Asia Pacific Mathematics Newsletter - Australian ... Pacific Mathematics Newsletter July 2011 Volume 1 Number 3 Behind the Great Wave at Kanagawa Institute for Mathematical Sciences,

Asia PacificMathematics NewsletterJuly 2011 Volume 1 Number 3

Behind the Great Wave at Kanagawa

Institute for Mathematical Sciences, NUS Roy Kerr

Volcanic eruption on the island of Krakatau

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]

Sze-Bi HsuDepartment of MathematicsNational Tsing Hua [email protected]

Michio JimboRikkyo University [email protected]

Dohan KimDepartment of MathematicsSeoul National UniversitySouth [email protected]

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

Ta-Tsien LiSchool of Mathematical SciencesFudan [email protected]

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

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

Le Tuan HoaInstitute of Mathematics, VAST18 Hoang Quoc Road10307 HanoiVietnam [email protected]

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

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

Yu Kiang LeongDepartment of Mathematics National University of Singapore S17-08-06 Singapore [email protected]

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

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

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

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

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

Advisory Board

Editorial Board

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

Jenn-Nan Wang Department of MathematicsNational Taiwan UniversityTaipei 106, [email protected]

Chengbo Zhu Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore [email protected]

Editorial

Jugendtraum of a Mathematician...............................................................................................................................1

Using the Finite Simple Groups .....................................................................................................................................7

Evolution of Tsunami Science ...................................................................................................................................... 11

Fighting Asian Catastrophes with Mathematics ...................................................................................... 17

Haibao Duan: Mathematics Should Trace Its Origin to FaceFuture Challenges ..................................................................................................................................................................... 20

Interview with Director of Institute for Mathematical Sciences Louis Chen .............. 23

A Brief Introduction to Mathematical Competitions in Shanghai ......................................... 28

Problem Corner ........................................................................................................................................................................... 32

SEAMEO Regional Centre for Mathematics Education ...................................................................... 34

Roy Kerr Gains New Zealand Honour .................................................................................................................. 36

Tackling the Big Unanswered Problems ........................................................................................................... 37

Stamps on Asian Mathematicians ........................................................................................................................... 38

Book Reviews ................................................................................................................................................................................. 39

Fifth International Congress on Mathematical Biology .................................................................... 42

MathWest Workshop and IMU Meeting ............................................................................................................ 43

News in Asia Pacific Region ............................................................................................................................................ 44

Conferences in Asia Pacific Region ......................................................................................................................... 52

Mathematical Societies in Asia Pacific Region ........................................................................................... 59

July 2011

Asia PacificMathematics Newsletter

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

Volume 1 Number 3

Electronic – ISSN 2010-3492

Editorial

In this issue, we are fortunate to be able to reprint two articles: Kyoji Saito’s “Jugendtraum of a Mathemati-cian” (斎藤恭司“一数学者の青春の梦”), which first

appeared in IPMU (Institute for the Physics and Mathematics of the Universe) News, and Cheryl Praeger’s “Using the Finite Simple Groups”, reprinted from the Australian Mathematical Society’s Gazette.

In view of recent natural calamities that have occurred in various parts of the world, we are publishing two articles which may be of relevance and interest. They are “Evolu-tion of Tsunami Science” by Pavel Tkalich, and “Fighting Asian Catastrophes with Mathematics” by Gordon Woo. We have also included an interview with Haibao Duan first published in Chinese but which has been translated into English.

Two articles on centres of mathematics are featured in this issue. The first consists of excerpts of an interview with Professor Louis Chen, the founding director of the Institute for Mathematical Sciences (IMS) of the National University of Singapore. The other centre featured is the SEAMEO Regional Centre for Mathematics Education in Yogyakarta, Indonesia. We also present a brief introduction to mathematical competitions in Shanghai and give readers a glimpse of how one of the best mathematics Olympiad teams is trained.

We plan to feature mathematics education in one Asia Pacific country in each issue of this newsletter. We would like to invite readers who are familiar with mathematics education in their respective countries to contribute articles.

Response to the Problems Corner is rather poor. We encourage readers to submit their solutions. Several book prizes have been prepared for solutions published.

We would again like to reiterate that this newsletter is primarily meant to serve the mathematics community in the Asia Pacific region. Your help and support are essential to the success and continuation of this publication. We appeal to our readers to participate more enthusiasti-cally by sending us suitable items which we can include in future issues of this newsletter. The following types of articles, news and information would be most welcome:

• 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 on relevant issues• Other items of interest to the mathematics community

We hope to receive a positive response from you soon. A successful newsletter needs interactive communication between readers, authors and editors. We hope you will join us in this venture.

Happy reading.

ErratumIn the article "Vietnamese Mathematician Ngô Bἀo Châu – From A Mathematical Olympiad Medallist to A Fields Medallist", the picture in page 26 is Ngô's answer script of a test (among many others) during the training camp held in Vietnam during 1988 in preparation for the IMO in Australia (image courtesy of Dr. Le Hai Khoi).

Jugendtraum of a MathematicianKyoji Saito

1

Jugendtraum of a MathematicianKyoji Saito

1. Kronecker’s Jugendtraum

There is a phrase “Kronecker’s Jugendtraum

(dream of youth)” in mathematics. Leopold Kro-

necker was a German mathematician who worked

in the latter half of the 19th century. He obtained

his degree at the University of Berlin in 1845

when he was 22 years old, and after that, he suc-

cessfully managed a bank and a farm left by his

deceased uncle. When he was around 30, he came

back to mathematics with the study of algebraic

equations because he could not give up his love

for mathematics. Kronecker’s Jugendtraum refers

to a series of conjectures in mathematics he had

in those days — maybe more vague dreams of

his, rather than conjectures — on subjects where

the theories of algebraic equations and of elliptic

functions intersect exquisitely. In the present note,

I will explain the dream itself and then how it is

connected with my dream of the present time.

2. Natural Numbers N, Integers Z and

Rational Numbers Q

Let us review systems of numbers for explaining

Kronecker’s dream. Some technical terms and

symbols used in mathematics will appear in the

sequel and I will give some comments on them,

but please skip them until Secs. 9 and 10 if you

do not understand them.

A number which appears when we count

things as one, two, three, . . . is called a natural

number. The collection of all natural numbers

is denoted by N. When we want to prove a

statement which holds for all natural numbers,

we use mathematical induction as we learn in

high school. It can be proved by using induction

that we can define addition and multiplication

for elements of N (that is, natural numbers) and

obtain again an element of N as a result. But

we cannot carry out subtraction in it. For ex-

ample, 2 − 3 is not a natural number anymore.

Subtraction is defined for the system of numbers

. . . ,−3,−2,−1, 0, 1, 2, 3, . . . . We call such a num-

ber an integer and denote by Z the collection of

integers. For Z, we have addition, subtraction, and

multiplication, but still cannot carry out division.

For example, −2/3 is not an integer. A number

which is expressed as a ratio p/q of two integers

(q � 0) is called a rational number (in particular an

integer is a rational number) and the collection of

them is denoted by Q. Rational numbers form a

system of numbers for which we have addition,

subtraction, multiplication, and division.1 Such a

system of numbers is called a field in mathematics.

We ask whether we can measure the universe

by rational numbers. The answer is “no” since

they still miss two type of numbers: (1) solutions

of algebraic equations, (2) limits of sequences.

In the following Secs. 3 and 4, we consider two

extensions Q and Q of Q, and in Sec 6, both

extensions are unified in the complex number

field C.

3. Algebraic Numbers Q

It was already noticed by ancient Greeks that

one cannot “measure the world” only by ra-

tional numbers. For example, the length of the

,×

,×,

,×, ,÷

=limn→∞

hypotenuse of a right-angled isosceles triangle

with the short edges of length 1 is denoted by√

2

(Fig. 1) and Greeks knew that it is not a rational

number. If we express√

2 by the symbol x, then

it satisfies the equation x2 − 2 = 0. In general, a

polynomial equality including an unknown num-

ber x such as a0xn+ a1xn−1

+ · · · + an−1x + an =

0 (a0 � 0, a1, . . . , an are known numbers called

coefficients) is called an algebraic equation. We

call a number x an algebraic number if it satis-

fies an algebraic equation with rational number

July 2011, Volume 1 No 3 1

Asia Pacific Mathematics Newsletter

2

＝＋

１１

１１

１

１

１

１２

２

２

Fig. 1. We consider a square whose diagonals have the length2. Then its area is equal to 2, since we can decompose andrearrange the square into two squares whose side lengths areequal to 1. Therefore, the side length of the original square isequal to

√2.

coefficients. The collection of algebraic numbers,

including rational numbers, is denoted by Q. It

is a field since it admits addition, subtraction,

multiplication, and division. Moreover we can

prove that solutions of algebraic equations whose

coefficients are algebraic numbers are again alge-

braic numbers. Referring to this property, we say

Q is algebraically closed. This Q is an extremely

exquisite, and charming system of numbers, but

we are far from complete understanding of it de-

spite the full power of modern mathematics. Is Q

sufficient to measure the world? Before answering

the question, let us consider another extension of

systems of numbers in the next section.

4. Real Numbers R

Analysis was started in modern Europe by New-

ton (1642–1723) and Leibniz (1646–1716) and fol-

lowed by Bernoulli and Euler. It introduced the

concept of approximations of unknown numbers

or functions by sequences of known numbers or

functions.2 At nearly the same time in modern

Japanese mathematics (called Wasan), started by

Seki Takakazu (1642(?)–1708) and developed by

his student Takebe Katahiro (1664–1739), approx-

imations of certain inverse trigonometric func-

tions by a power series and that of π by series

by rational numbers were also studied. Takebe

wrote “I am not so pure as Seki, so could not

capture objects at once algebraically. Instead, I

have done long complicated calculations.” We see

that Takebe moved beyond the algebraic world,

an area of expertise of his master Seki, and un-

derstood numbers and functions which one can

reach only by analysis (or series). Nowadays, a

number which “can be approximated as precisely

as required by rational numbers” is called a real

number and the whole of them is denoted by R.3

A number which has an infinite decimal repre-

sentation (e.g. π = 3.141592 . . .) is a real number

and the inverse is also true. Thus, numbers, which

we learn in school, are real numbers. Japanese

mathematicians of the time had high ability to

calculate such approximations by using abacuses,

and competed with each other in their skills.

However I do not know to what extent they

were conscious about the logical contradiction

that one cannot reach real numbers in general

without infinite approximations, while the size

of an abacus is finite (even nowadays, we meet

the same problem, when we handle real numbers

by computer). In Japan, we missed the tradi-

tion of Euclid. Some people, old Archimedes in

Greek, Cauchy in France, Dedekind in German

and his contemporary Cantor, tried to clarify the

meaning of “can be approximated as precisely as

required” and now the system of real numbers

R is usually described according to their work.

However, because of an embarrassing problem

found by Cantor,4 understanding of R involves

another kind of hard problem than that of Q.

5. Algebraic Numbers Versus Real

Numbers

Incidentally, I think many mathematicians con-

cern either the understanding of R or that of Q

and have their opinions. Some years ago, I talked

with Deligne, a great mathematician in this age,

at a conference about the completeness of real

numbers. I was deeply impressed, when I heard

him regretfully saying “Real numbers are difficult.

We are far from understanding them”. Actually, Q

has a clue called the absolute Galois group, which

aids our understanding of it,5 while R consists of

all convergent series, which offers little clue for

capturing its elements (in spite deep theory of

approximations of irrational numbers by rational

numbers).

6. Marvelous Complex Numbers C

A complex number z is a number expressed as

z = a + bi, using two real numbers a and b

where the symbol i (called the imaginary unit)

satisfies the relation i2 = −1. The whole R + Ri

of all complex numbers, denoted by C and called

complex number field, carries the both properties:

(i) algebraically closedness like Q, that is, any

non-trivial algebraic equation with coefficients in

July 2011, Volume 1 No 32


3

complex numbers always has a solution in com-

plex numbers (Gauss), and (ii) closedness under

taking limits where distance between two com-

plex numbers z1, z2 is measured by the absolute

value |z1 − z2|. Furthermore, every proof of (i)

essentially uses a property, called the conformality

of the product of complex numbers, where a

germ of complex analytic functions can be found.

Euler, who worked in 18th century, using complex

numbers, showed already that the trigonometric

functions and the exponential function, which

were studied separately before, are combined by

the beautiful relation eiz= cos(z) + i sin(z) (in

particular eπi = −1). Thus, the works of Gauss

and Euler, titans in mathematics, established the

role of complex numbers in mathematics. Then,

there appeared several theories in physics, like

electromagnetic theory, which are described by

an essential use of complex number field. Even

though what we observe are real numbers, quan-

tum mechanics cannot be described without the

use of complex number field. We have no choice

of words but mysterious for the usefulness of

complex numbers to describe laws of physics and

the universe. A complex number which does not

belong to Q is called a transcendental number. It

was proved by Lindemann in 1882 that π is a tran-

scendental number, using Euler’s identity eπi = −1

and the theory of approximations of the analytic

function exp(z) = ez by rational functions, which I

will explain in Sec. 7. Returning to a question at

the end of Sec. 3, we observe now that algebraic

numbers Q alone are not sufficient to measure

the world. However, the complex number field C,

likewise R, carries Cantor’s problem stated in [4],

and the question whether all complex numbers

are necessary or only a very thin part of it is

sufficient remains unanswered.

7. Rational Functions and Analytic

Functions

So far I have described systems of numbers. It is

not just to give an overview of the history, but be-

cause Q and R themselves carry profound actual

problems yet to be understood. Another reason is

that the development of the concepts of numbers

repeatedly became models of new mathematics.

For example, let us consider the collection of poly-

nomials in one variable z, denoted by C[z]. Similar

to Z, it admits addition, subtraction and multipli-

cation between its elements but not division. As

we constructed rational numbers from integers,

we consider a function which is expressed as a

fraction P(z)/Q(z) of two polynomials, called a ra-

tional function, and the whole of them, denoted by

C(z). Then similarly to constructing a real number

from Q, we consider a function which is a limit

of a sequence of rational functions (in a suitable

sense) and call it an analytic function. Let us denote

the collection of such analytic functions by C(z),

mimicking the notation in [3]. I think the study of

C(z) is easier than that of R = Q and expect that

the understanding of C(z) helps that of R = Q

as well as of C. The reason is that an element

of R (an element of C) is a limit of sequences of

(Gaussian) rational numbers that provides little

clue for capturing it, while for an element of C(z)

we have a clue, the variable z. For instance, we

have some freedom to substitute a favorable value

in the variable z as needed. Therefore, we contrast

Q with C(z) instead of contrasting Q with R = Q

as in Sec. 5.

8. Transcendental Functions and Period

Integrals

An element of C(z) which is not either a rational

function or an algebraic function (in a suitable

sense) is called a transcendental function. The

gamma function Γ(z) and zeta function ζ(z) are ex-

amples of them. However, in what follows let us

discuss about transcendental functions belonging

to different category, namely their Fourier duals.

The exponential function exp(z) and the

trigonometric functions, we have already seen,

are, from a certain viewpoint, the first elementary

transcendental functions appearing after rational

functions. Let us briefly explain the reason. We

learn in high school that the length of an arc

of the unit circle can be obtained as the integral

z =

∫ x

1

|dx|√

1 − x2(Fig. 2). For the correspondence

(or map) x �→ z defined by the integral, its inverse

map z �→ x is the trigonometric function x = cos(z).

