Phenomenology Advances Sai, Russia http://www.hmath.spbstu.ru/index.php/seminary

1 – 5 Oct 2013VII Baltic Education Forum 2nd International Conference “Jacobi-2013” High-Performance Computing: Mathematical Models and AlgorithmsKaliningrad, Russiahttp://www.balticeducationforum.ru/

1 - 5 Oct 2013 Nonlinear dynamics, Chaos, Fractals, Self-organization Saint Petersburg, Russia http://www.hmath.spbstu.ru/index.php/seminary

3 – 4 Oct 2013Australasian Conference onComputational MechanicsSydney, Australiahttp://web.aeromech.usyd.edu.au/ACCM2013/index.html

5 Oct 2013 Number Theory Down Under Newcastle, Australia http://carma.newcastle.edu.au/mcoons/DUNT.html

5 – 6 Oct 2013International Post Graduate Conference onScience and Mathematics (IPCSM 2013)Perak, Malaysiahttp://www.ipcsm2013.my/v1/

6 – 9 Oct 201324th International Conference onAlgorithmic Learning TheorySingaporehttp://www-alg.ist.hokudai.ac.jp/~thomas/ALT13/

6 – 9 Oct 201316th International Conference on Discovery Science (DS 2013)Singaporehttp://www.mathematik.uni-marburg.de/~discoveryscience2013/

7 – 9 Oct 2013 Seventh Global Conference on Power Control and Optimization PCO 2013Kota Kinabalu, Sabah, Malaysia http://www.pcoglobal.com/Kuta\%20Kinabalu.htm

7 – 11 Oct 2013International Conference "KolmogorovReadings – VI. General Control Problemsand Their Applications" (GCP2013)Derzhavin, Russiahttp://www.tambovopu2013.narod.ru

12 – 14 Oct 2013Chinese Mathematical Society Annual Conference 2013Taiyuan City, Shanxi Province, Chinahttp://www.cms.org.cn/cms/2013active.pdf

13 – 17 Oct 2013 Homogeneous Dynamics, Unipotent Flows and Applications: In honor of Marina Ratner and Her work Jerusalem, Israel http://www.as.huji.ac.il/content/research-group-conference-homogeneous-dynamics-unipotent-flows-and-applications

13 – 23 Oct 2013Topics in Algebraic Graph TheoryAlmora, Indiahttp://atmschools.org/2013/atmw/tagt

14 – 17 Oct 2013The Third National Conference on Combinatorial Number TheoryTianjin, Chinahttp://www.cim.nankai.edu.cn/

14 – 18 Oct 20135th East Asian Conference onAlgebraic GeometryBeijing, Chinahttp://www.amss.cas.cn/xshy/201211/t20121122_3687696.html

14 – 19 Oct 2013International Conference on StochasticAnalysis and ApplicationsHammamet, Tunisiahttp://pinguim.uma.pt/Investigacao/Ccm/icsaa13/

15 – 17 Oct 2013XIV All-Russian Conference of Young Scientistson Mathematical Modeling and InformationTechnologyTomsk, Russiahttp://conf.nsc.ru/ym2013/ru

15 – 19 Oct 20137th Moscow International Conference onOperations Research (ORM2013)Moscow, Russiahttp://io.cs.msu.su/

15 – 19 Oct 2013The 14th Asian Congress of Fluid MechanicsHanoi and Halong, Vietnamhttp://www.14acfm.ac.vn/

15 – 19 Oct 2013VII Moscow International Conference on Operations Research (ORM2013) Moscow, Russia http://io.cs.msu.su/

15 – 20 Oct 2013International Workshop on Numerical Methods of Stochastic Differential EquationsBeijing, Chinahttp://www.amss.ac.cn/xshy/201305/t20130502_3830239.html

16 – 18 Oct 2013SiPS 2013: 2013 IEEE Workshop onSignal Processing SystemsTaipei, Taiwanhttp://sips2013.org/

16 – 18 Oct 2013The Ninth International Conferenceon Intelligent Information Hidingand Multimedia Signal ProcessingBeijing, Chinahttp://bjut.edu.cn/college/dzxxkz/iihmsp13/

17 – 18 Oct 2013International Conference on Information Technology in Signal and Image Processing(itSIP2013)Mumbai, Indiahttp://itsip.theides.org/2013/

17 – 18 Oct 2013Statistics and Its ApplicationsTashkent, Uzbekistanhttp://nuu.uz/about/219-statistika-va-uning-tadbiqlari-ilmiy-amaliy-anjumani.html

17 – 18 Oct 20132013 POSTECH (Korea)-NCTS (Taiwan) Joint Workshop on PDEsPohang, Koreahttps://sites.google.com/site/2013postechncts/

17 – 18 Oct 2013COMSOL Conference 2013 BangaloreBangalore, Indiahttp://www.comsol.co.in/c/rrr

17 – 18 Oct 20132013 NIMS Hot Topics Workshops on Integral 3D Imaging & Holography WorkshopDaejeon, Koreahttp://open.nims.re.kr/new/event/event.php?workType=home&Idx=125

Conference CALENDAR Conference CALENDAR


17 – 20 Oct 2013 The Workshop on New Mathematical Developments Arising from Ecology, Epidemiology and Environmental Science Beijing, China http://www.bicmr.org/conference/nmda/

18 Oct 2013Mini-workshop “Differential Equations and Applications”Hanoi, Vietnam http://viasm.edu.vn/activities/dea2013/?lang=en

18 – 20 Oct 2013The 11th International Symposium on Financial Systems Engineering and Risk ManagementShanghai, Chinahttp://www.amss.ac.cn/xshy/201305/t20130502_3830334.html

19 – 21 Oct 2013 National Conference on New Horizons of StatisticsSolapur, Indiahttp://su.digitaluniversity.ac/WebFiles/Brochure_NCNHS_1.pdf

19 – 21 Oct 20136th International Conference on AdvancedComputational Intelligence (ICACI2013)Hangzhou, Chinahttp://www.iwaci.org/

19 – 23 Oct 2013Twelfth National ComputationalMathematics Annual MeetingChangsha, Chinahttp://www.chinacmam2013.com/list.aspx?classid=2

20 – 21 Oct 2013DIA/CDE Quantitative Science Forum (QSF) - Advancing Data Driven Regulatory Decision MakingBeijing, Chinahttp://www.eventdove.com/c/2383/m/5291?roi=echo4-23374502430-21966052-ea4396366684f325082bfca9dd21f2da&

20 – 23 Oct 2013 ICCAS — 13th International Conference on Control, Automaton and SystemsGwangju, South Koreahttp://2013.iccas.org

21 – 23 Oct 201311th International Conference on Statistical Sciences: Social Accountability, Global Economics and Human Resource Development with Special Reference to PakistanDera Ghazi Khan, Pakistanhttp://isi.cbs.nl/images/11th_ICSSDGK.pdf

21 – 23 Oct 2013International Conference on Mathematical Techniques in Engineering Applications Dehradun, Indiahttp://www.geu.ac.in/graphicneprd.aspx?pgid=104&nid=489

21 – 25 Oct 2013International Conference on Nonlinear Analysis: Fluid Dynamics and Kinetic TheoryTaipei, Taiwanhttp://www.math.sinica.edu.tw/www/file_upload/conference/201310FDKT/index.html

21 – 25 Oct 2013France-Taiwan Joint Conference on Nonlinear Partial Differential EquationsTaipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=171

22 – 25 Oct 20132013 NIMS-KMRS PDE Conference on Reaction Diffusion Equations for Ecology and Related ProblemsDaejeon, Koreahttp://open.nims.re.kr/new/event/event.php?workType=home&Idx=126

23 – 24 Oct 20132nd International Conference ofMathematics and Its ApplicationsBasra, Iraqhttp://basconmath.org/fos_math_icm_general_information.asp.htm