In other words, the trigonometric functions are

obtained as the inverse functions of the arc in-

tegrals over a circle (a quadratic curve). As we

learn in high school, they are periodic functions

with period 2π and satisfy the addition formulas

(in particular, we can obtain the coordinates of

the points that divide the arc equally into q parts

for a natural number q, by solving an algebraic



4

P

Fig. 2. We consider a point P on the circle of radius 1 in thex-y plane. Then the length (angle) of the arc 1P is given by the

integral z =

∫ P

1

√dx2 + dy2 =

∫ x

1

|dx|√

1 − x2. Then the inverse

of the function x �→ z, we obtain the trigonometric functionx = cos(z).

a-a x

yr

P

P

Fig. 3. For a positive number a, the lemniscate curve is char-acterized as the loci of point P where the product of distancesfrom two points ±a on the x-axis is the constant equal to a2,and is given by the equation (x2

+ y2)2= 2a2(x2 − y2). The

length z of the arc P0P on the lemniscate is given by the integral

z =

∫ P

P0

dr√

1 − r4where r =

√x2 + y2. Then, as the inverse of the

function x �→ z, we obtain an elliptic function r = ϕ(z) of periodZ + Zi.

equation of degree ≤ q). Then, arc integrals for

curves of higher degrees and their inverse func-

tions are natural subject of study. The theory of

elliptic functions and abelian functions was born

in that way.6 The length of arcs in a lemniscate

curve (see Fig. 3) is given by

∫dr√

1 − r4. This was

the first studied elliptic integral, 100 years before

Gauss, when an Italian, Fargano, found a formula

for the duplication of arc length of the lemniscate,

and later Euler did the addition formulas (Jacobi

approved it for the start of the theory of elliptic

functions). The inverse function of the lemniscate

integral is, from a modern viewpoint, an elliptic

function having Gaussian integers Z + Zi as its

periods.

9. Kronecker’s Theorem = The First

Contact Point Between Algebraic

Numbers and Transcendental

Functions?

Nowadays the following two statements are

known as Kronecker’s theorems (we refer readers

to the textbooks in [5] and [6] for terminology).

1. Any abelian extension field of the rational

number field is obtained by adjoining values

that are substitutions of rational numbers

p/q to the variable z of the exponential func-

tion exp(2πiz) (for short, the coordinates of

the points of the circle S1= {z ∈ C | |z| = 1}

that divide it equally into q parts, see Fig. 1)

to the field of rational numbers.

2. Any abelian extension of the Gaussian inte-

gers Z + Zi is obtained by adjoining the coor-

dinate values of the points of the lemniscate

that divide it equally, where the values are

expressed by special values of the elliptic

functions associated with the lemniscate.

Kronecker’s theorems (whose proofs he did not

leave behind) involve both number theory and

transcendental functions related to algebraic ge-

ometry. He devoted his later years of life to

a proof of the advanced proposition that any

abelian extension field of an imaginary quadratic

field is obtained by adjoining solutions of the

transformation equations for elliptic curves with

complex multiplication. He called it “the dearest

dream of my youth (mein liebster Jugend Traum)”

in a letter to Dedekind, a German contemporary

mathematician, when he was 58 years old.

It is said that Kronecker had many likes and

dislikes; “God made the integers, all else is the

work of man (Die ganzen Zahlen hat der liebe

Gott gemacht, alles andere ist Menschenwerk)”

is his saying. According to books of the history,

he thoroughly attacked the set theory of Cantor,

a contemporary German mathematician; Cantor

was distressed with this and entered a mental hos-

pital. Though Kronecker’s mathematics that treats

the exquisite structure of numbers, and Cantor’s

that was reached by thorough abstraction of those

structures4 are quite in contrast, I am attracted

by both of their thoroughness, and the unhappy

relation between them perplexes me. One may

think Kronecker is on the side of Q, but I think

this is a one sided opinion. His results or dreams

turn out to tell about some delicate points where



5

Q and C(z) contact. Kronecker’s Jugendtraum was

later solved by Takagi Teiji in Japan and others,

with the building of class field theory.

10. New Dream

Following Kronecker, let me write about a dream

of my own. Roughly speaking, Kronecker found

that the first step (i.e. abelian extension of Q) of

extending the rational number field Q to its alge-

braic closure Q corresponds to another first step

(i.e. exponential function) of extending the field

of rational functions C(z) to the field of analytic

functions C(z) in such a manner that the algebraic

extension is recovered by adjoining special val-

ues of the transcendental function. Let us expect,

though we have no evidence so far, that similar

correspondences between algebraic numbers and

transcendental functions exist further, and that

it causes certain “hierarchies” among the cor-

responding transcendental functions.7 Then the

problem is what transcendental functions should

appear.

My Jugendtraum is to construct (some candi-

dates for) such transcendental functions by pe-

riod integrals and their inverse functions, just

like that the classical circle integrals and elliptic

integrals gave birth to exponential and elliptic

functions. To do it, I proposed the theory of

primitive forms and their period integrals as a

higher-dimensional generalization of the theory

of elliptic integrals. More precisely, we have in-

troduced (a) semi-infinite Hodge theory (or non-

commutative Hodge theory) in order to define

the primitive form associated with a Landau–

Ginzburg potential, (b) torsion free integrable log-

arithmic free connections to describe the period

map, (c) the flat structure (or Frobenius structure)

on the space of automorphic forms given as the

components of the inverse maps of period inte-

grals, (d) several infinite-dimensional Lie algebras

(such as elliptic Lie algebras, cuspidal Lie alge-

bras, . . . ) in order to capture primitive forms in

(infinite) integrable systems which are associated

with a generalized root system and with a regular

weight system, and (e) derived categories for giv-

ing a categorical Ringel–Hall construction of those

Lie algebras (every one of them is unfinished). It

is mysterious that some pieces of these structures

I have considered from purely mathematical mo-

tivations have come to be observed in topological

string theory in recent physics. I sincerely wish

these attempts for understanding of the system of

numbers C should also lead to the understanding

of the physics of the universe.

Remarks

[1] To be precise, we do not allow division by 0.

[2] Let us explain a bit more precisely. The collection

of rational numbers is equipped with an ordering.

Then, for two numbers x and y, we define the

distance between them by |x − y| = max{x − y, y − x}and regard them being closer to each other when

the distance between them becomes smaller. We say

that a sequence y1, y2, y3, . . . approximates a number

x if |x − yn| (n = 1, 2, 3, . . . ) becomes smaller and

closer to 0. We say that an infinite sum (called a

series) y1 + y2 + y3 + · · · converges to x and write x =

y1+y2+y3+· · · , if the sequence y1, y1+y2, y1+y2+y3, . . .

approximates x. E.g. π2/6 = 1 + 1/22+ 1/32

+ · · · .[3] One may denote R by Q in the sense that it is an

analytic closure of Q. However Q is also equipped

with another distance than that in [2] called p-adic

non-Archimedean distance for each prime number

p, and we need to distinguish Q from the closure

Qp with respect to the p-adic distance.

[4] Cantor found that, forgetting the structures on

the sets N,Z,Q,Q, one can construct a one-to-one

map between any two of them, while the set R is

properly larger than them. This left the problem

whether an intermediate size between N and R ex-

ists. Although Cantor himself proposed the contin-

uum hypothesis that asserts no intermediate exist,

now it is known that the continuum hypothesis is

independent of the axioms of set theory. Namely

we do not know whether there exists a subset of

R which is properly smaller than R and properly

larger than N or not.

[5] Q is a union of subfields Q(ξ), called number fields

obtained by adjoining finitely many algebraic num-

bers ξ to Q. The projective limit: lim Gal(Q(ξ)/Q) of

Galois groups corresponding to Galois fields Q(ξ)

(where ξ is closed under conjugation) is called the

absolute Galois group. It is equipped with the in-

clusion relation among subgroups (hierarchy struc-

ture) corresponding to extensions of number fields.

Reference: Emil Artin, Algebra with Galois Theory,

American Mathematical Society, Courant Institute

of Mathematical Sciences.

[6] We refer the reader to one best text on elliptic func-

tions and period integrals from analytic viewpoint

by C. L. Siegel: Topics in Complex Function Theory,

Volume 1, Wiley-Interscience Publication.

[7] Hilbert has suggested certain automorphic forms

as such transcendental functions for real quadratic

fields. However, the author does not know whether

it is reasonable to expect further such correspon-

dences. If there exist such correspondences, such



6

transcendental functions form quite a thin (ℵ0) sub-

set of the field of all transcendental functions. Those

functions should be, in spite of their transcendency,

special functions which are controlled by an algo-

rithm in a suitable sense. We can imagine many

things, Moonshine for instance. What happens on

the side of transcendental functions correspond-

ing to algebraic extensions with non-abelian sim-

ple groups as their Galois groups. But I do not

think we have examples to assert mathematical

propositions. Can we “resolve” Cantor’s problem

(see [4]) considering only such a thin set of special

transcendental functions and their special values?

For the description of mathematics and physics of

the universe, is such a thin set of transcendental

functions sufficient?

This article was originally published in “Feature” of the

IPMU News, Vol. 09, the issue of the Institute for the

Physics and Mathematics of the Universe (IPMU) in Japan.

Kyoji Saito

Principal Investigator,

Institute for the Physics and Mathematics

of the Universe (IPMU), Japan

http://www.ipmu.jp

Kyoji SaitoPrincipal Investigator,Institute for the Physics and Mathematicsof the Universe (IPMU), Japan

http://www.ipmu.jp



Using the Finite Simple GroupsCheryl E. Praeger

1

Using the Finite Simple GroupsCheryl E. Praeger

Abstract. Ramifications of the finite simple group clas-sification, one of the greatest triumphs of twentiethcentury mathematics, continue to drive cutting-edgedevelopments across many areas of mathematics. Sev-eral key applications of the classification are discussed.

The finite simple group classification, announced

by Daniel Gorenstein in February 1981, was one

of the greatest triumphs of late twentieth cen-

tury mathematics, and to this day its ramifi-

cations continue to drive cutting-edge develop-

ments across many areas of mathematics. The

list of finite simple groups is surprisingly short:

for each prime p, the cyclic group Cp of order

p is simple; for each integer n at least 5, the

group of all even permutations of a set of size n

forms the simple alternating group An; there are

finitely many additional infinite families of simple

groups called finite simple groups of Lie type; and

there are precisely 26 further examples, called the

sporadic simple groups of which the largest is the

Monster.a

Already in 1981, some consequences of the

classification were “waiting expectantly in the

wings”. For example, we immediately could list

all the finite groups of permutations under which

all point-pairs were equivalent (the 2-transitive

permutation groups) [3].

1. Simple Groups and Algebraic Graph

Theory

For other problems it was unclear for a number

of years whether the simple group classification

could be applied successfully in their solution.

One of the most famous of these was a 1965 con-

jecture of Charles Sims at the interface between

permutation group theory and graph theory. It

was a question about finite primitive permutation

groups. The primitive groups form the building

blocks for permutation groups in a somewhat

similar way to the role of the finite simple groups

as building blocks (composition factors) for finite

groups. Sims conjectured that there is a function

aContaining 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements!

f on the positive integers such that, for a finite

primitive permutation group in which a point

stabiliser H has an orbit of size d, the cardinality

of H is at most f (d). In graph theoretic language:

for a vertex-primitive graph or directed graph

of valency d (each vertex is joined to d other

vertices), there are at most f (d) automorphisms

(edge-preserving permutations) fixing any given

vertex. Proof of the Sims Conjecture [5] in 1983

required detailed information about the subgroup

structure of the Lie type simple groups, and was

one of the first nontrivial applications of the finite

simple group classification in Algebraic Graph

Theory, see [6, Section 4.8C]. The new approach

in [5] was later developed into a standard frame-

work for applying the simple group classification

to many problems about primitive permutation

groups and vertex-primitive graphs.

Stunning new applications of the simple group

classification in Algebraic Graph Theory continue

to appear, and many new applications are accom-

panied by deep new results on the structure and

properties of the simple groups. The most recent

exciting developments relate to expander graphs.

These are graphs or networks which are simulta-

neously sparse and highly connected. They have

important applications for design and analysis of

robust communication networks, for the theory

of error-correcting codes, the theory of pseudo-

randomness, and many other uses, beautifully

surveyed in [11]. A family of finite graphs, all

of the same valency but containing graphs of

arbitrarily large size, is an expander family if there

is a constant c such that the ratio |∂A|/|A| is at

least c for every subset A of vertices of any of

the graphs Γ in the family, where A contains

at most half of the vertices of Γ and ∂A is the

set of vertices of Γ at distance 1 from A. The

new results confirm that many families of Cayley

graphs for simple Lie type groups of bounded

rank are expander families. This flurry of activity

began with a spectacular breakthrough by Helf-

gott [9] in 2008 for the 2-dimensional projective

groups PSL(2, p) over fields of prime order p. The



2

strongest current results for bounded rank Lie

type groups are consequences of new results for

“growth in groups” by Pyber and Szabo [19], and

independently by Breuillard, Green and Tao [2]

for the finite Chevalley groups.

2. Simple Groups, Primes and

Permutations

Several results about permutation groups have

“simple” statements making no mention of sim-

ple groups, but their only known proofs rely on

the simple group classification, often on simple

group theory developed long after the classifica-

tion was announced. In fact many recent results in

this area demand a deep and subtle understand-

ing of the finite simple groups, especially their

subgroup structure, element statistics, and their

representations.

A surprising link between the number of

primes and the finite simple groups was discov-

ered soon after the announcement of the simple

group classification. It is a result due to Cameron,

Neumann and Teague [4] in 1982. Each positive

integer n ≥ 5 occurs as the index of a maximal

subgroup of a simple group, namely the simple

alternating group An has a maximal subgroup

An−1 of index |An|/|An−1| = n. Let us call n a

maximal index if n = |G|/|H| for some nonabelian

simple group G and maximal subgroup H with

(G, H) � (An, An−1). It was proved in [4] that

max (x)/π(x)→ 1 as x→ ∞,

where max (x) is the number of maximal indices at

most x and π(x) is the number of primes at most x.

The limiting density of the set of maximal indices

is “explained” by the fact that, for each prime

p, the projective group PSL(2, p) acts primitively

on the projective line PG(1, p) of size p + 1, and

so has a maximal subgroup of index p + 1. The

major motivation that led to this result was its

consequence for primitive permutation groups,

also proved in [4]: the number Dprim(x) of integers

n for which there exists a primitive permutation

group on n points (that is, of degree n), other than

Sn and An, satisfies Dprim(x)/π(x) → 2 as x → ∞.

Beside the primitive actions of PSL(2, p) of degree

p+1, the cyclic group Cp acts primitively of degree

p, thus accounting for the limiting density ratio 2.

Two decades later I extended this result with

Heath-Brown and Shalev in [8] as part of our in-

vestigation of quasiprimitive permutation groups,

a strictly larger family of permutation groups than

the primitive groups and important in combinato-

rial applications.b The crucial quantity we needed,

in order to determine the behaviour of the degrees

of quasiprimitive permutation groups, turned out

to be the number sim(x) of simple indices at most

x, where by a simple index we mean an index

|G|/|H| of an arbitrary subgroup H of a non-abelian

simple group G such that (G, H) � (An, An−1). We

proved that sim(x)/π(x) also approaches a limit

as x → ∞, and we proved that this limit is the

number

h =∞∑

n=1

1

nφ(2n)= 1.763085 . . .

where φ(m) is the Euler phi-function, the number

of positive integers at most m and coprime to

m. The analogous consequence (which had been

our principal motivation for studying sim(x)) was

that the ratio Dqprim(x)/π(x) of the number Dqprim(x)

of degrees n ≤ x of quasiprimitive permutation

groups, apart from Sn and An, to π(x) approaches

h+ 1 as x→ ∞. In this case also, these ratios were

accounted for by various subgroups of the simple

groups PSL(2, p).

My “all-time favourite” example of a deep re-

sult with a deceptively uncomplicated statement

is due to Isaacs, Kantor and Spaltenstein [12] in

1995: let G be any group of permutations of a set

of size n and let p be any prime dividing the

order |G| of G (that is, the cardinality of G). Then

there is at least 1 chance in n that a uniformly

distributed random element of G has a cycle of

length a multiple of p. The hypotheses of this

result are completely general giving no hint that

the assertion has anything at all to do with simple

groups. However the only known proof of this

result relies on the finite simple group classifi-

cation, and in particular uses subtle information

about maximal tori and Weyl groups of simple

Lie type groups. These techniques were the same

as those introduced earlier in 1992 by Lehrer [13]

to study the representations of finite Lie type

groups. I recently worked with Alice Niemeyer

and others to understand the precise conditions

needed for this approach to be effective. We de-

veloped an estimation method in [16] and used

it to underpin several Monte Carlo algorithms

bA permutation group is quasiprimitive if each of its nontrivialnormal subgroups is transitive. Each primitive permutationgroup has this property, and so do many other permutationgroups.