23 – 24 Oct 2013The International Conference onMathematical and Computer SciencesBandung, Indonesiahttp://icmcs-2013.net/

23 – 25 Oct 20132013 The 4th International Conferenceon Network of The FuturePohang, Koreahttp://nof2013.postech.ac.kr/

23 – 25 Oct 2013International Conference on AdvancedComputing and ApplicationsHo Chi Minh City, Vietnamhttp://www.cse.hcmut.edu.vn/ACOMP2013/

23 – 26 Oct 201334th Annual Meeting ofThe TeX Users Group (TUG 2013)Tokyo, Japanhttp://tug.org/tug2013/

24 – 25 Oct 2013International Conference on MathematicalTechniques in Engineering ApplicationsUttarakhand, Indiahttp://www.geu.ac.in/graphicneprd.aspx?pgid=104&nid=489#

24 – 26 Oct 2013MATHTED International Conference inMathematics Education 2013Bacolod City, Philippineshttp://mathted.weebly.com/

24 – 26 Oct 20132013 Korean Mathematical Society (KMS) Fall MeetingSeoul, Koreahttp://www.kms.or.kr/meetings/fall2013/

25 – 28 Oct 2013The 14th International Symposium on Knowledge and Systems SciencesNingbo, Chinahttp://www.amss.ac.cn/xshy/201305/t20130502_3830325.html

25 – 29 Oct 2013The 6th International Symposiumof Domain Theory and Its ApplicationsChangsha, Chinahttp://math.hnu.cn/isdt13/

26 Oct – 2 Nov 2013 2013 IEEE NSS/MIC/RTSD — 2013 IEEE Nuclear Science Symposium and Medical Imaging ConferenceSeoul, Koreahttp://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=16827

27 – 29 Oct 2013 Symposium in Biomathematics (Symomath) 2013Bandung, Indonesiahttp://www.math.itb.ac.id/~symomath

27 – 30 Oct 2013 8th Bi-Annual Statistics Congress, Turkish Statistical Association Kemer, Turkeyhttp://www.istkon8.org/

28 – 29 Oct 2013 ISCID — 2013 6th International Symposium on Computational Intelligence and DesignHangzhou, Chinahttp://iukm.zju.edu.cn/iscid/

28 – 31 Oct 2013 Beijing-Tianjin Workshop on GeometryTianjin, Chinahttp://www.nim.nankai.edu.cn/nim_e/conference.html

28 – 31 Oct 2013International Conference on Complex Analysis and Geometry In Honor of Hassine El MirMonastir, Tunisiahttp://www.fsg.rnu.tn/AGC_2013.htm

28 – 31 Oct 2013Groups, Group Rings, and Related Topics(GGRRT 2013)Al Ain, United Arab Emirateshttp://www.cos.uaeu.ac.ae/department/mathematical/conferences/GGRRT_2013/

28 Oct – 9 Nov 2013Lévy Processes and Self-similarity 2013Tunis, Tunisiahttp://levy-autosimilarity-tunis2013.math.cnrs.fr/index.html

30 – 31 Oct 2013International Conference onNonlinear Quantum DynamicsBali, Indonesiahttp://www.biztradeshows.com/conferences/icnqd/

Conference CALENDAR


Conference CALENDAR

31 Oct – 2 Nov 2013 2013 NCTS Conference on Mathematical Physiology Hsinchu, Taiwanhttp://math.cts.nthu.edu.tw/Mathematics/2013MP.htm

NOVEMBER 2013

1 – 2 Nov 2013 2013 International Conference on Mathematics Education Seoul, Koreahttps://groups.google.com/forum/#!msg/mathfuture/0jWHJoGz0Hc/K1oCqQ49VlEJ

2 – 4 Nov 2013 ICAST – UMEDIA — 2013 International Joint Conference on Awareness Science and Technology & Ubi-Media ComputingAizuwakamatsu, Japanhttp://www.u-aizu.ac.jp/conference/conf2013/

3 – 7 Nov 2013 CONIP 2013 — The 20th International Conference on Neural Information ProcessingDaegu, South Koreahttp://www.iconip2013.org

3 – 10 Nov 2013 JSPS (JAPAN) – DST (India) Asian Academic Seminar 2013: Discrete Mathematics & its ApplicationsTokyo, Japanhttp://faculty.ms.u-tokyo.ac.jp/users/aas2013/

4 – 7 Nov 2013Representation Theory in Geometry, Topology and CombinatoricsMelbourne, Australiahttp://www.ms.unimelb.edu.au/~mainini/RepTheoryConference/

4 – 7 Nov 2013Asian Conference on Membrane ComputingChengdu, Chinahttp://www.acmc2013.org/

5 – 7 Nov 20132nd Hot Topics International Workshop on the Mathematics of Materials Science: Liquid Crystal, Liquid Crystal Colloids, and Complex Fluids and Related TopicsDaejeon, Koreahttp://open.nims.re.kr/new/event/event.php?workType=home&Idx=127

5 – 8 Nov 2013Workshop on Modeling Rare Eventsin Complex Physical SystemsSingaporehttp://www2.ims.nus.edu.sg/Programs/013wmodel/index.php

6 – 8 Nov 20132nd IAPR Asian Conference onPattern Recognition (ACPR2013)Okinawa, Japanhttp://www.am.sanken.osaka-u.ac.jp/ACPR2013/

6 – 8 Nov 201321st National Symposium onMathematical Sciences (SKSM 2013)Penang, Malaysiahttp://sksm21.usm.my/?page_id=188

6 – 8 Nov 2013 Phylomania—The UTas Theoretical Phylogenetics MeetingHobart, Australiahttp://www.maths.utas.edu.au/phylomania/phylomania2013.htm

7 – 9 Nov 20134th International Conference onComputational Systems-Biology andBioinformatics (CSBio 2013)Seoul, Koreahttp://www.csbio.org/2013/

8 – 9 Nov 2013 37th National Conference on Theoretical and Applied Mechanics (37th-NCTAM) and the 1st International Conference on Mechanics (1st-ICM) Taipei, Taiwan http://www.pme.nthu.edu.tw/~CTAM2013/

9 – 10 Nov 2013 The 12th China Logistics Annual Conference Beijing, China http://csl.chinawuliu.com.cn/html/19887285.html

9 – 16 Nov 2013International Conference andWorkshop on Fractals and WaveletsKerala, Indiahttp://icfwrajagiri.in/

10 – 12 Nov 201322nd FIM International Conference onInterdisciplinary Mathematics, Statisticsand Computational TechniquesKitakyushu, Japanhttp://www.f.waseda.jp/watada/FIM2013/

11 – 13 Nov 2013 The 9th International Conference on Mobile Ad-hoc and Sensor Networks Dalian, China http://ncc.dlut.edu.cn/msn2013/cfp.shtml

11 – 14 Nov 2013CoSMEd 2013: Fifth International Conferenceon Science and Mathematics EducationPenang, Malaysiahttp://www.recsam.edu.my/cosmed/

11 – 15 Nov 2013South East Asian Conference on Mathematicsand Its Applications (SEACMA)Surabaya, Indonesiahttp://www.seacma.its.ac.id/home.php

11 – 15 Nov 2013 Perspectives of Representation Theory of Algebras, Conference Honoring Kunio Yamagata on the Occasion of His 65th Birthday Nagoya, Japan http://www.math.nagoya-u.ac.jp/~iyama/Yamagata65/index.html

11 – 15 Nov 2013Mal'tsev MeetingNovosibirsk, Russiahttp://math.nsc.ru/conference/malmeet/13/Main_e.htm

11 Nov 2013 – 25 Jan 2014Inverse Moment Problems: The Crossroads of Analysis, Algebra, Discrete Geometry and Combinatorics Singaporehttp://www2.ims.nus.edu.sg/Programs/014inverse/index.php