3

for computing with Lie type simple groups (in

[14, 15]). It produces sharper estimates for the

proportions of various kinds of elements of Lie

type simple groups than alternative geometric

approaches.

3. Simple Groups and Involutions

One of the first hints that understanding the

finite simple groups might be a tractable problem

was the seminal “Odd order paper” of Feit and

Thompson [7] in 1963 in which they proved that

every finite group of odd order is soluble, or

equivalently, that every non-abelian finite simple

group contains a non-identity element x such that

x2= 1. Such an element is called an involution,

and the Feit–Thompson result, that each non-

abelian finite simple group contains involutions,

had been conjectured more than 50 years ear-

lier by Burnside in 1911. The centraliser of an

involution x consists of all the group elements

g that centralise x in the sense that xg = gx.

The involution centralisers in finite simple groups

are subgroups that often involve smaller simple

groups. Several crucial steps in the simple group

classification involved systematic analyses of the

possible involution centralisers in simple groups,

resulting in a series of long, deep and difficult pa-

pers characterising the simple groups containing

various kinds of involution centralisers.

Some important information about the simple

groups can be found computationally, and key for

this are efficient methods for constructing their

involution centralisers. To construct an involution,

one typically finds by random selection an ele-

ment of even order that powers up to an invo-

lution, then uses Bray’s ingenious algorithm [1]

to construct its centraliser. This worked extremely

well in practice for computing with the sporadic

simple groups. A more general development of

Bray’s method into proven Monte Carlo algo-

rithms for Lie type simple groups over fields of

odd order required delicate estimates of various

element proportions in simple groups — first

given in a seminal paper of Parker and Wil-

son [17] (available as a preprint for several years

before its publication), and then in full detail in

[10]. The estimates and complexity analysis give

a lower bound on the algorithm performance,

but do not match the actual (excellent) practical

performance. A major program is in train to find

a realistic analysis and the first parts have been

completed [14, 18].

The classification of the finite simple groups

was a water shed for research in algebra, combi-

natorics, and many other areas of mathematics. It

changed almost completely the problems studied

and the methods used. To realise further the

power of the classification for future applications,

new detailed information is needed about the

simple groups — and this will be gained both

as new theory and through new computational

advances.

Acknowledgement

The author acknowledges support of Aus-

tralian Research Council Federation Fellowship

FF0776186.

References

[1] J. N. Bray, An improved method for generating thecentralizer of an involution, Arch. Math. (Basel) 74(2000) 241–245.

[2] E. Breuillard, B. Green and T. Tao, Approximatesubgroups of linear groups, Geometric and Func-tional Analysis (to appear), arXiv:1005.1881v1.

[3] P. J. Cameron, Finite permutation groups and finitesimple groups, Bull. London Math. Soc. 13 (1981)1–22.

[4] P. J. Cameron, P. M. Neumann and D. N. Teague,On the degrees of primitive permutation groups,Math. Zeit. 180 (1982) 141–149.

[5] P. J. Cameron, C. E. Praeger, G. M. Seitz and J. Saxl,On the Sims’ conjecture and distance transitivegraphs, Bull. Lond. Math. Soc. 15 (1983) 499–506.

[6] J. D. Dixon and B. Mortimer, Permutation Groups(Springer, 1996).

[7] W. Feit and J. G. Thompson, Solvability of groupsof odd order, Pacific J. Math. 13 (1963) 775–1029.

[8] D. R. Heath-Brown, C. E. Praeger and A. Shalev,Permutation groups, simple groups and sievemethods, Israel J. Math. 148 (2005) 347–375.

[9] H. A. Helfgott, Growth and generation inSL2(Z/pZ), Annals of Math. 167 (2008) 601–623.

[10] P. E. Holmes, S. A. Linton, E. A. O’Brien, A. J. E.Ryba and R. A. Wilson, Constructive membershipin black-box groups, J. Group Theory 11 (2008)747–763.

[11] S. Hoory, N. Linial and A. Widgerson, Expandergraphs and their applications, Bull. Amer. Math.Soc. 43 (2006) 439–561.

[12] I. M. Isaacs, W. M. Kantor and N. Spaltenstein, Onthe probability that a group element is p-singular,J. Algebra 176 (1995) 139–181.

[13] G. I. Lehrer, Rational tori, semisimple orbits andthe topology of hyperplane complements, Com-ment. Math. Helv. 67 (1992) 226–251.

[14] F. Lubeck, A. C. Niemeyer and C. E. Praeger,Finding involutions in finite Lie type groups ofodd characteristic, J. Algebra 321 (2009) 3397–3417.



Cheryl PraegerUniversity of Western [email protected]

Cheryl Praeger is Winthrop Professor of Mathematics at the University of Western Australia. In 2007 she became the first pure mathematician to be awarded an Australian Research Council Federation Fellowship. For her achievements and service to mathematics, she was elected a Fellow of the Australian Academy of Science, and appointed a Member of the Order of Australia (AM). She was President of the Australian Mathematical Society from 1992 to 1994, and is currently on the Executive Committee of the International Mathematical Union.

4

[15] A. C. Niemeyer, T. Popiel and C. E. Praeger, Find-ing involutions with eigenspaces of given dimen-sions in finite classical groups, J. Algebra 324 (2010)1016–1043.

[16] A. C. Niemeyer and C. E Praeger, Estimatingproportions of elements in finite simple groups ofLie type, J. Algebra 324 (2010) 122–145.

[17] C. W. Parker and R. A. Wilson, Recognising sim-plicity of black-box groups by constructing invo-lutions and their centralisers, J. Algebra 324 (2010)885–915.

[18] C. E. Praeger and A. Seress, Probabilistic genera-tion of finite classical groups in odd characteris-tic by involutions, J. Group Theory, in press. doi:10.1515/JGT.2010.061

[19] L. Pyber and E. Szabo, Growth in finitesimple groups of Lie type, preprint (2010).arXiv:1005.1858v1.

Reproduced from Gazette of Australian Mathematical Soci-

ety, Vol. 38, No. 2, May 2011.

Reproduced from Gazette of Australian Mathematical Society, Vol. 38, No. 2, May 2011



Evolution of Tsunami Science

Pavel Tkalich

1. Introduction

Although tsunamis have been leaving tragic traces in

human history from ancient times, all earlier tsunami

descriptions were based on anecdotal evidence of a few

survivors, embedded in myths, folklore, and art. Thus, the

classical Plato description of death of legendary Atlantis

nowadays looks like a typical sequence of geological

events triggered by a destructive earthquake and followed

by a giant tsunami. More recent artwork by Hokusai

(1760–1849) keeps inspiring tsunami scientists and wave

professionals by the beauty and realism of depicted

breaking waves.

In modern history, the Japan Meteorological Agency

(JMA) initiated tsunami warning services in 1952, and

NOAA’s Pacific Tsunami Warning Centre (PTWC,

Honolulu) was established in 1948 following the deadly

1946 Aleutian Island earthquake and tsunami. Until

about 1980, semi-empirical charts (connecting tsunami

threats to seismic sources) were the only quick

forecasting tools available.

During the 80’s and 90’s, due to pioneering work of

F. Imamura, N. Shuto, C. E. Synolakis and many others,

fast computers and efficient models have been employed

for tsunami modelling. In the early stages of the

computing era, it was not possible to solve the two-

dimensional Boussinesq equations with nonlinear and

dispersion terms; instead, simplified alternatives became

popular. In 1999, JMA has introduced the computer

aided simulation system for quantitative tsunami

forecasting, in which tsunami arrival times and heights

are simulated and stored in the database for forecasting

Fig. 1. “ Behind the Great Wave at Kanagawa” by Katsushika

Hokusai (1760– 1849).

tsunamis. The JMA has been further updating the system

and now can issue the forecast 2 to 3 minutes after

occurrence of an earthquake. Still, the 2011 Tōhoku

earthquake and tsunami, which claimed 20,000 lives in

Japan, wiped out several nearshore cities, and critically

damaged Fukushima Nuclear Power Plant. The overall

cost could exceed US$300 billion, making it the most

expensive natural disaster on record.

Due to the half-century efforts by PTWC and JMA,

most of the tsunami modelling and forecasting

capabilities were focused on the Pacific Ocean; in other

regions, tsunami science and awareness were not

developed. Not surprisingly, the 2004 Indian Ocean

Tsunami caught off guard the coastal communities along

the Indian Ocean shores, killing almost 230,000 people.

The recent tragic events drew attention to the lack

of tsunami-warning infrastructure, and triggered a

worldwide movement to develop tsunami modelling and

forecasting capabilities. The number of scientists and

students migrating from different areas into the tsunami

field has increased significantly, resulting in a re-

examination of established approaches and perceptions,

and in the development of novel ideas and methods.

In Singapore, a similar movement has led to the

development of national earthquake and tsunami

predictive capabilities, and of a tsunami-warning system.

This publication highlights some of the most important

historical milestones that have led to our modern

understanding of tsunami behaviour.

2. Soliton Theory

2.1. The first scientific encounter of solitons

One may start the description of tsunami behaviour using

soliton theory, which is a simplified substitute for a full-

scale tsunami model. In mathematics and physics, a

soliton is a self-reinforcing solitary wave (a wave packet

or pulse) that maintains its shape while it travels at

constant speed. The soliton phenomenon was first

described by John Scott Russell [12, 13] (Fig. 2), the

British hydraulic engineer Scott Russell who observed a

solitary wave in the Union Canal, Edinburgh (UK).

He reproduced the phenomenon in a wave tank

(Fig. 3) and named it the “Wave of Translation” [13]. The

discovery is described here in his own words:

Evolution of Tsunami SciencePavel Tkalich



Fig. 2. John Scott Russell (1808– 1882).

“I was observing the motion of a boat which was rapidly

drawn along a narrow channel by a pair of horses, when

the boat suddenly stopped—not so the mass of water in the

channel which it had put in motion; it accumulated round

the prow of the vessel in a state of violent agitation, then

suddenly leaving it behind, rolled forward with great

velocity, assuming the form of a large solitary elevation, a

rounded, smooth and well-defined heap of water, which

continued its course along the channel apparently without

change of form or diminution of speed. I followed it on

horseback, and overtook it still rolling on at a rate of some

eight or nine miles an hour [14 km/h], preserving its

original figure some thirty feet [9 m] long and a foot to a

foot and a half [300−450 mm] in height. Its height

gradually diminished, and after a chase of one or two miles

[2–3 km] I lost it in the windings of the channel.

Such, in the month of August 1834, was my first chance

interview with that singular and beautiful phenomenon

which I have called the Wave of Translation.”

Following this discovery, Scott Russell built a 9 m

wave tank in his back garden and made observations of

the properties of solitary waves, with the following

conclusions [12]:

• Solitary waves have the shape −2 sech ( ( ))a k x ct ,

where a is the wave height, k is the wave number, and

c is the wave speed;

• A sufficiently large initial mass of water produces two

or more independent solitary waves;

• Solitary waves can pass through each other without

change of any kind;

• A wave of height a and travelling in a channel of

depth h has a velocity given by the expression

= +( )c g a h , where g is the acceleration of gravity,

implying that a large amplitude solitary wave travels

faster than one of low amplitude.

Throughout his life Russell remained convinced

that his “Wave of Translation” was of fundamental

importance, but 19th and early 20th century scientists

thought otherwise, partly because his observations could

Fig. 3. Russell’ s (1844) wave tank to study solitons.

not be explained by the then-existing theories of water

waves. Subsequently, the observations were reinforced by

theoretical work of the French mathematician and

physicist J. Boussinesq [3].

2.2. Behaviour of solitons

Soliton propagation could be understood by means of a

simple convective wave equation

η η+ = 0t xc (1)

where the wave speed η= ( , , )c c x t is a function of

surface elevation η , space x, and time t.

If c = const, this equation has travelling wave solutions,

and all waves propagate at the same speed c. Particular

interest for the subsequent examples attaches to the initial

condition illustrated in [4] at t = 0

2( ,0) sech ( )x xη = , (2)

for which the exact solution of Eq. (1) at time t for

c = const is

2( , ) sech ( )x t x ctη = − . (3)

Here −= = +sech( ) 1/ cosh( ) 2 / ( )x xx x e e .

If the wave speed is dependent on the wave elevation,

η= ( )c c , initial wave profiles are generally not self-

preserving. The simplest example is given by η=c ,

which being substituted into the linear, non-dispersive

wave Eq. (1) yields

η ηη+ = 0t x . (4)

This equation governs a nonlinear wave propagation.

Using the initial wave profile Eq. (2), solutions for η( , )x t

describe waves such that the profile eventually becomes

multi-valued and gradient blowup occurs (Fig. 4a).

Dispersion behaviour of the waves is described with a

dispersive wave equation

η η+ = 0t xxx . (5)



This equation has travelling wave solutions

η∞

−∞= +∫ 3( , ) ( )exp( )x t a k ik t ikx dk

where a(k) is the component amplitude of the Fourier

transform of the initial profile. If the initial wave profile is

again in the form of Eq. (2), one can observe that a single

propagating wave splits (disperses) from the tail and

resulting in oscillatory waves of different frequency that

continue to propagate at different speed as in Fig. 4b. This

behaviour is explicitly embedded in the dispersive wave

solution depicting shorter harmonics (with larger k)

propagating left relative the peak of the wave. Hence,

the solutions η( , )x t do not describe localised travelling

waves of constant shape and speed.

Wave propagation exhibits both nonlinear and

dispersive behaviour if described with the Korteweg–de

Vries (KdV) equation:

η ηη η+ + = 0t x xxx . (6)

The equation is named after Korteweg and de Vries

[9], though the equation was in fact first derived by

Boussinesq [3]. This equation has localised travelling

wave solutions (solitary waves) in the form of

( )2( , ) 3 sech ( ) / 2x t c x ctη = − . (7)

It was then understood that balancing dispersion

against nonlinearity leads to travelling wave solutions

(Fig. 4c) as earlier observed by Scott Russell, and this is

precisely the physical feature of solitons.

For a tsunami propagating in the ocean, dispersion

and nonlinearity are not necessarily in equilibrium. In

somewhat simplistic terms, if nonlinearity dominates

(usually nearshore) the incident soliton tends to break

from the front side; whereas in deepwater conditions

dispersion results in the soliton shedding waves from the

tail. A tsunami can propagate across the ocean as a series

of several solitons probably originating from a single

wave at source.

Fig. 4. Nonlinear and dispersive soliton behaviour: (a) nonlinear

term only; (b) dispersion term only; (c) nonlinear and dispersion

terms balanced together.

3. Boussinesq-type Equations

To draw a more complete and accurate picture of

tsunami behaviour in the ocean, one can use the

nonlinear water-wave model involving Laplace’s equation

combined with boundary conditions, nonlinear at the

free-surface and linear at the sea bottom [5], which can be

rewritten in dimensionless form as

δ ϕ ϕ ϕ+ + =( ) 0xx yy zz in fluid (8)

ε εϕ ϕ ϕ ϕ η

δ+ + + + =2 2 2( ) 0

2 2t x y z at εη=z (9)

δ η ε ϕ η ϕ η ϕ+ + − =[ ( )] 0t x x y y z at εη=z (10)

ϕ = 0z at 1z = − . (11)

Here ϕ is the velocity potential, giving fluid velocity

components ϕ∂=∂

ux

, ϕ∂=∂

vy

, ϕ∂=∂

wz

and η(x ,y ,z , t)

is the free surface. The scale parameters ε = /a h and 2 2/h lδ = are introduced to represent nonlinearity and

dispersion, respectively. The horizontal length-scale of

the sea bed non-uniformities L is assumed to be much

larger than the wave length l (i.e., γ γ≡ <</ , 1l L ),

resulting in the sea bed being “mild slope”, and the

gradient of the sea-bed shape being neglected.

For the 2004 Indian Ocean Tsunami, a = 1 m in the

ocean, and up to 10 m nearshore; h = 4000 m and 10 m,

respectively; l = 400 km and 50 km, respectively. Thus,

the introduced scale parameters may have ranges: ε = 10−4

in the ocean and up to 1 nearshore; δ = 10−4 and 10−5,

respectively.

Integration of Eqs. (8)–(11) is complicated by the fact

that the moving surface boundary is part of the solution.

Direct numerical methods for solving the full equations

exist, but they are extremely time-consuming and can

only be applied to small-scale problems. As it is currently

impracticable to compute a full solution valid over any

significant domain such as the entire Indian or Pacific

Ocean, approximations must be adopted, including the

so-called Boussinesq-type formulations of the water-wave

problem.

Following Boussinesq [2], we expand the velocity

potential in terms of δ without any assumption about ε:

2

0 1 2ϕ ϕ δϕ δ ϕ= + + +⋯ (12)

and substitute into Eqs. (8)–(11) to derive the unknown

terms ϕ ϕ ϕ0 1 2, , .

The idea behind the Boussinesq approximation

(12) was to incorporate the effects of non-hydrostatic

pressure, while eliminating the vertical coordinate z, thus

reducing the computational effort relative to the full

three-dimensional problem. The assumption that the

0=t 0>t

(a)

(b)

(c)



magnitude of the vertical velocity increases polynomially

from the bottom to the free surface (Fig. 5) inevitably

leads to some form of depth limitation in the accuracy of

the embedded dispersive and nonlinear properties. Hence,

Boussinesq-type equations are conventionally associated

with relatively shallow water.

Let us retain all terms up to order δ, ε in Eq. (9) and 2 2, ,δ ε δε in Eq. (10) to obtain 2-D Boussinesq-type

equations

δη εη εη+ + + + − ∇ + ∇ =2 2( (1 ) ( (1 ) (( ) ( ) ) 06

t x y x yu v u v

(13)

ε η δ+ + + − + =1( ) ( ) 0

2t x y x txx txyu uu vu u v (14)

ε η δ+ + + − + =1( ) ( ) 0

2t x y y txy tyyv uv vv u v . (15)

To simplify the set of Eqs. (13)–(15) to a single one,

we assume a similar small scale for the introduced

parameters, i.e., δ ε~ ; retain only one dimension

(x-dependence); eliminate u in linear terms of Eq. (13)

using Eq. (14), and in nonlinear terms using linearised

relationship η γ= + ( )u O .

Fig. 5. Vertical structure of the water column beneath the waves:

(a) hydrostatic assumption; (b) non-hydrostatic assumption.

Resulting expression (the Boussinesq equation)

comprised of second and higher order derivatives, can be

simplified further by letting δ ε γ~ ~ . In physical terms

the assumption γ <<1 impose wave parameters, such as

height, length and direction of propagation, to be slow

varying at a distance of the wave length. In contrast with

the Boussinesq equation, the condition allow to consider

the progressive wave solution travelling to one direction

only, positive or negative with respect to x direction.

For the positive direction we obtain a single equation,

universally known as the Korteweg and de Vries (KdV)

η εη η δη + + + = 3 1

1 02 6

t x xxx . (16)

While deriving Eqs. (13)–(15) we have implicitly

assumed that δ ε γ<< << <<1, 1, 1 and ~δ ε ;

therefore, the Boussinesq equations include only the

lowest-order effects of frequency dispersion and

nonlinearity. They can account for transfer of energy

between different frequency components, changes in the

shape of the individual waves, and the evolution of wave

groups in the shoaling irregular wave train. However,

the standard Boussinesq equations have two major

limitations in their application to long waves on shallow

water:

• the depth-averaged model describes poorly the frequency

dispersion of wave propagation at intermediate depths

and deep water;

• the weakly nonlinear assumption is valid only for

waves of small surface slope, and so there is a limit

on the largest wave height that can be accurately

modeled.

Modern tsunami research experiences two contradictory

trends, one is to include more physical phenomena

(previously neglected) into consideration, and another is

to speed up the code to be used for the operational

tsunami forecast.

Although higher-order Boussinesq equations for

the improvement of the description of nonlinear and

dispersive properties in water waves have been attempted

and have been successful in certain respects, most of these

attempts have involved numerous additional derivatives

and hence made the accurate numerical solution

increasingly difficult to obtain. In justification of such

derivations of higher-order terms in the Boussinesq

equations, preference has often been given to artificially

constructed test cases having little (if any) correspondence

with real tsunamis. The Northern Sumatra (December

2004) tsunami had provided a new test case for the

various models. After several decades of intensive

worldwide research, it is interesting to read the

conclusion of Grilli et al. [7] that “…in view of the

apparently small dispersive effects, it could be argued that

the use of a fully nonlinear Boussinesq equation model is

overkill in the context of a general basin-scale tsunami

model. However, it is our feeling that the generality of

the modelling framework provided by the model is

advantageous in that it automatically covers most of the

range of effects of interest, from propagation out of the

generation region, through propagation at ocean basin

scale, to runup and inundation at affected shorelines.”

Even the presence of the third-order derivative terms

for dispersion in the standards Boussinesq Eqs. (13)–(15)

is considered challenging enough to be omitted in

popular operational tsunami modelling codes, such as

Tunami-N2 [6, 8].

Boussinesq equations with omitted dispersion terms

often are referred to as the Nonlinear Shallow Water

Equations (NSWE). Alternative simplification suggested

in MOST [15] and COMCOT [10] is to use NSWE, but

implicitly include dispersion phenomenon by shaping a

numerical approximation error in the form of the third-

order derivatives (dispersion terms).

The optimal code for tsunami modelling must be

sufficiently fast and accurate; however, the notions of

speed and accuracy are quickly changing to reflect

(a) (b)



Fig. 6. Maximum wave height computed for the 2004 Indian

Ocean Tsunami [4].

current understanding of tsunami physics as well as

growing computational power. Hence, in order to assess

parameters of the currently optimal code, established and

new approaches need to be regularly re-evaluated to

ensure that the most important (and yet computationally

affordable) phenomena are taken into account. The

importance of some phenomena, potentially capable

of affecting tsunami propagation characteristics, has

been quantitatively evaluated by Dao and Tkalich [4].

Computations (Figs. 6 and 7) show that the following

phenomena have been important for the Northern

Sumatra Tsunami (in reducing order of importance):

• Astronomical tide at high phase may lead to nonlinear

increase of the tsunami height up to 0.5 m during high

tide and increase arrival time by 30 minutes;

• Reduction of bottom friction lead to increases of

0.5–1.0 m in the maximum tsunami height nearshore,

where as in the deep ocean the effect of bottom

friction is negligible;

• Dispersion effects have significant influence in the

deep ocean, leading to a drop of 0.4 m (40%) in the

computed maximum tsunami height. No significant

change in arrival time is observed.

To avoid complex derivatives and unnecessary

complications posed by the Boussinesq model, Stelling

and Zijlema [14] proposed a semi-implicit finite

difference model, which accounts for dispersion through

a non-hydrostatic pressure term. In both, the depth-

integrated and multi-layer formulations, they decompose

the pressure into hydrostatic and non-hydrostatic

components. The solution to the hydrostatic problem

remains explicit; the non-hydrostatic solution derives

from an implicit scheme to the 3-D continuity equation.

The depth-integrated governing equations are relatively

simple and analogous to the nonlinear shallow-water

equations with the addition of a vertical momentum

equation and non-hydrostatic terms in the horizontal

momentum equations. Numerical results show that both

Fig. 7. Arrival time of first wave computed for the 2004 Indian

Ocean Tsunami [4].

depth-integrated models estimate the dispersive waves

slightly better than the classical Boussinesq equations.

4. Tsunami Warning

Long before the modern instrumental era, people were

trying to predict earthquakes and tsunamis using various

nonscientific means (i.e., all that was then available). In

Japan, one of the earliest forms of tsunami warning is

literally cast in stone. “If an earthquake comes, beware of

tsunamis,” and “Remember the calamity of the great

tsunamis. Do not build any homes below this point,” read

stone slabs, hundreds such markers doted Japanese

coastline, some more 600 years old.

Nowadays, many scientifically-based methods of

Earth observation are sufficiently developed and utilised

[1], or could be developed in a short time-frame [11].

As most tsunamis are triggered by earthquakes,

seismometers are the first obvious choice to trigger a

tsunami warning system and to estimate the source

parameters. Seismic signals from the near-real-time IRIS

Global Seismographic Network (Fig. 8a) are commonly

used to infer an earthquake’s magnitude and epicenter

location. If a tsunami has been generated, the waves

propagate across the ocean eventually reaching one of the

NOAA-developed DART buoys (Fig. 8b), which report sea-

level measurements back to the tsunami-warning centre.

Two auxiliary sources of tsunami information have to

be mentioned, i.e., near-shore tide gauges and open-sea

satellite altimetry. The tide gauge measurements are

complicated by variations in local bathymetry and

harbour shapes, which severely limit the effectiveness of

the data for providing useful measurements for tsunami

forecasting. Tide gauges can provide verification of

tsunami forecasts, but they cannot provide the data

necessary for efficient forecast itself, and definitely not for

the coast where they are installed. Tsunami detection by

satellite altimetry is currently restricted by the high cost of

imaging and low frequency of sampling.



(a) IRIS Global Seismographic Network

(b) Deep-ocean Assessment and Reporting of

Tsunamis (DART) global map Fig. 8. Existing observation networks.

References

[1] E. N. Bernard, H. O. Mofjeld, V. Titov, C. E. Synolakis and F. I. Gonzalez, Tsunami: scientific frontiers, mitigation, forecasting and policy implications, Phil. Trans. R. Soc. A 364 (2006) 1989–2007, doi:10.1098/rsta.2006.1809.

[2] J. Boussinesq, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, Journal de Mathématique Pures et Appliquées, Deuxième Série 17 (1872) 55–108.

[3] J. Boussinesq, Essai sur la théorie des eaux courantes. Mémoires présentés par divers savants, l’Acad. des Sci. Inst. Nat. France, XXIII (1877) 1–680.

[4] M. H. Dao and P. Tkalich, Tsunami propagation modelling – a sensitivity study, Nat. Hazards Earth Syst. Sci. 7 (2007) 741–754.

[5] R. G. Dean and R. A. Dalrymple, Water Wave Mechanics for Engineers and Scientists (Prentice-Hall, Inc., Englewood Cliffs, New Jersey 07632, 1984).

[6] C. Goto, Y. Ogawa, N. Shuto and F. Imamura, Numerical method of tsunami simulation with the leap-frog scheme (IUGG/IOC Time Project), IOC Manual, UNESCO, No. 35 (1997).

[7] S. T. Grilli, M. Ioualalen, J. Asavanant, F. Shi, T. J. Kirby and P. Watts, Source Constraints and Model Simulation of the December 26, 2004 Indian Ocean Tsunami, ASCE J. Waterways, Port, Ocean and Coastal Engineering 133(6) (2007) 414–428.

[8] F. Imamura, A. C. Yalciner and G. Ozyur, Tsunami Modelling Manual (2006).

[9] D. J. Korteweg and G. de Vries, On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves, Philosophical Magazine 39 (1895) 422–443.

[10] P. L.-F. Liu, S.-B. Woo and Y.-S. Cho, Computer Programs for Tsunami Propagation and Inundation (Cornell University, 1998).

[11] A. Rudloff, J. Lauterjung, U. Munch and S. Tinti, The GITEWS Project (German-Indonesian Tsunami Early Warning System) Nat. Hazards Earth Syst. Sci. 9 (2009) 1381–1382.

[12] J. S. Russell, Report on waves, Fourteenth meeting of the British Association for the Advancement of Science (1844).

[13] J. S. Russell, The Wave of Translation in the Oceans of Water, Air and Ether (London, 1885).

[14] G. S. Stelling and M. Zijlema, An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation, Inter. J. Numer. Methods Fluids 43(1) (2003) 1–23.

[15] V. V. Titov and F. I. Gonzalez, Implementation and testing of the method of splitting tsunami (MOST) model. NOAA Technical Memorandum ERL PMEL-112, November (1997).

Pavel TkalichNational University of [email protected]

Pavel TKALICH is Associate Professor at the Department of Civil and Environmental Engineering, NUS; and Head of Physical Oceanography Research Laboratory of Tropical Marine Science Institute.

Pavel Tkalich has been trained in applied mathematics and cybernetics in Kiev University (Ukraine). His PhD dealt with linear and nonlinear water waves, including soliton-type solutions of the Bousinesq equations. Starting from water quality impact assessment after the Chernobyl Accident, Tkalich's interests have extended to modelling of algal blooms, oil spills, and other pollutants in the aquatic environment. The latest areas of research include also sea level rise and extremes, projections of storm surges and wind waves with respect to the climate change. Since repatriation to Singapore, Pavel Tkalich has been leading a number of national-importance projects, including development of Singapore Tsunami Warning System and Climate Change Vulnerability Study.



Fighting Asian Catastrophes with Mathematics

Gordon Woo

Abstract. The Asian continent is particularly exposed to

catastrophes, both natural and man-made. When disaster strikes,

event accounts tend to be descriptive and phenomenological,

leaving open the deeper questions of understanding suited to

mathematical enquiry. Not only are these questions of intrinsic

mathematical interest, but their solution contributes to

mitigating the devastating economic and human loss wrought by

Asian catastrophes.

As is apparent from the country’s very own name, in

the Netherlands, flooding is an ever present threat. When

an eminent Dutch mathematician, Laurens de Haan,

wrote a paper titled, “Fighting the Arch-Enemy with

Mathematics”, it was evident to its people that the subject

was extreme flood risk, which has historically been a

lethal scourge of the Netherlands. If a dike is overtopped

by a coastal storm surge, the consequences can be

calamitous when the land inside the dike is below sea-

level. Regardless of the height of a dyke, there is always

a chance, however slim it may be, that it may be

overtopped. The designated annual tolerance is set very

low accordingly: 1/10,000. From the statistics of coastal

water heights measured, it is possible to estimate

appropriate dike design levels using extreme value

distributions. De Haan was a prolific contributor to

extreme value theory, in particular, to distributions F in

the domain of attraction of an extreme value distribution

G, where sequences an > 0 and bn (n ≥ 1) exist, such that

F n (an x + bn) → G(x).

Although the Netherlands is intrinsically flood-prone,

the Dutch are thankful to be less vulnerable to other

forms of geological hazards; windstorms are typically

more of a threat to agriculture than to people. However,

for Asians, earthquakes, volcanic eruptions, tsunamis,

landslides and typhoons may be as severe a personal

threat as a flood. Indeed, for Dutch researchers analysing

Earth hazards, their primary scientific laboratory has

been Indonesia, formerly a Dutch colony known as the

Dutch East Indies. If the Netherlands is a key example of

extreme flood risk, Indonesia forms an even more

important example of extreme geological risk. The

greatest historical volcanic eruption was the eruption of

Tambora in 1815, which discharged 150 cubic kilometres

of ash into the atmosphere. Scientific understanding of

Nature starts with observations such as this; but why

should we anticipate cataclysmic events on such an

enormous scale?

It took a mathematician, Benoit Mandelbrot, to find

the answer. For any empirical observation to be deeply

understood, there needs to be the discovery of a

mathematical representation. Nature has its own

geometry, which is not composed of the regular shapes

familiar from Euclid. Mandelbrot observed that “clouds

are not spheres, mountains are not cones, and lightning

does not travel in a straight line”. Furthermore, there is a

continuum of distinct length scales of patterns: a

photograph of a small rock may look similar to a

photograph of a cliff face. Discovering the self-similar

geometry of coastlines from a British scientist, Lewis Fry

Richardson, Mandelbrot developed fractal geometry into

a powerful tool for understanding the natural world, and

for comprehending the fundamental logarithmic scale of

natural hazards.