12 – 14 Nov 2013The 2nd International Conference onInformatics Engineering & InformationScience (ICIEIS2013)Kuala Lumpur, Malaysiahttp://sdiwc.net/conferences/2013/icieis2013/

13 – 15 Nov 2013The Third International Workshop on Extreme Scale Computing Application Enablement Modeling and Tools (ESCAPE) to be held in conjunction with The 15th IEEE International Conference on High Performance Computing and Communications (HPCC 2013) Zhangjiajie, China http://www.cs.nthu.edu.tw/~cherung/workshop/escape3.html

13 – 15 Nov 2013International Conference: MathematicalAnalysis of Nonlinear Partial DifferentialEquationsFukuoka, Japanhttp://www2.math.kyushu-u.ac.jp/FE-Seminar/MANPDE/

13 – 16 Nov 2013 2013 Workshop on Computational Mathematics and Its Applications Fuzhou, China http://math.fjnu.edu.cn/newmath/xkky/HTML/xkky_20130913151046.html

13 – 16 Nov 2013 2013 Fudan-Kaist Workshop on Algebra and Geometry Shanghai, China http://math.fudan.edu.cn/show.aspx?info_lb=766&flag=527&info_id=3398

16 – 17 Nov 2013The 13th Takagi LecturesKyoto, Japanhttp://www.ms.u-tokyo.ac.jp/~toshi/jjm/JJM_HP/contents/takagi/13th/index.htm

17 – 20 Nov 2013 VCIP — 2013 Visual Communications and Image Processing Kuching, Malaysia http://www.vcip2013.org

17 – 22 Nov 2013 Bioinformatics and Statistics for Large-Scale Data Yantian District, China http://events.embo.org/13-large-scale-data/



17 – 22 Nov 2013 2013 EMBO Practical Course - Bioinformatics and Statistics for Large-scale Data Shenzhen, China http://events.embo.org/13-large-scale-data/

18 – 21 Nov 2013IEEE International Workshop on InformationForensics and Security (WIFS 2013)Guangzhou, Chinahttp://www.wifs13.org

18 – 22 Nov 201325th Workshop on Topological Graph Theory(TGT25)Yokohama, Japanhttp://tgt.ynu.ac.jp/tgt25/index.html

18 – 30 Nov 2013Fourier Analysis of Groups in CombinatoricsShillong, Indiahttp://math.univ-lille1.fr/~bhowmik/cimpa/CIMPA_Shillong.html

18 Nov 2013 – 25 Jan 2014Inverse Moment Problems: The Crossroadsof Analysis, Algebra, Discrete Geometryand CombinatoricsSingaporehttp://www2.ims.nus.edu.sg/Programs/014inverse/index.php

19 – 21 Nov 2013Gulf International Conference on AppliedMathematics (in cooperation with SIAM)Mubarak, Kuwaithttps://conferences.gust.edu.kw/

19 – 22 Nov 2013The 3rd India-Taiwan Conference on Discrete MathematicsHsinchu, Taiwanhttp://www.math.nctu.edu.tw/amms201307/home.php

21 – 24 Nov 2013The 27th Pacific Asia Conference on Language, Information, and ComputationTaipei, Taiwanhttp://paclic27.nccu.edu.tw/

21 – 24 Nov 2013Japanese-Turkish Joint Geometry MeetingIstanbul, Turkeyhttp://math.gsu.edu.tr/2013jpn-tr.html

22 – 24 Nov 20132013 Korean Society for Industrial and Applied Mathematics (KSIAM) Annual MeetingJeju, Koreahttp://www.ksiam.org

22 – 24 Nov 2013The 6th International Conference onPairing-Based Cryptography (Pairing 2013)Beijing, Chinahttp://www.ieccr.net/2013/Pairing2013/index.html

24 – 26 Nov 2013Workshop of Quantum Dynamicsand Quantum Walks (QDQW)Okazaki, Japanhttp://qm.ims.ac.jp/qdqw/

24 – 27 Nov 20132013 Joint NZSA+ORSNZ ConferenceHamilton, New Zealandhttps://secure.orsnz.org.nz/conf47/

24 – 29 Nov 2013The 9th Delta Conference on Teachingand Learning of UndergraduateMathematics and StatisticsKiama, Australiahttp://delta2013.net

25 – 27 Nov 2013ROBIONETICS — 2013 IEEE International Conference on Robotics, Biomimetics, & Intelligent Computational SystemsBandung, Indonesiahttp://robionetics.org/

25 – 28 Nov 2013 ICCAIS — 2013 International Conference on Control, Automation and Information SciencesNha Trang, Vietnamhttp://www.2013iccais.irobotics.ac.vn

25 – 29 Nov 2013Recent Developments of Nonlinear PDEsCanberra, Australiahttp://maths.anu.edu.au/events/recentdevelopments-nonlinear-pdes

25 Nov – 6 Dec 2013Generalized Nash Equilibrium Problems, Bilevel programming and MPECNew Delhi, Indiahttp://www.cimpa-icpam.org/spip.php?article512

26 – 28 Nov 2013International Conference on Pure andApplied Mathematics (ICPAM-LAE 2013)Lae, Papua New Guineahttp://www.unitech.ac.pg

26 – 28 Nov 2013 "Turbulence and Wave Processes" Dedicated to the Centenary of Mikhail D Millionshchikov Moscow, Russia http://www.dubrovinlab.msu.ru/turbulencemdm100/

27 – 29 Nov 2013International Symposium on Computational Models for Life Sciences (CMLS-13)Sydney, Australiahttp://cmls-conf.org/2013/

27 – 29 Nov 2013ANZAMP Annual Meeting 2013Queensland, Australiahttp://www.maths.uq.edu.au/cmp/Workshops/ANZAMP2013/ANZAMP_2013.html

27 – 29 Nov 2013Image and Vision Computing New Zealand(IVCNZ 2013)Wellington, New Zealandhttp://ecs.victoria.ac.nz/Events/IVCNZ2013/WebHome

27 – 29 Nov 2013The 16th Annual International Conferenceon Information Security and Cryptology(ICISC 2013)Seoul, Koreahttp://www.icisc.org/icisc13/asp/01.html

27 – 30 Nov 2013The 9th China International Conferenceon Information Security and Cryptology(INSCRYPT 2013)Guangzhou, Chinahttp://www.inscrypt.cn/2013/Inscrypt_2013.html

28 – 30 Nov 2013ACWO2013: The 6th Australia-China Workshop on Optimization: Theory, Methods and ApplicationsBallarat, Australiahttp://www.ballarat.edu.au/schools/school-of-science-and-technology/research/conferences-and-workshops/the-6th-australia-china-workshop-onoptimization-theory-methods-and-applications

29 Nov – 1 Dec 20132013 Conference on ComputationalMechanics (CACM 2013)Sanya, Chinahttp://www.engii.org/workshop/cacm2013november/

29 Nov – 1 Dec 2013The 2nd Abu Dhabi University AnnualInternational Conference: MathematicalScience and ApplicationsAbu Dhabi, United Arab Emirateshttp://www.adu.ac.ae/en/section/internationalconference-mathematical-sciences-andapplications

DECEMBER 2013

1 – 2 Dec 2013 2013 The Second International Conference on Innovative Computing and Cloud Computing (ICCC 2013)Wuhan, Chinahttp://www.ier-institute.org/

1 – 4 Dec 201311th Engineering Mathematics andApplications Conference (EMAC2013)Brisbane, Australiahttp://emac2013.com.au/

1 – 5 Dec 2013The International Biometric SocietyAustralasian Region Conference 2013Mandurah, Australiahttp://www.biometricsociety.org.au/conferences/Mandurah2013/