If natural catastrophes are pathological events

punctuating the relative tranquillity of geodynamic

processes, it is because the underlying geometry of Nature

is also pathological, in a classical Euclidean sense. Taking

the simple example of a coastline, measured in intervals

of length ε , approximation by a broken line requires a

number of intervals proportional to ε –D, where the

exponent D depends on the jaggedness of the coast.

The fractal geometry of fault movement is central to

the size distribution of earthquakes. The magnitude of an

Fig. 1. On 1 February 1953, a great North Sea storm surge killed

almost 2000 people in the Netherlands. After this tragedy,

mathematicians were brought in to assist in calculating dike

heights. [Photo from BBC News archive]

Fighting Asian Catastropheswith Mathematics

Gordon Woo



earthquake is correlated to the length of rupture, which

varies self-similarly from metres to hundreds of

kilometres. Across the Indian Ocean, from Sri Lanka to

Thailand, fatalities of the Sumatra tsunami of December

26, 2004 fell victim to the fractal geometry of Nature. For

most Asian coastlines threatened by tsunamis, there are

no engineered tsunami barriers to prevent the ingress of

tsunami waves. The word “tsunami” is Japanese for

harbour wave, and the Japanese archipelago is especially

prone to tsunamis. Tsunami barriers have been

constructed in Japan, but the design basis has traditionally

been deterministic, as once it was for dikes in the

Netherlands. In the absence of any risk-based criterion,

the worst historical event may be taken as the reference

for design, possibly with a modest increment as a safety

margin to reach some notional upper plausible bound.

The Japanese tsunami of March 11, 2011 was a

catastrophe of gigantic proportions, greatly exacerbated

by the under-design of the tsunami protection around the

Fukushima nuclear power plant. Civil engineers are

predominantly responsible for safety construction

standards, but their education has traditionally focused

on deterministic principles of Newtonian mechanics,

with comparatively little time for a basic training in

stochastic processes. Following the practical example of

Laurens de Haan, mathematicians are needed to assist

engineers in coming to terms with quantifying the

uncertainties in the threat environment, so as to improve

the design of safety-critical infrastructure.

The magnitude of the earthquake that generated the

tsunami was 9.0, which was a record for the region, and

higher than the maximum hitherto anticipated by

Japanese seismologists from geological arguments, which

was 8.3. The mathematical theory of records is of intrinsic

interest in itself, but also can illuminate event sequence

patterns. Suppose that the following event sequence is

observed X1, X2, X3…, and that the maxima are M1, M2… .

The elegant mathematical structure of such record

sequences has been explored, and affords insight into

maximum magnitudes, where the regional earthquake

catalogue is sufficiently extensive.

Once a tsunami is generated by an earthquake of large

magnitude, the ocean propagation of the tsunami and its

run-up on land are analysable by applied mathematicians,

using the principles of classical hydrodynamics. However,

the task of forecasting accurately the run-up heights along

an irregular coastline, allowing for spatial variability in

bathymetry and topography, is a significant numerical

modelling challenge. Solution of the nonlinear shallow

water equations itself can lead to some idealised run-up

formulae, expressible succinctly and elegantly in terms of

Bessel function integrals, but the greater spatial

complexity of actual run-ups is captured on videos of

destructive tsunamis. Where tsunami barriers are absent

or deficient, the timing of a call for evacuation is crucial.

Natives of islands vulnerable to the occurances of

tsunamis have a reflex reaction to tremors, which is to

run to higher ground. Repeated false alarms due to

earthquakes not generating significant tsunamis are

perceived as a small cost compared with the potential

benefit of saving lives one day. In modern industrialised

societies, where the inconvenience of a false alarm is

much harder to accept, the economic cost of false alarms

should be quantitatively balanced against the safety

benefits.

The quarter of a million who died from the Sumatra

earthquake and tsunami of December 26, 2004 do

not constitute the worst death toll in recent times. The

1976 Tangshan earthquake, which occurred shortly

before the end of the Maoist era in China, was even more

tragic. Ranking of the number of fatalities from

earthquakes around the world yields a power-law known

as Zipf ’s Law, whereby the frequency of events of rank k out of N is proportional to 1/kS. The normalisation factor

is =∑ 1

1/N

S

nn . In the limit of infinite N, this is the zeta

function ς (S). Zipf ’s Law applies to a multitude of

disaster statistics, from the spread of forest fires to stock

price plunges. Explorative analysis of Zipf ’s Law affords

interesting mathematical opportunities for combining

probability with number theory.

Because of the fat tails of catastrophe loss

distributions, it is hardly ever possible to identify and

prepare for the worst event that might happen. Think of a

historical Indonesian eruption worse than Krakatau in

1883, (which killed more than the Japanese tsunami of

March 11, 2011), and you have Tambora in 1815, which

caused mass starvation. Imagine an Indonesian eruption

with a greater global impact than Tambora, and you have

Toba, which decimated the human population 74,000

years ago. Funding for disaster preparedness, risk

On July 28, 1976, a massive earthquake destroyed the

Chinese city of Tangshan, causing the highest earthquake death

toll in modern times, exceeding a quarter of a million. [Photo

from US Geological Survey photographic library]

earthquake is correlated to the length of rupture, which

varies self-similarly from metres to hundreds of

kilometres. Across the Indian Ocean, from Sri Lanka to

Thailand, fatalities of the Sumatra tsunami of December

26, 2004 fell victim to the fractal geometry of Nature. For

most Asian coastlines threatened by tsunamis, there are

no engineered tsunami barriers to prevent the ingress of

tsunami waves. The word “tsunami” is Japanese for

harbour wave, and the Japanese archipelago is especially

prone to tsunamis. Tsunami barriers have been

constructed in Japan, but the design basis has traditionally

been deterministic, as once it was for dikes in the

Netherlands. In the absence of any risk-based criterion,

the worst historical event may be taken as the reference

for design, possibly with a modest increment as a safety

margin to reach some notional upper plausible bound.

The Japanese tsunami of March 11, 2011 was a

catastrophe of gigantic proportions, greatly exacerbated

by the under-design of the tsunami protection around the

Fukushima nuclear power plant. Civil engineers are

predominantly responsible for safety construction

standards, but their education has traditionally focused

on deterministic principles of Newtonian mechanics,

with comparatively little time for a basic training in

stochastic processes. Following the practical example of

Laurens de Haan, mathematicians are needed to assist

engineers in coming to terms with quantifying the

uncertainties in the threat environment, so as to improve

the design of safety-critical infrastructure.

The magnitude of the earthquake that generated the

tsunami was 9.0, which was a record for the region, and

higher than the maximum hitherto anticipated by

Japanese seismologists from geological arguments, which

was 8.3. The mathematical theory of records is of intrinsic

interest in itself, but also can illuminate event sequence

patterns. Suppose that the following event sequence is

observed X1, X2, X3…, and that the maxima are M1, M2… .

The elegant mathematical structure of such record

sequences has been explored, and affords insight into

maximum magnitudes, where the regional earthquake

catalogue is sufficiently extensive.

Once a tsunami is generated by an earthquake of large

magnitude, the ocean propagation of the tsunami and its

run-up on land are analysable by applied mathematicians,

using the principles of classical hydrodynamics. However,

the task of forecasting accurately the run-up heights along

an irregular coastline, allowing for spatial variability in

bathymetry and topography, is a significant numerical

modelling challenge. Solution of the nonlinear shallow

water equations itself can lead to some idealised run-up

formulae, expressible succinctly and elegantly in terms of

Bessel function integrals, but the greater spatial

complexity of actual run-ups is captured on videos of

destructive tsunamis. Where tsunami barriers are absent

or deficient, the timing of a call for evacuation is crucial.

Natives of islands vulnerable to the occurances of

tsunamis have a reflex reaction to tremors, which is to

run to higher ground. Repeated false alarms due to

earthquakes not generating significant tsunamis are

perceived as a small cost compared with the potential

benefit of saving lives one day. In modern industrialised

societies, where the inconvenience of a false alarm is

much harder to accept, the economic cost of false alarms

should be quantitatively balanced against the safety

benefits.

The quarter of a million who died from the Sumatra

earthquake and tsunami of December 26, 2004 do not

constitute to the worst death toll in recent times. The

1976 Tangshan earthquake, which occurred shortly

before the end of the Maoist era in China, was even more

tragic. Ranking of the number of fatalities from

earthquakes around the world yields a power-law known

as Zipf ’s Law, whereby the frequency of events of rank k out of N is proportional to 1/kS. The normalisation factor

is �� 1

1/N

S

nn . In the limit of infinite N, this is the zeta

function ς (S). Zipf ’s Law applies to a multitude of

disaster statistics, from the spread of forest fires to stock

price plunges. Explorative analysis of Zipf ’s Law affords

interesting mathematical opportunities for combining

probability with number theory.

Because of the fat tails of catastrophe loss

distributions, it is hardly ever possible to identify and

prepare for the worst event that might happen. Think of a

historical Indonesian eruption worse than Krakatau in

1883, (which killed more than the Japanese tsunami of

March 11, 2011), and you have Tambora in 1815, which

caused mass starvation. Imagine an Indonesian eruption

with a greater global impact than Tambora, and you have

Toba, which decimated the human population 74,000

years ago. Funding for disaster preparedness, risk

�

Fig. 2. On July 28, 1976, a massive earthquake destroyed the

Chinese city of Tangshan, causing the highest earthquake death

toll in modern times, exceeding a quarter of a million. [Photo

from US Geological Survey photographic library]



mitigation and resilience planning is strictly finite in

every country; a serious misallocation of funding can

divert resources away from urgent needs to those of lesser

importance. On many issues, debates on the foibles of

human behaviour may be rather academic, but on the

mitigation of the risk from catastrophes, lives are at

stake.

Throughout history, mathematicians have fought

enlightenment battles against irrationality and illogical

reasoning and thinking. Disaster prediction is one

domain where irrationality has been rife, sometimes

confounded with numerology. Featured in a 2009

Hollywood disaster movie, “Knowing”, is the integer

911012996, which happened to be a fifty year-old time

capsule future reference to the 2,996 victims of the

terrorist attacks on September 11, 2001. Long integers do

actually have a link with terrorism; not in forecasting

disasters but in preventing them. The decryption of

encoded messages sent by terrorist operatives is vital for

interdicting plots early, before terrorists move towards

their targets. With the prospect of communication

interception, graph-theoretic analysis of the social

networks of terrorists enables the interdiction likelihood

to be calculated as a function of cell size. This is a neat

piece of applied mathematics, but cryptography stands

out as the quintessential area where man-made Asian

catastrophes are being fought with mathematics.

Fig. 3. In 1883, a cataclysmic volcanic eruption occurred on

the Indonesian island of Krakatau, which generated a giant

tsunami which killed at least 36,000 people. [1888 lithograph]

Gordon WooRisk Management Solutions, [email protected]

Dr. Gordon Woo was trained in mathematical physics at Cambridge, MIT and Harvard, and has made his career as a calculator of catastrophes. His diverse experience includes consulting for IAEA on the seismic safety of nuclear plants and for BP on offshore oil well drilling. As a catastrophist at Risk Management Solutions, he has advanced the insurance modelling of catastrophes, including designing a model for terrorism risk.



“I’d like to talk about the history of the subject I am working on, rather than about my own personal story.” Professor Haibao Duan reluctantly agreed to be interviewed only after the author agreed to his request. He reiterated, “It is important to trace the historical origin of mathematical topics in order to encounter their future development.”

Haibao Duan, a professor at the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS), was awarded Second Prize of National Natural Science Award 2010 for the achievements in his work “Multiplicative rule of Schubert classes”.

Solving the Fundamental Problem of Schubert Calculus Using Algebraic Topology Method

A reviewer wrote in Mathematical Reviews (US) about Duan’s work “Multiplicative rule of Schubert classes” said that “This paper contains an important contribu-tion to the intersection theory on homogeneous spaces.”

When talking about why one plus one equals two, one often associates it with Goldbach Conjecture, which is known as the jewel in the crown of Mathematics. It is just one of the subproblems of the eighth of Hilbert’s 23 problems.

As early as 1900, the famous mathematician Hilbert, who was also known as Alexander the Great of Math-ematics, put forth a list of 23 important problems at the International Congress of Mathematicians in Paris. These problems are also referred to as Hilbert Prob-lems, which had a profound influence on integrated development of mathematics in the 20th century, and has subsequently become the focus of research of many mathematicians.

Haibao Duan: Mathematics Should Trace Its Historical Originto Face Future Challenges

Jiang Jing

“Rigorous foundation of Schubert’s enumera-tive calculus”, which is Hilbert’s 15th problem, has become one of the key topics in algebraic geometry. By 1950, its theoretical foundation had been laid by great mathematicians Van der Waerden and André Weil and others based on a rigorous treatment of intersection theory.

However, various attempts to look for the formula of Schubert calculus had lasted over one hundred years, and it was recognised as a long standing unsolved significant point and fundamental problem of Schubert calculus. Many authoritative papers and authors had focused attention to it. Haibao Duan developed the method of algebraic topology in his work, obtained a unified formula for multiplying Schubert classes, and resolved the fundamental problem of Schubert calculus.

“Just from the question of the Hilbert’s fifteenth problem, one can see its core requirement: what is Schubert calculus? As a mathematical operation, what is the algorithm or formula for it?” According to Duan, Schubert calculus was regarded as a topic in algebraic geometry, so researchers in algebraic geometry has tried to find such a formula with the method of algebraic geometry.

Duan said, “I obtained the formula and solved the multiplicative problem of Schubert classes by using the method of algebraic topology, which differs substan-tially from methods using predecessors. The results obtained have subsequently been applied to other topics in topology and geometry.”

According to Mathematical Reviews, Duan’s work was an important contribution to the intersection theory as it solved one of the fundamental problems in the intersection theory on homogeneous spaces.



In 2009, two authors in this field commented in their work that “Schubert calculus has now been well understood” by the works of A. Borel in 1953, I. N. Bernstein, I. M. Gel’fand and S. I. Gel’fand in 1973, and Haibao Duan in 2005.

“It struck a chord with me because of the legendary history of early mathematicians.”

During the interview, Duan emphasised the impor-tance of the historical development of mathematics. “Presenting the history of the work is to show its significance.”

“Among many problems in mathematics, some could be solved within a decade or two. There are others that are global and wide-ranging in nature, these are more challenging and attracted researchers to spend a long time to explore and investigate them.”

Solving polynomial equations has a long history and it is a basic problem in mathematics, and it is required in many practical problems. At the beginning of the 19th century, a group of geometers represented by Jean Victor Poncelet (1788–1867), Michel Chasles (1793–1880), and Hermann Schubert (1848–1911) created “intersection theory”, in their attempts to solve polynomial system with an intuitive and geometrical method. According to their approach, each polynomial equation determines one curved surface, and every solution to the polynomial system is given exactly by the intersection point of these spatial surfaces. “This is the origin of the name ‘Intersection Theory’.”

“Hilbert’s 15th problem struck a chord with me because of the bumpy research experience of the pioneers of intersection theory.” Poncelet is the first of the pioneers mentioned by Duan.

After graduating from École Polytechnique in 1812, Poncelet joined the army. As a military engineer, he served in Napoleon’s campaign against the Russian Empire. He was captured and put imprisoned in Siberia. During his imprisonment, Poncelet recalled his descriptive geometry education and draw figures on the wall with charcoals. In this harsh environment, he acquired many important achievements for intersection theory, such as the principle of duality, the principle of continuity, conic section polar and polar line, and projective harmonic conjugation, and recorded his results in “Cahiers de Saratov”, in which “Saratov” is the name of the place where his concentration camp was located.

In Duan’s opinion, every era will bring forth a number of “new mathematics, new methods”, but

many of them will be eliminated, and the process would subsequently repeat over and over again. “As a mathematician, one should look to the future and define and decide precisely one’s research topic and direction.”