1 – 5 Dec 2013ASIACRYPT 2013Bangalore, Indiahttp://www.iacr.org/conferences/asiacrypt2013/

Conference CALENDAR


Conference CALENDAR

1 – 6 Dec 2013MODSIM2013: International Congresson Modelling and SimulationAdelaide, Australiahttp://mssanz.org.au/modsim2013

1 – 8 Dec 2013 ICCV — 2013 IEEE International Conference on Computer VisionSydney, Australiahttp://www.iccv2013.org/

2 – 3 Dec 20137th Global Conference on Power Control and Optimization PCO 2013Yangon, Myanmarhttp://www.pcoglobal.com/Yangon.htm

2 – 4 Dec 2013International Conference on Computational & Network Technologies Adelaide, Australiahttp://thescipub.com/iccnt/

2 – 4 Dec 2013Fourth Wellington Workshop inProbability and Mathematical StatisticsWellington, New Zealandhttp://msor.victoria.ac.nz/Events/WWPMS2013/WebHome

2 – 5 Dec 2013Second International Workshop on Complex Networks and Their ApplicationsKyoto, Japanhttp://www.complexnetworks.org/

2 – 5 Dec 2013New Zealand Mathematical Society ColloquiumTauranga, New Zealandhttp://nzmathsoc.org.nz/colloquium2013/home.php

2 – 5 Dec 2013The 9th International Conference on Signal Image Technology & Internet Based Systems Kyoto, Japanwww.sitis-conf.org

2 – 5 Dec 2013Complex Analysis and GeometryArmidale, NSW, Australiahttp://www.amsi.org.au/index.php/events-mainmenu/forthcoming-events/165-events/science-events-2013/1129-complex-analysis-and-geometryworkshop

2 – 6 Dec 2013BioInfoSummer: AMSI Summer Symposium in Bioinformatics Adelaide, Australiahttp://mathsofplanetearth.org.au/events/bioinfosummer-2013-2/

2 – 14 Dec 2013Geometry and Topology of Singular Varieties. Theory and Applications.Hanoi, Vietnamhttp://www.cimpa-icpam.org/spip.php?article496

3 – 4 Dec 20132013 4th Global Congress on Intelligent Systems and 2013 4th world Congress on Software Engineering Hong Kong, Chinahttp://2013.gcis-conf.org/ and http://2013.wcse-conf.org/

3 – 5 Dec 2013Statistics and Operational ResearchInternational Conference (SORIC) 2013Sarawak, Malaysiahttp://einspem.upm.edu.my/soric2013/

3 – 5 Dec 2013New Zealand Mathematical Society ColloquiumTauranga, New Zealandhttp://nzmathsoc.org.nz/colloquium2013/home.php

4 – 6 Dec 20132013 NIMS International Conference on Geometry, Number Theory and Representation TheoryDaejeon, Koreahttp://open.nims.re.kr/new/event/event.php?workType=home&Idx=128

4 – 6 Dec 2013Modernization of Economics and Social Spheres in Russia: Quantitative Research MethodsMoscow, Russiahttp://www.rea.ru/

5 – 6 Dec 2013 The 2nd International Conference on Mathematical Sciences & Computer Engineering Kuala Lumpur, Malaysia http://www.icmsce.net/cms/

5 – 7 Dec 2013International Conference on Facets of Uncertainties and Applications (ICFUA 2013)Calcutta, Indiahttp://www.icfua.org/

6 – 7 Dec 2013International Symposium on MathematicalSciences and Computing Research 2013Ipoh, Malaysiahttp://www.perak.uitm.edu.my/ismsc2013/

6 – 7 Dec 2013 3rd Journal Conference on Applied Physics and Mathematics (JCAPM 2013 3rd) Sydney, Australia http://www.ijapm.org/jcapm/3rd/

6 – 8 Dec 2013 TAAI '13 — 2013 Conference on Technologies and Applications of Artificial Intelligence Taipei, Taiwan http://taai2013.nccu.edu.tw

7 – 8 Dec 2013 2013 Annual Meeting of the Taiwan Mathematical Society Kaohsiung, Taiwan http://amms2013.math.nsysu.edu.tw/bin/home.php

7 – 10 Dec 201314th International Conference onCryptology in India (Indocrypt 2013)Mumbai, Indiahttp://indocrypt.hbni.ac.in/

7 – 11 Dec 2013A Joint Session of 18th ATCM and 6th TIMEConferences (ATCM&TIME2013)Mumbai, Indiahttp://atcm.mathandtech.org

8 – 13 Dec 20135th East Asian Conference onAlgebraic TopologyBeijing, Chinahttp://www.amss.cas.cn/xshy/201211/t20121122_3687707.html

9 – 11 Dec 20132013 IEEE Second International Conference onImage Information Processing (ICIIP 2013)Waknaghat, Indiahttp://juit.ac.in/iciip_2013/

9 – 11 Dec 2013 AIRS '13 — The Ninth Asia Information Retrieval Societies Conference Singapore http://www.colips.org/conference/airs2013/

9 – 12 Dec 20132013 NCTS Workshop on Numerical Linear Algebra and High Performance Computing (2013 NLA-HPC)Hsinchu, Taiwanhttp://math.cts.nthu.edu.tw/Mathematics/2013NLA-HPC.htm

9 – 13 Dec 2013 CMI-IMSc Joint Mathematics Colloquium Conference on Analytic Theory of Automorphic Forms Chennai, Indiahttp://www.hri.res.in/~thanga/automorph/venue/

9 – 13 Dec 201337th Australasian Conference onCombinatorial Mathematics andCombinatorial ComputingPerth, Australiahttp://37accmcc.wordpress.com/

10 – 13 Dec 2013International Conference on Information,Communications and Signal Processing(ICICS 2013)Tainan, Taiwanhttp://www.icics.org/2013/home.asp

11 – 12 Dec 2013Limits to GrowthKensington, Australiahttp://mathsofplanetearth.org.au/events/limits-to-growth-beyondthe-point-of-inflexion/

11 – 14 Dec 20138th Conference on Nonlinear Systemsand DynamicsIndore, Indiahttp://iiti.ac.in/people/~cnsd2013/



11 – 14 Dec 20135th Asia Pacific Congress onComputational Mechanics & 4th International Symposium on Computational MechanicsSingaporehttp://www.apcom2013.org/

12 – 16 Dec 2013The 9th International Conference on Optimization: Techniques and Applications (ICOTA 9)Taipei, Taiwanhttp://icota9.conf.tw/

12 – 16 Dec 2013The International Conference on RecentAdvances in Experimental DesignsGuangzhou, Chinahttp://maths.gzhu.edu.cn/siced2013/

13 – 15 Dec 20132013 International Conference on Control,Communication and ComputingKerala, Indiahttp://iccc.cet.ac.in/

13 – 15 Dec 2013 International Conference on Special Functions & Their Applications (ICSFA 2013) and Symposium on "Applications in Diverse Fields of Engineering and Technology" Jaipur, India http://www.ssfaindia.webs.com/conf.htm

13 – 19 Dec 2013Representation Theory and Applicationsto Combinatorics, Geometry andQuantum PhysicsMoscow, Russiahttp://bogomolov-lab.ru/rep2013/conf.html

14 – 15 Dec 2013Second Guangzhou International Workshop on Mathematical ImagingGuangzhou, Chinahttp://www.compsci.sysu.edu.cn/conf/con01/index.htm

14 – 16 Dec 20139th International Conference on AdvancedData Mining and Applications (ADMA 2013)Hangzhou, Chinahttp://www.adma2013.org/

14 – 18 Dec 2013The Fifth East Asian Conference on Algebraic GeometryBeijing, Chinahttp://www.amss.cas.cn/xshy/201211/t20121122_3687696.html