Prof. Duan also cited the example of Newton. In the 17th century, Newton wrote his famous work “Philosophiae Naturalis Principia Mathematica”, in which he invented the infinitesimal calculus. At the very beginning, this work was not very popular, as it was difficult to understand and it contained many imprecise statements, thus hindering its popularity and applications. Until 19th century, after the joint efforts of many mathematicians during the past hundred years, the theory of infinitesimal calculus became more rigorous and precise, systematised and structured. It was then taught in universities, accepted and studied by more and more people. Today, infinitesimal calculus had finally made important impact and applications in many areas of natural science.

“This is the reason why we need to review the past, and at the same time focus on the future,” said Duan.

Hilbert, who was indeed a mathematician with a strategic vision, was able to be keenly aware of future opportunities and highlights for mathematical develop-ment. He focused his attention on intersection theory in the 19th century by proposing the 15th problem “rigorous foundation of Schubert calculus” to empha-sise its importance.

“It proved his foresight and discernment by the development of algebraic geometry in the 20th century.” The Encyclopedia of Mathematics, published by Kluwer Press in 2001, summarised in the entry on “Schubert calculus” that “Justifying Schubert’s enumerative calculus was a major theme of twentieth century algebraic geometry”. W. Fulton recalled in his book “Intersection Theory” in 1993 that “Through the triumphs of algebraic geometry during the past two centuries, intersection theory has played a central role.”

Schubert calculus is not only a topic with a long history, progress of its in-depth research has increas-ingly revealed clearly the nature of its contact and relation with other branches of mathematics. Here it is worthy to note that the famous Wu formula in differential topology, a basic formula in the theory of characteristic classes, was discovered by Professor Wenjun Wu using the method of Schubert calculus in the late 1940s. Recently, the tool of Schubert calculus has found applications in control theory.

Translated from Chinese, Science and Technology Daily, April 6, 2011



Interview with Director of Institute for Mathematical Sciences

Louis ChenY. K. Leong

Haibao DuanAcademy of Mathematics and Systems Science, Chinese Academy of Sciences, China

Haibao Duan obtained his PhD at Peking University in 1987. He then joined the Institute of System Science as a postdoctor. Duan worked in Peking University from 1991 to 2000. He was selected into One Hundred Person Project of the Chinese Academy of Sciences in 2000. In 2005 he received Shiing S. Chern Mathematics Award of Chinese Mathematical Society.

Duan’s work mainly focuses on algebraic topology, differential topology and algebraic geometry. His early achievements include: extending the classical Borsuk–Ulam theorem; solving the bitangent sphere problem jointly with E. Rees, Brown conjecture for self-maps of topological group and the Kreck problem on Poincare manifold; and solving the fundamental problem of Schubert calculus: multiplicative rule of Schubert classes.

Jiang Jing was born in 1983. She obtained a master degree of Communication Science in Graduate University of Chinese Academy of Sciences in 2008. She is currently a reporter and editor of Science and Technology Daily.

Jiang Jing



Interview with Director of Institute for Mathematical Sciences

Louis ChenY. K. Leong

Louis Hsiao Yun Chen has been the founding Director of the Institute for Mathematical

Sciences (IMS) of the Nat ional University of Singapore (NUS) since 2000 and holds a Tan Chin Tuan Centennial Professorship in NUS. He is well-known for his impor-tant work in probability theory. His pioneering work on Stein’s Method for the Poisson approximation is encap-sulated in a result often called the “Chen–Stein Method” or “Stein–Chen Method”, which is widely applied to many areas ranging from computational biology to computer science.

As part of the 10th anniversary celebration of IMS in June 2010, he was interviewed by Y. K. Leong in February and March 2010. The interview was included in a commemorative booklet Celebrating 10 Years of Mathematical Synergy issued for the celebration. Asia Pacific Mathematics Newsletter would like to thank IMS for its kind permission to reproduce excerpts of this interview.

Y. K. Leong: Let us begin the interview in reversed chronological order, starting from the present. You have been the Director of IMS since its establishment in 2000. For IMS to reach its present international status within a short span of 10 years it is undoubt-edly an achievement. Would you have thought that this was possible when you became the Director? What are the factors that made this possible?

Louis Chen: It is very nice of you to say that it was undoubtedly an achievement. When I first became the Director, I was not really thinking about the achieve-ment I could attain. It was something given to me. I have seen what institutes were like elsewhere and I wanted to be like them. It was more or less what I wanted to do, and I tried to do my best. As to what factors made this possible, I think the time was right. But one has

to see things historically and see how it [IMS] evolved. 1991 was the first time we submitted a proposal and we knew why we didn’t succeed. We tried again in 1996 and we also didn’t succeed. In 1998, the time was right.

L: When was the idea of establishing IMS first mooted? What was decisive in turning a dream into reality?

C: By 1991, two NSF [US National Science Foundation]-funded institutes MSRI (Mathematical Sciences Research

Institute) and IMA (Institute for Mathematics and its Applications) had been set up for 10 years, we thought that Singapore should have a similar institute. So a group of us got together, and led by Peng Tsu Ann, who was then Head of the Department of Mathematics, submitted a proposal. I forgot who exactly was in the group. Chong Chi Tat was there, and Jon Berrick was asked to help make a first draft. Before this, Tsu Ann wrote to S. S. Chern, who came back with a very enthusiastic letter to support us. We attached Chern’s letter with our proposal, which was submitted to the University through the Dean (Bernard Tan). I believe the Dean supported us, but probably the time was not right and it was not successful.

Then in 1996, the Dean asked us to submit again. This time many more people became involved. Peng Tsu Ann was still the Head and he played the key role. We beefed up the proposal. Of course, we got the support of the University (Lim Pin) and we were asked to write to NSTB (National Science and Technology Board) to apply for funding. But we failed again.

Then in 1998, Lee Soo Ying became the Dean and he wanted to revive the proposal. So he talked to us, and Chow Shui Nee was around at that time and he wanted to chair the Committee. It consisted of Chow Shui Nee as chair, Tan Eng Chye, Ling San, Jon Berrick, Judy Jesudason and myself. Judy was asked to do the new draft. We all discussed together and members of

Louis Chen (photo in courtesy of IMS)



the Department were asked to give their views.

Again it was a departmental project. This time, things were different because Chi Tat was the Deputy Vice Chancellor and in charge of research. Shui Nee was the Dean of Research and Graduate Studies. We submitted a proposal to the Ministry of Education (MOE) to apply for academic research funding and I gave a presenta-tion at the Academic Research Fund Committee meeting. The University, in order to support us, also committed a sum of money as startup funding. Chi Tat was on the Academic Research Fund Committee and played a very crucial role in helping this proposal accepted by MOE.

L: Why didn’t it succeed the first time in 1991?

C: I think there are two aspects. First of all, the research environment — we had three research departments at that time [1998] — Department of Mathematics, Department of Statistics and Applied Probability (DSAP), and Department of Computational Science. Altogether we had 107 people. The two departments [Mathematics Department and DSAP] were a lot stronger in 1998 than in 1991 with more international connections.

The University had a new mission, that is, to turn the University into a research university. Then that was the time when the Government began to recognise the importance of a knowledge-based economy. The environment was right for people to regard such a proposal as relevant and important to Singapore. The human factors are the people involved — they came out with a very good proposal. Of course, Judy’s proposal was based on previous proposals. From 1991 to 1998, we had about 8 years of experience with writing this kind of proposal.

L: At that time, was there some kind of research institute that had already been established in NUS?

C: We were the first mathematical institute. By the way, in the first two proposals, we called it the Center for Mathematical Sciences, but this time we aimed higher and called it an institute. It wasn’t clear at that time whether the center should be at the faculty level or university level.

L: Did IMS use any overseas research institutes as models? How does IMS differ from such institutes at the present stage of its development?

C: From the beginning, IMS was modeled after the Mathematical Sciences Research Institute (MSRI) and the Institute for Mathematics and Applications (IMA). That is to say, we provide a platform for research interaction but we don’t hire researchers. Basically, we have a Director and a Deputy Director and the rest are all support staff. The active people are visitors who come here to participate in programs and activities. In fact, our interest in establishing such an institute was inspired by them [MSRI, IMA] in 1991. These two NSF-funded institutes were set up in 1982 and they became very successful. The Newton Institute was set up later and is also one of this kind of institutes. We followed the three of them. We get people to submit proposals and organise programs on particular themes and bring people together for interaction and do joint research. But Singapore being different, we can’t do exactly what they are doing. For example, our programs are short compared to theirs. In IMA and MSRI, they have year-long [nine academic months] programs; in Newton Institute, half a year. We started with half a year for the first two years, but very soon we found that this did not work quite well because our scientific community base here is small and also because we want our programs to have some local relevance and involve local people.

L: On the average, how many programs are there in one academic year?

C: On the average, about five. It is not possible to have

IMS Building (photo in courtesy of IMS)



a continuous running of programs, but if nothing is happening, it doesn’t mean that we are free. There are a lot of things to do. We are preparing for coming programs. In some years, we have six programs, and in some, as few as four. In between programs, we usually have workshops and conferences. This will cover more or less the whole year, but usually there is one or two months that are low, usually September or October when we will have workshops. April is not a good time — we usually cannot get people to organise things during this month.

L: With a few exceptions like programs on logic, Lie groups and analysis, most of the Institute’s programs are focused on applications of mathematics to other fields rather than on pure mathematics. Why is that so?

C: First of all, we model ourselves along the NSF-funded institutes, in particular, the IMA, which hosts mostly programs on mathematics applied to other disci-plines. But we would not leave out pure mathematics. If you look at our mission statement which is to foster research both fundamental and multi-disciplinary, then applied mathematics and applications of mathematics to other disciplines will be an important component of the institute. At the same time, we also serve the pure mathematics community. In Singapore, we cannot have too narrow a focus. We have to broaden our focus. We are a small community. If you focus only on applied mathematics or pure mathematics, then we have less people coming forward to organise programs at the Institute.

L: IMS was launched with generous funds from NUS and MOE. Are such grants still forthcoming and adequate or is IMS seeking funding from other independent sources? How difficult is it to get such funding?

C: Of course, we get some funding from MOE and NUS. Initially, it was adequate. After that, it was actually very difficult to get funding. What MOE gave us was only for startup and we have to seek funding for recurrent costs and programs. For some reason, the local funding agencies do not give funding for this kind of institute. So we cannot get funding from them because we don’t have researchers working on a term project of say two years. Fortunately, the University is willing to support and continue funding the Institute. We don’t get a lot of money but we are able to survive.

We are very lucky that recently the logic group has

been able to secure a grant of about one million US dollars from the John Templeton Foundation for a project called AII (Asian Initiative for Infinity). This is through the work of top logicians in Berkeley, Hugh Woodin and Ted Slaman, and our colleague Chong Chi Tat. This grant is to fund logic at the Institute for the next three years. We are applying for dollar for-dollar matching from the Government. If we succeed in getting the matching, the one million dollar matching fund will go into an endowment fund for the Institute. The Institute will use the proceeds of this endowment fund for logic activities and other projects.

L: As early as 1993, you were actively involved with the Bernoulli Society for Mathematical Statistics and Probability and in 1997 you became the first Asian President of the Bernoulli Society. Since then your engagement with international scientific bodies has continued unabated. In 2004 you became the first East Asian President of the Institute of Mathematical Statistics. So in a sense, you antici-pated the “globalization” of NUS. What motivated you to take on such heavy responsibilities?

C: I won’t say that I anticipated the globalisation of NUS. Globalisation of the University is very much synonymous with the globalisation of its faculty members. Over the years faculty members have “globalised”. Many of us have international linkages; many of us are well-known scientists and mathemati-cians. I have some linkages and I was nominated [for the presidency of Bernoulli Society and Institute of Mathematical Statistics]. I didn’t want to turn them down, so I said yes and I got elected.

L: About your research — I believe that there is so much research generated by Stein’s Method that it has now become a field in itself. Could you briefly describe some of the recent developments in this field?

C: There are three developments which impress me. One is the work of Sourav Chatterjee who has applied Stein’s Method to concentration of measures inequali-ties, eigenvalues of random matrices and problems in statistical mechanics. The other is the work of Jason Fulman who has applied Stein’s Method to problems with a strong algebraic component such as characters of Lie groups. The third is the work of Giovanni Peccati and Ivan Nourdin who combined Stein’s Method with the Malliavin Calculus to do normal approximation for functionals on infinite dimensional Gaussian spaces.



I think these are fascinating developments of Stein’s Method.

L: Are these very theoretical?

C: All these are theoretical in a sense although you can say they have applications in mechanics and random matrices. Actually the sort of things we do in probability is kind of like pure mathematics.

L: Your work on Poisson approximation published in 1975 began to be applied in many areas inside and outside of probability theory some 15 years later. Did you yourself contribute to these applications?

C: Unfortunately no. I did not contribute to these appli-cations using Poisson approximation. But in studying compound Poisson approximation and Poisson process approximation, which are generalisations of Poisson approximation, my collaborators and I did apply our results to problems in probability as well as in compu-tational biology.

L: What is your most recent research about?

C: My main focus in the last few years has been on normal approximation. One of my recent works is on moderate deviations, which is about relative errors in the approximation of tail probabilities. This has been submitted for publication in a joint paper with Shao Qi-Man and my PhD student Fang Xiao.

L: What about books? I don’t think you have written too many books.

C: I’m actually in the process of jointly writing a book with Larry Goldstein and Shao Qi-Man. They are very kind and are writing more than I do. This book is based on our work. It’s a monograph called Normal approximation by Stein’s Method which is going to be published by Springer Verlag. The book is coming to its final stage. My co-authors are “pressurising” me to finish a chapter on discretised normal approximation.

L: You did not go overseas for graduate studies immediately after your Honours degree at the then University of Singapore. Was it due to the limited opportunities for overseas graduate studies at that time?

C: Not exactly. Although it is true that opportuni-ties for graduate studies were more limited in those days, I did not go overseas for graduate studies after my Honours degree because I failed to get a PhD

scholarship from PSC (Public Service Commission). I wanted to do pure mathematics and I chose complex analysis as my field of study. At the PSC interview I was asked what applications complex analysis would have to Singapore. I was dumbfounded and could not give a satisfactory answer, and that, I believe, cost me the scholarship.

I then got a lectureship to teach at the Singapore Polytechnic. I taught there for a year before returning to the then University of Singapore to study for a Masters degree under U. C. Guha. I was working on summability, some very classic stuff. After a year, I was appointed temporary assistant lecturer and I taught one or two classes. I recall that you and Cheng Kai Nah were in my class. It was during that time that I saw a circular about the Fulbright–Hayes Travel Grant. I applied for it and was successful. At the same time the Department of Statistics at Stanford University offered me an assistantship. Of course I accepted both and headed for Stanford. That was in 1967, three years after my Honours degree.

L: Before you went to Stanford, you didn’t know who was going to be your advisor. How did you choose your advisor?

C: I was looking for people who could advise me on probability theory, like Kai Lai Chung and Samuel Karlin in the Mathematics Department. But it would not be easy because I had to leave the Department of Statistics and go to the Mathematics Department and start all over again. That meant I would lose two years. The Chairman of the Department of Statistics at that time was Rupert Miller. He was a very nice man and I asked him whether he could advise me. He had advised somebody else in applied probability before. But he told me that he had stopped working in applied probability and could not advise me. “However,” he said, “Charles Stein has come up with a new theory, a new technique for normal approximation. Why don’t you work with him?” I took his advice and went to Charles Stein. I asked him, “Could I be your student?” Then Charles said, “I think it’s okay since I don’t have any students right now.”

L: Did Stein suggest the problem that you should work on?