14 – 20 Dec 20132013 Taiwan International Conference on Geometry Taipei, Taiwan http://www.math.ntu.edu.tw/~ctsdev/workshop/Default/index.php?WID=154

15 – 17 Dec 2013 International Conference on Frontiers of Probability and Statistics Hangzhou, China http://www.math.zju.edu.cn/HZPS2013/

15 – 20 Dec 2013MaxEnt 2013: 33rd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and EngineeringCanberra, Australiahttp://www.maxent2013.org/

16 – 18 Dec 201324th International Symposium on Algorithmsand Computation (ISAAC 2013)Hong Kong, Chinahttp://www.cs.hku.hk/isaac2013/

16 – 18 Dec 2013International Conference on Role ofStatistics in The Advancement of Science and TechnologyPune, Indiahttp://stats.unipune.ac.in/Conf13.html

16 – 18 Dec 2013FIT — 2013 11th International Conference on Frontiers of Information Technology Islamabad, Pakistan http://www.fit.edu.pk/

16 – 18 Dec 2013 ECM 2013: 2nd International Conference on Engineering and Computational Mathematics (in cooperation with SIAM) Hong Kong, China http://www.polyu.edu.hk/ama/events/conference/ECM2013

16 – 19 Dec 2013International Conference on Advancesin Applied Mathematics (ICAAM 2013)Hammamet, Tunisiahttps://sites.google.com/site/icaam2013/

16 – 19 Dec 2013Taipei Winter School in Representation Theory IIITaipei, Taiwanhttp://www.math.sinica.edu.tw/chengsj/winterschool_2013.htm

16 – 20 Dec 20132013 Taiwan International Conferenceon GeometryTaipei, Taiwanhttp://www.math.ntu.edu.tw/~ctsdev/workshop/Default/index.php?WID=154

16 – 20 Dec 2013Commutative Algebra and Its Interaction toAlgebraic Geometry and CombinatoricsHanoi, Vietnamhttp://vie.math.ac.vn/CA-2013/

16 – 20 Dec 2013XXIVth International Workshop on OperatorTheory and Its Applications (IWOTA 2013)Bangalore, Indiahttp://math.iisc.ernet.in/~iwota2013/

17 – 19 Dec 20133rd International Conference onMathematical SciencesKuala Lumpur, Malaysiahttp://www.ukm.my/confukm/index.php/ICMS/ICMS3

17 – 20 Dec 2013Quantitative Methods in FinanceSydney, Australiahttp://www.qfrc.uts.edu.au/qmf/

17 – 20 Dec 2013 International Conference on Mathematics Education and Mathematics in Engineering and Technology Thiruvananthapuram, India http://www.mcetonline.com/icmet

18 – 20 Dec 2013 67th Annual Conference of the Indian Society of Agricultural Statistics Varanasi, India http://www.isas.org.in/

18 – 20 Dec 2013 6th Indian International Conference on Artificial Intelligence Tumkur (near Bangalore), India http://www.iiconference.org

18 – 21 Dec 2013HiPC 2013: 20th IEEE International Conferenceon High Performance ComputingBangalore, Indiahttp://www.hipc.org/hipc2013/index.php

18 – 21 Dec 2013Third Tunisian-Japanese Conference ofGeometric and Harmonic Analysis onHomogeneous Spaces In Honor of HidenoriFujiwaraHammamet, Tunisiahttp://www2.math.kyushu-u.ac.jp/~tnomura/HammConf/

19 – 20 Dec 2013Vietnam International Applied MathematicsConference (VIAMC 2013)Binh Duong, Vietnamhttp://viamc.dongan.edu.vn/

19 – 21 Dec 2013 NCVPRIPG — 2013 Fourth National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics Jodhpur, India http://www.iitj.ac.in/ncvpripg/

20 – 22 Dec 2013 The International Conference on Nonlinear Analysis and Optimization (ICNAO2013)Kaoshiung, Taiwanhttp://icnao2013.math.nsysu.edu.tw/bin/home.php

20 – 22 Dec 201318th International MathematicsConference 2013Dhaka, Bangladeshhttp://www.secs.iub.edu.bd/18matconf/

20 – 23 Dec 2013Taipei Conference on Representation Theory IVTaipei, Taiwanhttp://www.math.sinica.edu.tw/chengsj/lie_2013.htm

Conference CALENDAR


Conference CALENDAR

20 – 23 Dec 2013The Ninth ICSA International Conference:Challenges of Statistical Methods forInterdisciplinary Research and Big Data(ICSA2013)Hong Kong, Chinahttp://www.math.hkbu.edu.hk/ICSA2013/

21 – 22 Dec 2013 The International Congress on Science and Technology Allahabad, U.P., India http://sites.google.com/site/intcongressonsciandtech/ 21 – 23 Dec 2013 ICMIRA — 2013 International Conference on Machine Intelligence and Research Advancement Katra JK, India http://www.icmira.com

21 – 23 Dec 20137th International Conference of IMBIC on “Mathematical Sciences for Advancement of Science and Technology” (MSAST 2013)Calcutta, Indiahttp://www.imbic.org/forthcoming.html

24 – 26 Dec 2013 International Conference on "Recent Advances in Mathematical Sciences and Applications" (ICRAMSA-2013) Gandhi Nagar, Bhopal (M. P.), India http://www.rgpv.ac.in

26 – 28 Dec 2013 International Conference on Recent Advances in Statistics and Their Applications in Conjunction with the XXXIII Annual Convention of the Indian Society For Probability and Statistics Aurangabad, India http://www.bamu.ac.in/icrastat2013/

26 – 29 Dec 2013International Conference on Mathematics and Computing – 2013Haldia, Indiahttp://hithaldia.in/icmc2013/

28 – 30 Dec 20133rd International Conference on Mathematics and Information SciencesLuxor, Egypthttp://conf.naturalspublishing.com/

28 – 31 Dec 2013Statistics 2013: Socio-Economic Challenges and Sustainable SolutionsHyderabad, Indiawww.statistics2013-conference.org.in

29 – 31 Dec 2013 International Conference on Computer Analysis of the Problems of Science and Technology Dushanbe, Tajikistanhttp://www.yunusi.tj

JANUARY 2014

2 – 4 Jan 2014 ICCTN-2014 — The 3rd International Conference on Computational and Theoretical NanoscienceSanya, Hainan, Chinahttp://www.iamset.org/icctn/

3 – 5 Jan 2014International Conference on AppliedMathematical Models (ICAMM 2014)Coimbatore, Indiahttp://www.psgtech.edu/icamm2014/

5 – 26 Jan 2014 and 9 Feb – 1 Mar 2014Workshop on Birational Geometry and Stability of Moduli Stacks and Spaces of CurvesHanoi, Vietnamhttp://viasm.edu.vn/20130807/hdkh/moduli2014/

6 – 9 Jan 2014 7th Jagna International Workshop: Analysis of Fractional Stochastic Process and Applications Jagna, Bohol, Philippines http://physics.msuiit.edu.ph/spvm/

6 – 10 Jan 2014 COMSNETS '14 - International Conference on Communication Systems and NetworksBangalore, Indiahttp://comsnets.org/

6 – 10 Jan 2014MAM8 2014 — Eighth InternationalConference on Matrix AnalyticMethods in Stochastic ModelsCalicut, Kerala, Indiahttp://mam8.nitc.ac.in/

6 – 10 Jan 2014NZ Probability WorkshopTe Anau, New Zealandhttp://www.stat.auckland.ac.nz/~mholmes/workshop/TeAnau2014

6 – 17 Jan 20145th Indian School on Logicand Its ApplicationsTezpur, Indiahttp://www.tezu.ernet.in/isla2014/

6 – 31 Jan 2014 2014 AMSI Summer SchoolCanberra, Australiahttp://mathsofplanetearth.org.au/events/ss2014/