C: I never really took Stein’s course on what is now called “Stein’s Method”. I learned it from some lecture notes taken by other graduate students. As far as I remember, those were the lecture notes of Bobby Mariano who is now the Dean of the School of Economics at SMU. The notes had been passed on to



another fellow student, Dick Shorrock, who gave them to me and encouraged me to learn Stein’s Method. Dick unfortunately passed away 15 years ago. When I went to Charles Stein, I was, for some reason, inter-ested in getting the rate of convergence in Donsker’s Theorem. That wasn’t an easy problem. You need to master a core of special techniques first, but I didn’t have the opportunity. Charles gave me some advice but that did not seem to work. One day, Charles saw me and said, “Mr Chen, I have bad mathematical news for you. Your problem has been solved by a Russian mathematician by the name of Nagaev. The paper is in Russian but there is an English summary.” Then he gave me the reference.

That was a blessing in disguise because after that, I said, “Okay, I’ll have to work on a problem of Stein.” Then I thought I would work on decision theory, another of Charles’ major contribution to statistics. Charles said, “Go and read this book on topological groups by Nachbin.” This was to prepare the background. I was reading the lecture notes [on Stein’s Method] at the same time that I was reading the book by Nachbin. But somehow I was more interested in the lecture notes. Maybe it’s because I didn’t see the connection of topological groups with decision theory. Then I started to try to prove theorems. I thought I proved a theorem but it turned out to be wrong. After reading those notes, I thought to myself, “Well, all these are about normal approximation. Maybe I should do Poisson approximation, the discrete analogue of normal approximation.” I asked Charles what he thought of applying his method to the Poisson approximation, and he said, “Of course, it will work.” That was how I got into Poisson approximation.

L: You have been practically working non-stop in research and administration for some 40 years. What is the source of all this mental and physical energy?

C: It is true that I have been involved in administra-tion in one way or another from the beginning of my career and still get engaged in research all these years. But there were periods when I had few administrative duties and periods when I was very slow in research. The problem is that it is difficult to mix them and strike a balance between the two. I think what keeps me going is interest. If you are interested in something, you can go on doing it for a long time.

L: If you do ever retire from your formal duties, what do you plan to do?

C: Well, I will spend more time on my second love, music. I will read about music, attend more concerts and go back to playing the recorder, a woodwind instrument from medieval times. In fact, when I was in The Hague, Netherlands, last year, I made it a point to go to a music store and I bought many musical scores composed or arranged for the recorder. I have four very good recorders, two Hans Coolsma and two Moeck Rottenburgh. I will also spend some time re-learning some Chinese literature which I had neglected when I was in school.

L: As you reflect on the past 10 years’ of accomplish-ments for IMS, in what direction would you like to see IMS developing in the next 10 years?

C: The current model for the Institute will remain the same. IMS will continue to contribute in a significant way to research vibrancy in the mathematical sciences in Singapore. It will continue to bring about greater interaction and research collaboration between math-ematicians and scientists of different disciplines and between the local scientific community and the wider international community. For the future I would like to see IMS developing into a major player in the world contributing to mathematical research internationally. It should come to everybody’s mind as a foremost mathematical institute in Asia.

Y. K. Leong is an Associate Professorial Fellow in the Department of Mathematics of the National University of Singapore (NUS). He obtained his BSc (Honours) from the University of Singapore and his PhD (in group theory) from the Australian National University. He has taught in University of Singapore and its successor NUS since 1972. He was an academic advisor to the Open University Degree Programmes (Singapore Institute of Management). He has held offices in the Singapore Mathematical Society. He has been an editor in the Singapore Chess Federation and the Institute for Mathematical Sciences, NUS. His research interest is in algebra.

Y. K. LeongNational University of [email protected]



1. A Profile of Mathematical Competition in Shanghai

Shanghai was one of the four cities in China holding math competitions. In 1956, the Shanghai Mathematics Society, with instructions from the China Mathematics Society and support from the Shanghai Municipal Education Commission and the Shanghai Science Associated Body, held the first and second Shanghai Municipal Middle School Mathematical Competitions. Both competitions were supervised by the mathemati-cian Buqing Su. They were efficacious in triggering students’ interest in learning math and improving the quality of math education in middle schools. The partic-ipants were the 11th and 12th graders from schools. The competitions each comprised three rounds, namely the preliminary round, the second round and the final round. The preliminary rounds were organised by and held separately in the individual schools, where the outstanding students were selected to participate in the second round. The second and final rounds were organ-ised by the Municipal Competition Committee. The Secondary Math Education Committee under Shanghai Mathematics Society compiled the general experience of holding these two competitions in a book — Collec-tion of Shanghai Municipal Middle School Mathematics Competition Problems (1956–1957), published by the New Knowledge Publishing House in 1958.

Following this, the third, fourth, fifth and sixth Middle School Mathematical Competitions were organ-ised in 1958, 1960, 1962, and 1963 respectively, out of which many math talents were discovered and selected. From 1966 to 1977, the mathematical competitions were suspended due to political reasons.

In 1978, the seventh Shanghai Middle School Math-ematical Competition resumed and 50 outstanding participants also took part in the National Middle School Mathematical Competition. In that competi-tion, candidates from Shanghai got excellent results. Out of the 57 outstanding candidates (of which 5

A Brief Introduction to Mathematical Competitions

in ShanghaiBin Xiong and Zhigang Feng

got First Prize, 20 got Second Prize and 32 got Third Prize), 25 were from Shanghai. For example, Jun Li of Luxun Middle School won the First Place; 12 students including Youyu Xu of Changfeng Middle School and Yinping Wang of Hongkou Middle School got Second Prize. Twelth students including Hongmin Chen from Peiguang Middle School were awarded Third Prize.

Since 1978, Shanghai Mathematics Society has been holding the Shanghai Municipal High School Mathematical Competition in the first half of each year. Participants are mainly 12th graders with a small number of 10th and 11th graders. The Shanghai Municipal High School Mathematical Competition has been held 40 times in total.

Students from Shanghai also achieved good results in the China Mathematical Olympiad with many First-Place Team Prizes. China first partici-pated in the International Mathematical Olympiad (IMO) in 1985, and since then, 19 students from Shanghai have been selected to join the national team and have won 20 medals including 15 gold medals, 3 silver medals and 2 bronze medals. The following table gives the details.

2. Shanghai Municipal Math School for Middle School Students

In the recent 20 years, the achievements of students from Shanghai in mathematical competitions at home and abroad have much to do with the Shanghai Municipal Math School for Middle School Students. This school is the one authorised by the Shanghai Municipal Education Committee, endorsed by the Shanghai Mathematics Society, and guided by the Teaching Research Team of the Shanghai Municipal Education Committee.

Thanks to the support from the Shanghai Math-ematics Society, Shanghai Education Committee, and middle schools, the school has been established



Year Medal Winner Medal School

1985 Sihao Wu Bronze Xiangming High School

1986 Hao Zhang Gold Datong High School

1987 Zigang Pan Silver Xiangming High School

1988 Xi Cheng Gold High School Affiliated to Fudan University

1993 Jiong Feng Gold Xiangming High School

1994 Jian Zhang Gold (Full marks) Jianping High School

Haidong Wang Silver No. 2 High School of East China Normal University

1995 Haidong Wang Gold No. 2 High School of East China Normal University

Yijuan Yao Silver High School Affiliated to Fudan University

1996 Fu Liu Bronze High School Affiliated to Fudan University

1999 Zhenhua Qu Gold Yan’an High School

2000 Zhongtao Wu Gold Shanghai High School

2002 Wenjie Fu Gold No. 2 High School of East China Normal University

2004 Yuncheng Lin Gold Shanghai High School

2005 Hansheng Diao Gold (Full marks) No. 2 High School of East China Normal University

Xuancheng Shao Gold (Full marks) High School Affiliated to Fudan University

2008 Xiaosheng Mu Gold (Full marks) Shanghai High School

Cheng Zhang Gold No. 2 High School of East China Normal University

2009 Fan Zheng Gold Shanghai High School

2010 Zipei Nie Gold (Full marks) Shanghai High School

Since 1981, Shanghai Mathematics Society has also been holding math competitions for junior school students every December. By 2010, 30 such competitions had already been held.

China won the 1st place in 2008 IMO. Two of the six participants were from Shanghai.



for more than 20 years, since 1987. Chaohao Gu now is Honorary Prin-cipal of this school. The students studying in this school, range from Grade 6 to 12 and are the best math students in Shanghai. Each grade consists of about 400 students. Every Sunday, these students go to this school for intensive math lessons. The school hired profes-sors from Fudan University and East China Normal University as well as experienced senior teachers from high schools in Shanghai to conduct the lessons. The faculty team consists of the best math teachers that can be found in Shanghai.

In this math school, students learn some math knowledge and methods beyond the general math courses in high school, including Number Theory, Combinatorics mathematics, some famous theo-rems in Geometry, as well as methods and tech-niques in solving math problems. Through lectures conducted by the teachers and discussions among students, the standard of mathematics of students can be improved quickly. Thus far, all the Shanghai candidates in the national team have been trained in the Shanghai Municipal Math School for Middle School Students.

In addition, entrusted by the Shanghai Math-ematics Society, the Shanghai Municipal Math School for Middle School Students organises and prepares tests for the Shanghai Municipal Mathematical Competitions for high school and junior school Students. The best-performing students in these competitions are selected and form small classes to be specially tutored.

3. Shanghai High School

The success of the mathematics competitions held in Shanghai are closely related to several prestigious high schools in Shanghai, including Shanghai High School, High School Affiliated to Fudan University, No. 2 High School of East China Normal University and Yan’an High School. The aforementioned schools not only have gifted students and excellent teachers, but also have good ways of training and cultivation. In this article, we take Shanghai High School’s practice as an example.

Each year, many students from Shanghai High

School attain prizes in various math competitions at different levels. From 2008, on a yearly basis, approximately one third of all winner of the First Prize in Shanghai are from Shanghai High School, with two of them entering the national trainee team and one entering the China IMO national team. For the recent three consecutive years, there have been students from Shanghai High School winning IMO gold medals each year. In 2009 and 2010, there was one student winning the First Place in the Romanian Masters in

Mathematics Competition (RMM). All these medal winners are from the intensive math class (a math-featuring class, established by Principal Shengchang TANG in 1990) of Shanghai High School.

Every year Shanghai High School selects some excellent students who have participated in junior school math competitions in Shanghai to form an intensive math class. More than 10 of the best students are selected from the intensive math class to form an even smaller class for further math competition education. In these classes, the teaching method adopted is the “1+n” mentoring method, where one math teacher is assigned as a core teacher to act as a mentor to the highly-gifted students whilst integrating the wisdom of the members of the math-teaching team at school and a mentoring team of math professors outside the school. The school encourages students who have similar math abilities, share the same interest in math, but exhibit individual characteristics, to form study groups and conduct brainstorm sessions of cooperation and communication among themselves. The Shanghai High School also pays special attention to the sustainable development of these students by properly handling the relationship between the development of generic intelligence and special intelligence. For this reason, Shanghai High School develops students’ math potentials on the basis of consolidating their overall knowledge.

After getting to understand the characteristics of every student in the small class and his/her potential academic maximisation, Shanghai High School makes personalised development plans which make a holistic arrangement for the three years of teaching and learning so as to accomplish the teaching

The sole perfect scorer for 2010 IMO, Zipei Nie from Shanghai, received award from Kazakhstan Prime Minister Karim Massimov.



Bin XiongEast China Normal University, Shanghai, [email protected]

Bin Xiong is currently a professor at the East China Normal University. His research interests lie in problem solving and gifted education. He is a member of the Chinese Mathematical Olympiad committee and the Problem subcommittee. He was the Leader of China’s IMO national team in 2005, 2008, 2010 and 2011.

Zhigang FengShanghai High School, Shanghai, [email protected]

Born in 1969, Zhigang Feng is the Vice Principal of Shanghai High School and a master teacher of math. He was the Deputy Leader of China’s IMO national team in 2003, 2008, 2010 and 2011, dedicated to researching on and mentoring in high school math contests.

tasks efficiently and without compromising on the standard. In the meantime, the school designs appro-priate time lines so that specialists and professors from different areas are invited at appropriate time slots to give useful instructions. The advantage of this arrangement is that the strengthening of students’ academic foundations and teaching of higher level skills and knowledge are given equal weighting.

This gives the students chances to learn of different thinking habits and perspectives of specialists and professors from different areas, so the students may get more in-depth and more well-rounded develop-ment.

It is due to these carefully planned and well devel-oped arrangements that Shanghai High School has always done well in mathematical competitions.



Problem CornerSend your answers by 31 October 2011

to [email protected] to win book prizes

I’m glad to say that we have a book winner for a solution to Problem 2.1. He is Wu Cheng Yuan, an undergraduate majoring in mathematics at the

National University of Singapore. His was not the only

Problem 2.2: Bob wins by making sure that the number of stones at each stage is a multiple of 3.

It’s probably easiest to see this by starting from the bottom up. So if there are 3 stones and Alice takes 1, Bob takes 2, while if Alice takes 2 Bob takes 1. On the other hand if there are 6 stones and Alice takes 1, Bob takes 2 and we know he’ll win from here.

By Mathematical Induction, Bob will win any game that has 3k stones, for any whole number k.

In a similar way, you can show that Alice will win if the number of stones is not a multiple of 3.

What difference does it make if we change the rules of the game so that the one who takes the last stone loses?

Problem 2.3: I’ll explain the men’s reasoning and leave the probabilities to you.

solution we received. Cheng Yuan has chosen the book Galois Theory of Algebraic Equations (by Jean-Pierre Tignol) published by World Scientific.

Cheng Yuan’s solution has been included below.

Second Problem Set Solutions

Problem 2.1:

There are four such ways, namely, 5 2 4 5 3 1 6 4 5 1 2 44 2 6 1 5 3 2 3 6 3 6 1

Method:We can narrow our search to 20, compared to 6!, by fixing the numbers on the vertices. There are 6C3 = 20 ways of doing so. For instance, we can fix the vertices A, D, F A B CD E Fby letting A = 1, D = 2, F = 3.Then we get an equation,1 + B + C + 2 + E + F = 1 + 2 + 3 + 4 + 5 + 6 = 21B + C + E = 15.Furthermore, we have 1 + B + 2 = 1 + C + 3 = 2 + E + 3.From here, we have enough information to solve for all the variables, and get C = 5, B = 6, E = 4.We do the same for the other 19 ways of fixing the vertices.

But there are other ways to do this. Most of them entail finding the possible sums on the sides. One way to restrict these sums is to note that 1 has to be in the largest side sum, so the largest possible side sum would be 1 + 5 + 6 = 12. Similarly the smallest side sum is 6 + 1 + 2 = 9. There are only three ways to make 9 (6 + 1 + 2, 5 + 1 + 3, 4 + 2 + 3). The numbers that appear in more than one of these sums has to be in a corner circle. From there it is easy to complete the only possible arrangements.

Clearly if B and C were wearing a hat of the same colour, then A will know the colour of his own hat. Suppose his hat is black. Then B will immediately know that his hat is white because (i) the only reason that A will call out his hat colour is that B and C have the same coloured hat; and (ii) he can see that C has

Derek Holton



After an academic career lasting for over 40 years, Derek retired from his posi-tion as Professor of Pure Mathematics at the University of Otago in early 2009. During that time he published about 130 papers on mathematics and math-ematics education; about 20 books ranging from school texts to popular books on mathematics to tertiary texts; about 20 chapters in books, largely involving research into aspects of mathematical education; and about 90 articles for teach-ers and students on mathematics.

He participated actively in the training of New Zealand International Mathematical Olympiad teams and was New Zealand’s IMO Team Leader for several years between 1988 and the turn of the century. He was involved in the mathematics curriculum at the national level, and chaired the Numeracy Projects Reference Committee and initiated, with Gill Thomas and Joe Morrison, the web site www.nzmaths.co.nz.

Derek [email protected]

a white hat. At that point, B will realise that his hat is white too. Then D knows that his hat has to be black.

Suppose that B and C have different coloured hats. Without loss of generality I’ll assume that C is wearing white and B black. A is stuck. But B now knows that he and C are wearing different coloured hats so his hat must be different from C and so is black. As a result, C deduces that his hat is white. Unfortunately for A he

has no further information. Perhaps he’ll guess and D will either fall in with A’s guess or not, depending on how he’s feeling at the time.