9 – 11 Jan 2014 ICUIMC '14 — The 8th International Conference on Ubiquitous Information Management and Communication Siem Reap, Cambodia http://www.icuimc.org/

10 – 17 Jan 20142014 POSTECH Winter School – SpectralTheory and Automorphic FormsPohang, Koreahttps://sites.google.com/site/2014pmiwinterschool/

12 – 17 Jan 2014 2nd International Optimisation Summer School Kioloa Beach, New South Wales, Australia http://optimisationmelbourne.wordpress.com/2013/09/07/summer-school/

13 – 14 Jan 20142014 International Conference on Science & Engineering in Mathematics, Chemistry and Physics (ScieTech 2014)Jakarta, Indonesiahttp://scietech.org/

13 – 16 Jan 2014Sydney Random Matrix Theory WorkshopSydney, Australiahttp://www.maths.usyd.edu.au/u/olver/conferences/RMT.html

13 – 17 Jan 2014 2014 NZMRI Summer School on Operator Algebra Te Anau, New Zealand http://www.maths.otago.ac.nz/nzmri14/

17 – 19 Jan 2014The Twelfth Asia-Pacific BioinformaticsConferenceShanghai, Chinahttp://admis.fudan.edu.cn/apbc2014/

19 – 22 Jan 2014 International Conference on the Analysis and Mathematical Applications in Engineering and Science Miri, Sarawak, Malaysia http://csri.curtin.edu.my/?page_id=31

20 – 23 Jan 2014International Conference on Recent Advances in Mathematics (ICRAM 2014)Nagpur, Indiahttp://www.icram2014.com/

20 – 24 Jan 2014Islamabad International Conference on Topology and Its Applications (IICTA 2014)Islamabad, Pakistanhttp://atlas-conferences.com/cgi-bin/calendar/d/fagb72

22 – 23 Jan 20142014 International Conference on Physical Science and Technology (ICPST 2014) Macau, Chinahttp://www.conferencealerts.com/show-event?id=122144

22 – 23 Jan 2014 RISTCON 2014 — 1st Ruhuna International Science and Technology ConferenceRuhuna, Matara, Sri Lankahttp://www.sci.ruh.ac.lk/conference/ristcon2014/home/

25 – 30 Jan 2014 From Random Walks to Lévy Processes Kioloa, Australiahttp://maths.anu.edu.au/events/kioloa-conference-random-walks-levy-processes



27 – 30 Jan 2014 Symmetries, Differential Equations and Applications (SDEA-II) Islamabad, Pakistanhttp://sdea2.nust.edu.pk/ 27 – 30 Jan 2014 4th BIU Winter School on Crypto: Symmetric Encryption — Theory & PracticeTel-Aviv, Israelhttp://crypto.biu.ac.il/winterschool2014/

27 Jan – 2 Feb 2014 Moscow Workshop in Combinatorics and Number TheoryMoscow, Russiahttp://mjcnt.phystech.edu/conference/moscow/

28 Jan – 1 Feb 2014Mathematics in Industry Study Group(MISG) 2014Brisbane, Australiahttp://mathsinindustry.com/

29 – 31 Jan 2014The Second Fluids in New Zealand Workshop(FiNZ 2014)Auckland, New Zealandhttp://homepages.engineering.auckland.ac.nz/~jden259/FiNZ2014/Welcome.html

FEBRUARY 2014

2 – 6 Feb 2014ANZIAM 2014Rotorua, New Zealandhttp://anziam2014.auckland.ac.nz/

3 – 4 Feb 20143rd Annual International Conference onComputational Mathematics, ComputationalGeometry and StatisticsSingaporehttp://www.mathsstat.org/

10 – 13 Feb 2014Symposium on Projective Algebraic Varieties and Moduli 2014 in Honor of Professor Changho Keem's 60th BirthdaySeoul, Koreahttp://www.math.snu.ac.kr/~kiem/2014symposium

15 – 16 Feb 2014 International Conference On Advances in Computing and Information Technology - ACIT 2014 Bangkok, Thailand http://www.acit.theired.org/

19 – 20 Feb 20144th International Conference on AppliedPhysics and Mathematics (ICAPM 2014)Singaporehttp://www.icapm.org/

26 - 28 Feb 2014 Living Analytics: Analyzing High-Dimensional Behavioral and Other Data from Dynamic Network Environments Singaporehttp://www2.ims.nus.edu.sg/Programs/014wliv/index.php

27 – 28 Feb 2014 2014 International Conference on Information Security and Artificial Intelligence (ICISAI 2014)Hanoi, Vietnamhttp://www.icisai.org/

MARCH 2014

3 – 7 Mar 2014Workshop on IDAQP and Their ApplicationsSingaporehttp://www2.ims.nus.edu.sg/Programs/014widaqp/index.php

5 – 7 Mar 2014 International Workshop on Discrete Structures (IWODS) Islamabad, Pakistan http://www.camp.nust.edu.pk/IWODS2014/

10 – 26 Mar 2014School and Workshop on Classificationand Regression TreesSingaporehttp://www2.ims.nus.edu.sg/Programs/014swclass/index.php

12 – 14 Mar 2014 IAENG International Conference on Operations Research 2014 Hong Kong, Chinahttp://www.iaeng.org/IMECS2014/ICOR2014.html

13 – 15 Mar 2014Advances in Control and Optimizationof Dynamical Systems (ACODS-2014)Kanpur, Indiahttp://www.iitk.ac.in/acods2014/Home_ACODS-2014.html

15 – 18 Mar 2014MSJ Spring Meeting 2014Tokyo, Japanhttp://mathsoc.jp/en/meeting/gakushuin14mar/

21 – 23 Mar 2014 CoDS '14 — 1st IKDD Conference on Data Sciences Delhi, India http://ikdd.acm.org/Site/CoDS/index.html

22 – 23 Mar 2014 2014 International Conference on Robotics, Mechanics and Mechatronics (ICRMM 2014) Bali, Indonesia http://www.icrmm.org/

24 – 28 Mar 2014 29th Symposium on Applied Computing Gyeongju, Korea http://oldwww.acm.org/conferences/sac/sac2014/

26 – 30 Mar 2014 Mathematical Physics: Past, Present, and Future St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

APRIL 2014

28 – 29 Apr 20144th Annual International Conference onOperations Research and Statistics (ORS 2014)Phuket, Thailandhttp://orstat.org/

29 Apr – 2 May 2014IEEE International Symposium onBiomedical Imaging (ISBI 2014)Beijing, Chinahttp://biomedicalimaging.org/2014/

MAY 2014

1 – 30 May 2014Self-normalized Asymptotic Theory in Probability, Statistics and Econometrics Singaporehttp://www2.ims.nus.edu.sg/Programs/014self/index.php

10 – 14 May 2014 9th International Statistics Day Symposium Antalya, Turkey http://igs2014.org/

12 – 14 May 2014The 10th International Conference on Information Security Practice and Experience (ISPEC 2014)Fuzhou, China http://icsd.i2r.a-star.edu.sg/ispec2014/

12 – 14 May 2014SIAM Conference on Imaging Science (IS14)Hong Kong, Chinahttp://www.siam.org/meetings/is14/

26 – 29 May 2014 2014 International Conference on Modelling and Simulation of Complex Biological SystemsTianjin, China http://202.113.29.3/~icmcbs/

26 – 30 May 2014 Annual International Conference Diffraction Days 2014 St. Petersburg, Russia http://www.pdmi.ras.ru/~dd/

26 – 31 May 2014Inverse Problems: Modeling and SimulationFethiye, Turkeyhttp://ipms-conference.org/

27 – 29 May 20147th International Conference of Mathematics and Engineering Physics (ICMEP-7)Cairo, Egypthttp://www.mtc.edu.eg/calls_for_papers/2014/Mathematics.pdf

Conference CALENDAR


Conference CALENDAR

JUNE 2014

2 – 10 Jun 2014CIMPA/TUBITAK/GSU Summer School:Algebraic Geometry and Number TheoryIstanbul, Turkeyhttp://math.gsu.edu.tr/2014agnt.html

4 – 6 Jun 201412th International Symposium on Functional and Logic Programming (FLOPS 2014)Kanazawa, Japanhttp://www.jaist.ac.jp/flops2014/

8 – 12 Jun 2014Group Analysis of Differential Equationsand Integrable SystemsProtaras, Cyprushttp://www2.ucy.ac.cy/~symmetry/

9 – 11 Jun 2014 SOCG'14 — Annual Symposium on Computational Geometry Kyoto, Japan http://www.dais.is.tohoku.ac.jp/~socg2014/

9 – 12 Jun 2014Nexus 2014: Relationships BetweenArchitecture and MathematicsAnkara, Turkeyhttp://www.nexusjournal.com/call-forpapers/305-cfp-nexus-2014.html

9 – 14 Jun 2014 Representations, Dynamics, Combinatorics: in the Limit and Beyond St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

10 – 12 Jun 2014 COMS 2014 — The 5th Workshop on Computational Optimization, Modeling and Optimization Cairns, Australia http://iccs2014.ivec.org/

16 – 19 Jun 2014 International Workshop on Applied Probability (IWAP 2014) Antalya, Turkeywww.iwap2014.org

16 – 19 Jun 2014Second Joint International Meeting of The Israel Mathematical Union and The American Mathematical SocietyTel-Aviv and Bar-Ilan, Israelhttp://imu.org.il/Meetings/IMUAMS2014/index.html

16 – 20 Jun 2014 Stochastic Processes and High Dimensional Probability Distributions St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

23 – 25 Jun 2014 10th Conference of East Asia Section of SIAM (EASIAM 2014) Bangkok, Thailand https://www.siam.org/sections/easiam/

23 Jun – 4 Jul 2014Partial Differential Equations: Analysis,Numerics and Applications to Floodsand TsunamisQuezon City, Philippineshttp://www.math.upd.edu.ph/cimpa_research_school2014/

25 – 30 Jun 2014 23rd St. Petersburg Summer Meeting in Mathematical Analysis St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

29 Jun – 1 Jul 2014 International conference on Geometric Modeling and Processing (GMP) Singapore http://gmp.sce.ntu.edu.sg/

30 Jun – 3 Jul 2014The 3rd Institute of Mathematical StatisticsAsia Pacific Rim MeetingTaipei, Taiwanhttp://www.ims-aprm2014.tw/

JULY 2014

3 – 8 Jul 2014 6th St. Petersburg Conference in Spectral Theory St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

6 – 11 Jul 2014IEEE World Congress on ComputationalIntelligence (IEEE WCCI 2014)Beijing, Chinahttp://www.ieee-wcci2014.org/

7 – 9 Jul 2014Building Statistical Methodology and Theory: An International Conference in Honor of Jeff C. F. Wu for His 65th BirthdayMile, Yunnan, China http://www.stat.purdue.edu/~sunz/Jeff_2014/index.html

7 – 9 Jul 2014 19th Australasian Conference on Information Security and Privacy (ACISP 2014) Wollongong, Australia https://ssl.informatics.uow.edu.au/acisp2014/

7 – 10 Jul 2014IMS Annual MeetingSydney, Australiahttp://www.ims-asc2014.com/

7 Jul – 29 Aug 2014The Geometry, Topology and Physicsof Moduli Spaces of Higgs BundlesSingaporehttp://www2.ims.nus.edu.sg/Programs/014geometry/index.php

18 – 20 Jul 2014 ICCS 2014 - The International Conference on Cryptography and Security Bangkok, Thailand http://www.iccs.asdf.org.in/

21 – 24 Jul 2014The 20th International Conference on Difference Equations and ApplicationsWuhan, Chinahttp://icdea2014.csp.escience.cn/dct/page/1

21 – 25 Jul 2014 GAGTA8: Geometric and Asymptotic Group Theory with Applications Newcastle, Australia https://sites.google.com/site/gagta8/

21 – 25 Jul 2014 SSAC '14 — International Symposium on Symbolic and Algebraic ComputationKobe, Japanhttp://www.issac-conference.org/

24 – 29 Jul 20148th International Conference for Computational Fluid DynamicsChengdu, Chinahttp://www.cstam.org.cn/templates/lxxh_1/index.aspx?nodeid=94&page=ContentPage&contentid=172140

28 Jul – 1 Aug 2014 Diagrams 2014 - Eighth International Conference on the Theory and Application of DiagramsMelbourne, Australia http://www.diagrams-conference.org/2014

28 Jul – 1 Aug 2014 Commutative Algebra and Singularity Theory Toyama, Japan http://www.commalg.org/2014/07/ca-and-singularity-theory-toyama/

28 Jul – 1 Aug 20142014 Annual Meeting of The Society forMathematical Biology and Japanese Society for Mathematical BiologyOsaka, Japanhttp://www.smb.org/meetings/annual.shtml

28 Jul – 8 Aug 2014Mock Modular Forms: A Joint CIMPA-ICTPResearch SchoolKozhikode, Indiahttp://www.ksom.res.in/MMF/

30 Jul – 5 Aug 2014The 7th MSJ-SI Hyperbolic Geometryand Geometric Group TheoryTokyo, Japanhttp://www.is.titech.ac.jp/msjsi2014/

AUGUST 2014

7 – 11 Aug 20142014 17th Conference on Fuzzy Systems and Fuzzy Mathematics Beijing, Chinahttp://mohu.org/zh/html/450.html#more-450

7 – 11 Aug 2014Eleventh Algorithmic Number Theory Symposium ANTS-XI Gyeongju, Koreahttps://ants2014.kookmin.ac.kr/



12 – 14 Aug 2014 International Conference on Quantitative Sciences and Its Applications Langkawi, Malaysiahttp://icoqsia2014.uum.edu.my/

12 – 14 Aug 2014 The 2nd International Statistical Conference (ISM-II 2014) Kuantan, Malaysia http://ism2.ump.edu.my/

13 – 21 Aug 2014International Congress of Mathematicians (ICM) 2014Seoul, Koreahttp://www.icm2014.org/

14 – 19 Aug 2014 International Conference of Bridges: Mathematics in Art, Music, and Science Seoul, Korea http://www.bridgesmathart.org/

25 – 27 Aug 201412th Iranian Statistical ConferenceKermanshah, Iranhttp://isc12.razi.ac.ir/index.php?slc_lang=en&sid=1

25 – 29 Aug 2014Stochastic Processes, Analysisand Mathematical PhysicsOsaka, Japanhttp://stoc-proc.com/sympo/2014/SPAMP2014.htm

SEPTEMBER 2014

9 – 11 Sep 2014Advanced Mathematical and Computational Tools in Metrology and Testing (AMCTM 2014)St. Petersburg, Russiahttp://www.cs.utep.edu/interval-comp/metrology14.pdf

22 – 25 Sep 2014The 14th International Conference of The International Association for ComputerMethods and Advances in Geomechanics(14IACMAG)Kyoto, Japanhttp://www.14iacmag.org/

25 – 28 Sep 2014MSJ Autumn Meeting 2014Hiroshima, Japanhttp://mathsoc.jp/en/

OCTOBER 2014

8 – 10 Oct 2014IAOS Vietnam 2014 conference: Challengesin Official Statistics: Meeting The Needs ofa Changing WorldHanoi, Vietnamhttp://isi.cbs.nl/iaos/Conferences/2014Vietnam.htm

13 – 15 Oct 2014Hans Freudenthal Summit Forum on the Topic of Theory and Practice in Mathematics Education Concept Beijing, Chinahttp://www.xsj21.com/huiyi/index.html

17 – 20 Oct 2014Geostatistical and Geospatial Approaches for The Characterization of Natural Resources in The Environment: Challenges, Processes and StrategiesNew Delhi, Indiahttp://www.jnu.ac.in/Conference/IAMG2014/background.htm

24 – 26 Oct 201415th SPVM National Conference2013 International Conference on Applied Physics and Materials Science2013 Meeting on Complex SystemDavao City, Philippineshttp://physics.msuiit.edu.ph/spvm/

25 – 29 Oct 2014The Fifth International Conference on Numerical Algebra and Scientific ComputingShanghai, Chinahttp://www.amss.ac.cn/xshy/201309/t20130903_3923162.html

NOVEMBER 2014

10 – 21 Nov 2014Dynamical Systems and Applications:Geometrical, Topological, and NumericalAspectsLahore, Pakistanhttp://www.sms.edu.pk/cimpa2014.php

DECEMBER 2014

8 – 12 Dec 2014 Joint Meeting of New Zealand Mathematical Society and Australian Mathematical Society Melbourne, Australiahttp://www.math.canterbury.ac.nz/ANZMC2008/

9 – 19 Dec 2014 Recent Advances in Operator Theory and Operator Algebras-2014 Bangalore, Indiahttp://www.isibang.ac.in/~jay/OTOA2014/OTOA14.html

APRIL 2015

19 – 24 Apr 201540th International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2015Brisbane, Australiahttp://www.icassp2015.org/

JUNE 2015

22 – 26 Jun 2015 Analytic Tools in Probability and Applications St. Petersburg, Russia http://www.pdmi.ras.ru/EIMI/imiplanC.html

JULY 2015

20 – 24 Jul 2015 The 11th International Conference on Fixed Point Theory and its Applications Istanbul, Turkeyhttp://www.icfpta.org/

AUGUST 2015

10 – 14 Aug 20158th International Conference on Industrial and Applied Mathematics (ICIAM2015)Beijing, Chinahttp://www.iciam2015.cn/

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/

International Congress of Mathematics Satellite Conferences

The following are conditionally pre-approved ICM Satellite Conferences in Korea

Jul or Aug 2014Pacific Rim Conference on Complex GeometryVenue to be announced

28 Jul – 1 Aug 2014Geometry and Physics of Gauged Linear Sigma ModelKIAS, Korea

4 – 8 Aug 2014Homological Mirror Symmetry and Symplectic TopologyIBS Center for Geometry & Physics,Pohang, Korea

4 – 8 Aug 2014Variational Methods in Nonlinear Elliptic PDE'sGyeongju (to be announced)

4 – 8 Aug 2014ICM 2014 Satellite Conference in Harmonic AnalysisChosun University, Gwangju, Korea

4 – 9 Aug 2014Pan Asia Number Theory (PANT)POSTECH, Pohang, Korea

5 – 9 Aug 2014ICM 2014 Satellite Conference on Extremal and Structural Graph TheoryThe-K Gyeongju Hotel, Gyeongju, Korea

5 – 9 Aug 2014The 4th International Congress of Mathematical Software (ICMS 2014)Hanyang University, Seoul, Korea

6 – 9 Aug 2014Representation Theory and Related TopicsEXCO, Daegu, Korea

6 – 9 Aug 2014Classification TheoryYonsei University, Seoul, Korea

6 – 9 Aug 2014ILAS (International Linear Algebra Society) 2014Sungkyunkwan University, Suwon, Korea

6 – 10 Aug 2014Algebraic and Complex GeometryKAIST, Daejeon, Korea

6 – 11 Aug 20147th International Conference on Stochastic Analysis and Its Applications 2014Seoul National University, Seoul, Korea

7 – 9 Aug 2014Imaging, Multi-scale and High Contrast PDENIMS, Daejeon, Korea

7 – 11 Aug 2014Topology of Torus Actions and Applications to Geometry and CombinatoricsDaejeon Convention Center, Daejeon, Korea

7 – 11 Aug 2014Quadratic Forms and Related TopicsHotel Hyundai, Gyeongju, Korea

7 – 11 Aug 2014The KSCV Symposium #10: International Conference on Complex Analysis and GeometryPOSTECH, Pohang, Korea

7 – 11 Aug 2014Algorithmic Number Theory Symposium – ANTS XIHotel Hyundai, Gyeongju, Korea

7 – 12 Aug 2014Geometry on Groups and SpacesKAIST, Daejeon, Korea

8 – 12 Aug 2014Dynamical Systems and Related TopicsChungnam National University, Daejeon, Korea

8 – 12 Aug 2014Operator Algebras and ApplicationsCheongpung, Jecheon, Korea

9 – 12 Aug 2014International Workshop on Computational Mathematics – Advances in Computational PDEs Yonsei University, Seoul, Korea

11 – 12 Aug 2014ICM 2014 Satellite Conference on Algebraic Coding TheoryEwha Womans University, Seoul, Korea

11 – 12 Aug 2014ICWM 2014 (International Conference of Women Mathematicians)Ewha Womans University, Seoul, Korea

22 – 24 Aug 2014Geometric Analysis: Relationships between Partial Differential Equations, Differential Geometry and Algebraic TopologySungkyunkwan University, Korea

22 – 26 Aug 2014International Conference on Quantum Probability and Related TopicsChungbuk National University, Cheongju, Korea

22 – 26 Aug 2014Knots and Low-Dimensional ManifoldsBusan, Korea

25 – 28 Aug 2014Automorphic Forms and ArithmeticPOSTECH, Korea

The following are conditionallypre-approved ICM SatelliteConferences in neighbouringcountries

21 – 25 Jul 2014ISSAC 2014Kobe University, Kobe, Japan

Early AugMathematical Challenge to a New Phase of Materials ScienceRIMS, Kyoto University, Kyoto, Japan

4 – 8 Aug 2014The Geometry, Topology and Physics of Moduli SpacesThe Institute for Mathematical Sciences (IMS), National University of Singapore

5 – 9 Aug 2014The 4th Asian Conference on Nonlinear Analysis and OptimisationNational Taiwan Normal University, Taipei, Taiwan

6 – 8 Aug 2014The 9th East Asia PDE ConferenceTokyo, Japan (venue to be announced)

7 – 11 Aug 2014Recent Advances in Computational MathematicsWeihai Campus of Shandong University, Shandong, China

8 – 12 Aug 2014International Conference on Combinatorics and GraphsBeijing, China

9 – 12 Aug 2014Lie and Jordan Algebras, Their Representations and ApplicationsVladivostok, Russia

22 – 29 Aug 2014The 7th International Conference on Differential and Functional Differential Equations (DFDE-2014)Steklov Mathematical Institute, Moscos, Russia

25 – 29 Aug 2014International Conference on Stochastic Processes, Analysis and Mathematical PhysicsKansai University, Osaka, Japan

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



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: Budi Nurani Ruchjana,Address: Fakultas Matematika dan Ilmu

Pengetahuan Jurusan Matematika Universitas Padjadjaran Jalan Raya Bandung-Sumedang Km. 21 Jatinangor Sumedang 45363 IndonesiaTel.: 022-7797712Fax: 002-7794545Email: [email protected]://indoms.or.id/

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 Society

President: Myung-Hwan Kim Address: Department of Mathematics Seoul National University Seoul 151-747, Korea Tel.: +82-2-880-6551 Fax: +82-2-887-4694Email: [email protected]

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: Graham WeirContact: 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 Society

President: 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: Jumela F. SarmientoAddress: Department of Mathematics Ateneo de Manila University Loyola Heights, Quezon City, 1108 PhilippinesEmail: [email protected]

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

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