Of course, I’m assuming that A is an honourable man. He could always see the different hats on B’s and C’s heads and call out a random colour. The random colour might well depend on whether he likes B or C best.

Third Problem Set

Problem 3.1: The internationally famous cereal Barley Bits has been having a promotional campaign in the wilds of Western Australia. It has based its campaign around a final competition at Barley Bits headquarters on the edge of the scenic Lake Eyre. To enter the final round of the competition, participants have to find Barley Bits icons in their favourite cereal. Some 25 of these icons have been put into the cereal packets.

On the day, 21 people turn up at Barely Bits building at Lake Eyre. (Court cases are pending regarding the swallowing of the other 4 icons.) They are seated round a large table and given numbers 1 to 21 in order, clockwise round the table.

Then the CEO moves around the table. He counts 1 in and 2 out; 3 in and 4 out; and so on around and around the table until only one person is left. That person is the winner. He was given number 11.

If there were N people at the table, which numbered person would have won?

Problem 3.2: Four Aliens and four Humans were the only creatures ‘manning’ the small planet of Eos. After

a month on Eos, they have to move on to the neigh-bouring unoccupied planet of Helios. They have a small shuttle that will hold at most two creatures at a time.

Now if on any planet, including the shuttle, there are more humans than aliens, the Aliens Minority League will sue the International Federation for insensitivity, which will likely cost the dominant Human Race, the desirable planet of Earth. So the humans will ensure that they are never, ever in the majority.

Can the eight creatures get across to Helios without the Human Race losing Earth? If so, how will this be done? If not, why not?

Problem 3.3: Every month I have to transfer a sum of money to an international colleague. Every month I need a new 4-digit PIN number in order to complete the transaction. My colleague always sends me a message telling me what the current PIN number is. Last month I got the following message:

“29 is a divisor; it has exactly 8 factors; and it is the biggest such odd number.”

What was the PIN number?



The SEAMEO Regional Centre for QITEP in Mathematics is located in Yogyakarta, Indo-nesia and was launched on July 13, 2009. The

Centre promotes programs and activities in improving the quality of teachers and education personnel in the area of Mathematics through training courses, workshops, research, information dissemination, publications and other activities related to the needs of Southeast Asia in area of mathematics education.

Some of the most significant courses are in the following areas:

• Scientific/Mathematical Thinking • Student Centred-Learning in Science/Mathematics • Problem Based Learning in Science/Mathematics • Realistic Mathematics • Active Teaching and Learning in Science • Integration of ICT in Science/Mathematics

Instruction

No. Course Title Course Schedule Specification of Participant (mathematics teacher)

Application Deadline

1 Developing Lesson Study in Mathematics Education

20 March – 9 April 2011 Junior Secondary School Teacher

5 March 2011

2 Teacher Made Teaching Aid

1–21 May 2011 Junior Secondary School Teacher

15 April 2011

3 Differentiated Instruction/Heterogeneous Mathematics Class Instruction

29 May–18 June 2011 High School Teacher/Vocational School Teacher

10 May 2011

4 Joyful Mathematics Learning

2–22 July 2011 Primary School Teacher 17 May 2011

SEAMEO Regional Centre for Quality Improvement of Teachers and Education Personnel (QITEP)

in Mathematics • Alternative Assessment • Teachers as Researchers • ICDL Programme • SEAMEO RECSAM-Deakin University Programs• SEAMEO QITEP in Mathematics Training Schedule

for 2011

Courses Offered:

• Enhancing Mathematics Learning Using Realistic Mathematics Education

• Clinical Supervision for Mathematics Education • Utilisation and Development of Computer Software

for Teaching Math • School-based Mathematics Curriculum Develop-

ment (SBCD) • Teacher-made Teaching Aids • Assessment in Mathematics • Tailor-made Mathematics Courses

In 2011, SEAMEO Regional Centre for QITEP in Mathematics has prepared several regular courses as follows



Country Number of Participant

Specification of Participant

Indonesia 14 key teachersCambodia 1 key teacherLao PDR 1 key teacher

Myanmar 1 key teacherVietnam 1 key teacher

Timor Leste 1 key teacherMalaysia 1 key teacher

Philippines 1 key teacherThailand 1 key teacherBrunei 1 key teacher

Singapore 1 key teacher

The number of participants needed for each course is as follows

QITEP in Mathematics is one of the SEAMEO (Southeast Asian Ministers of Education Organisa-tion) Regional Centres. The main function of QITEP in Mathematics is developing capacity building for mathematics teachers and education personnel (supervisor, headmasters, and administration staff) in SEAMEO Member Countries and conducting research on mathematics education.

In the fiscal year 2010, QITEP in Mathematics has successfully managed the 7 (seven) courses which are the core business of the Centre. This year, QITEP in Mathematics has conducted research on mathematics education which involved mathematics teachers in SEAMEO member countries. All of the programs done by Centre are fully funded by the Government of Indo-nesia. Since SEAMEO QITEP in Mathematics is a new Centre, in running the program the Centre absolutely needs to conduct benchmark to some other recognised Centres in Southeast Asia. Therefore, some official of QITEP in Mathematics conducted benchmark to Japan and Australia. In addition, QITEP in Mathematics has managed its first Governing Board Meeting fruitfully.

In the beginning of 2011, QITEP in Mathematics

has the opportunity to evaluate all the programs done in the previous year and set out the objectives for the future programs. This year, the Centre will organise four regular courses and three in-country courses. All the courses will accommodate the seven themes of the Centre’s core business. QITEP in Mathematics has a commitment to improve the quality of math-ematics education in Southeast Asia. In line with this commitment, the Centre conducts research focusing on Lesson Study. This research is a program to follow up the Lesson Study course that has been conducted the year before. The result of the research will be used as a guidance to develop the lesson study program in SEAMEO QITEP in Mathematics.

In addition to those main programs, the Centre plans to publish its first journal on mathematics educa-tion in the year of 2011. It will also continue benchmark to other international institutions to have best-practice sharing in improving the quality of programs set by QITEP in Mathematics. To improve the quality of teaching and learning in Mathematics education, QITEP in Mathematics prepares the Symposium on mathematics education innovation. In terms of assess-ment for the student’s achievement, the Centre plans to set the instruments for mathematics assessment within the Workshop on region-wide assessment program. In line with its vision, the issue of Education for Sustain-able Development will be implemented in QITEP in Mathematics’ programs.

In the fiscal year 2009/2010 and 2010/2011 the Government of Indonesia fully supports the programs of QITEP in Mathematics. I would like to seize this opportunity to extend our great gratitude to His Excel-lency Ministry of National Education of the Republic of Indonesia for the valuable support to QITEP in Mathematics’ programs. Hopefully, the programs of SEAMEO QITEP in Mathematics will be helpful for the quality improvement of Mathematics education in SEAMEO member countries.

Message from Director of Centre for QITEP

Prof. SubanarDirector

Tel. +62 881717Fax. +62 885752Email: [email protected], [email protected]: http://new.qitepinmath.org/index.php



In the 2011 New Years Honours list Professor Roy Kerr was given the award of Companion of the NZ

Order of Merit (CNZM) for his services to Astrophysics. This was for his work in the theory of rotating black holes, in the 1960s and later. This very high recogni-tion results from his discovery of the exact solution of Einstein’s equations for a rotating black hole. Subsequently, the Kerr solution was shown to be the only possible solution for these astrophysical phenomena. Consequently, his theoretical discovery is the basis for almost all research in astrophysics today. Indeed, the Kerr solution has been described by many as “the most important exact solution to any equation in physics”.

Well-known astrophysicist Stephen Hawking, in his bestselling book A Brief History of Time, describes the uniqueness of the Kerr solution. “In 1963, Roy Kerr, a New Zealander, found a set of solutions of the equa-tions of general relativity that described rotating black holes. These “Kerr” black holes rotate at a constant rate, their size and shape depending only on their mass and rate of rotation. If the rotation is zero, the black hole is perfectly round and the solution is identical to the Schwarzschild solution. If the rotation is nonzero, the black hole bulges outward near its equator (just as the earth or the sun bulge due to their rotation), and the faster it rotates, the more it bulges. So, to extend Israel’s result to include rotating bodies, it was conjectured that any rotating body that collapsed to form a black hole would eventually settle down to a stationary state described by the Kerr solution. . . [Subsequent research showed] that this conjecture had to be correct: such a black hole had indeed to be the Kerr solution.”

The Kerr solution, using what is now known as the Kerr metric, correctly and elegantly describes how space-time behaves in the four dimensional world about massive objects, such as steadily rotating stars or black holes. Such black holes are described by only their mass and angular momentum. This great mathematical simplicity reveals a deep and surprising simplicity

in Nature regarding such important objects. Professor Andy Fabian, OBE, FRS, points out that recent research proves that large black holes “define the final mass of virtually all galaxies through a feedback action of their own output. Kerr black holes thereby play a defining role in producing the Universe we see around us.” His historic paper published in Physics Letters A has been cited an amazing number of 767 times (up to 2009) Professor Kerr was born and

educated in NZ, entering immediately into year 3 at the University of Canterbury direct from school (St Andrews College), in 1951. He subsequently gained his PhD in 1959 from the University of Cambridge, and held appointments in the US before returning to NZ in 1971 as Professor of Applied Mathematics at his Alma Mater, the University of Canterbury. He became Head of the Department of Mathematics and Statistics in 1983. Today he is an Emeritus Professor at the University of Canterbury, and continues to be active in his research, both here and overseas (mostly in Italy). Expert referees involved are very much from a famous list of “Who’s Who” in Astrophysics: Sir Roger Penrose of Oxford, Professor A. C. Fabian of Cambridge, and Professor Fulvio Melia of Arizona. The last of these has recently published a book entitled Cracking the Einstein Code, in October, 2009, by the University of Chicago Press which is essentially a biography of Roy. It is highly recommended as a good read. We note he is very much at the top of this distinguished list and are glad that New Zealand (at last) has recognised the star amongst us. Your colleagues warmly congratulate him on this award.

Reproduced from New Zealand Mathematics Society Newsletter, No. 111, April 2011

Graeme WakeMassey University Auckland, New Zealand

Graham WeirIndustrial Research Ltd, Wellington, New Zealand

Roy Kerr Gains New Zealand Honour



Scientific Research is known to happen slowly but the t ime f rames pale into

insignificance compared to the years spent on some of the great unsolved mathematical problems.

One of these problems is the subject of a Marsden funded project for which Victoria Univer-sity mathematician Dr. Dillon Mayhew (pictured) is principal investigator. Dr Mayhew estimates that, despite working with a team of five collaborators, the central problem of the project may not be cracked until 2020, if at all.

One of those team members is Prof. Geoff Whittle who is also part of a separate collaborative research effort that has already spent 12 years working to prove Rota’s Conjecture. That was put forward by Italian Mathematician Gian-Carlo Rota in the early 1970s and is one of the central problems in matroid geom-etry. Prof. Whittle’s team is close to achieving its goal although close in the world of mathematics means at least a few more years.

Dr Mayhew’s research is also in the field of matroid theory which is a more modern form of geometry than the Euclidean geometry most of us studied at secondary school.

Rather than focusing on distance and angles, matroid theory concentrated on a finite number of points which do not change under projection — three points, for example, are always on a line no matter how you project the line.

Matroids live under the surface of “a tonne of different mathematical objects,” explains Dr Mayhew, “but are often bound together by a matrix or arrays of numbers.” But the matrices he is studying are not part of the rational number system that we use every day.

Instead they come from one of an infinite number of less well known systems. These include Galois Fields, or finite fields, which contain a finite number of elements, sometimes as few as two.

“For each number system you get a different family of matroids,” says Dr Mayhew. “Mathematicians have spent decades on the huge task of characterising each family of matroids for each number system.”

One discovery that has made the task easier is that

obstacles exist which mean certain matroids will never arise in a particular number system. In 1958, researchers proved that the two number system has one obstacle and, 21 years later, proof came that there are four obstacles in the three number system. In 2000, the four number system was found to have seven obstacles.

“ T h e l e n g t h o f t i m e between the results was not because we were being lazy, it just takes that long to figure it out,” says Dr Mayhew.

And here Rota’s Conjecture comes in. His yet to be proven theory is that there are a finite number of obstacles for every infinite number system.

While work continues on that question, Dr Mayhew’s team is tackling the five number system and trying to work out how many obstacles it contains.

Using computers, they have worked it out that it is at least 564. “Matroids are stubborn little creatures and they tend to grow explosively,” says Dr Mayhew.

“This one is much more difficult to figure out than the earlier ones. We know that 564 is the lowest number but we have no idea of the upper bound. If it turns out to be billions, even the most advanced computer won’t be able to find them all.”

And that is why the team cannot be sure it will succeed in its goal although Dr Mayhew says that they are unlikely to even consider giving up before another decade’s research.

As to how mathematicians solve these thorny prob-lems, Dr Mayhew says they brainstorm just as many other groups do.

“We sit around and think hard, stare that a white-board, draws things, argue, write results and get them published, and meet regularly with the other 30 or 40 mathematicians around the world working full time in matroid research.”

Dr Mayhew, who is also an accomplished French Horn player, says the most satisfying part of his work is bringing the unknown into the known.

“We are pushing ourselves and the technology we use as far as we can go to discover new and beautiful things.”

Reprinted with permission from Victoria University of Wellington, New Zealand, May 2011

Tackling the Big Unanswered Problems



Xiong Qinglai (1893–1921)

Xiong Qing lai was a Chinese mathematician from Yunnan. He was the person who introduced modern mathematics to China. He studied in Europe for eight years (1913 to 1921) before returning to China to teach. In 1921, he set up the Department of Mathematics of National Southeastern University (which was later renamed as the National Central University and Nanjing University). In 1926, Xiong became a professor of mathematics at Tsinghua University, where he influenced the path taken by Hua Luogeng, who later became another prominent mathematician.

Hua Luogeng (1910–1985)

Hua Luogeng was one of the leading mathematicians of his time and one of the two most eminent Chinese mathematicians of his generation, S S Chern being the other. Hua was the founder and pioneer of many fields

in China’s mathematics research. He wrote more than 200 thesis papers and monographs, many of which have become invaluable classic documents. Besides pure mathematics research, Hua also did a lot of work in the field of mathematics applications. The Hua Luogeng Prize was set up in 1992 in memory of him. The award is now the highest honour in Chinese mathematics community.

Chen Jingrun (1933–1996)

Chen Jingrun was a Chinese mathematician who made significant contributions to the area of number theory. His doctoral advisor was Hua Luogeng. Chen is ranked as one of the leading mathematicians in the 20th century and one of the most influential mathematicians in the history of China. In 1999, China issued an 80-cent postage stamp, titled “The Best Result of Goldbach Conjecture”, with a silhouette of Chen and the inequality:

Srinivasa Aiyangar Ramanujan (1887–1920)

Srinivasa Ramanujan was one of India’s greatest mathematicians. Even though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series and continued

Stamps on Asian Mathematiciansfractions. According to the prominent mathematician G H Hardy, Ramanujan is in the same league as Euler, Gauss, Newton and Archimedes. Ramanujan was brought by Hardy to Trinity College, Cambridge in 1914, and he graduated in 1916 with a Bachelor of Science by Research (the degree has been termed as a PhD from 1920). In 1918, Ramanujan was elected a fellow of the Cambridge Philosophical Society and a fellow of the Royal Society of London. He died one year after he returned to India.

Two Prizes have been created in Ramanujan’s name, one by the International Centre for Theoretical Physics (ICTP), in cooperation with the International Mathematical Union (IMU), another by the Shanmugha Arts, Science, Technology, Research Academy (SASTRA).

Damodar Dharmananda Kosambi (1907–1966)

Damodar Dharmananda Kosambi was an Indian mathematician and stat-istician who contributed to genetics by introducing Kosambi’s map function. He is well-known for his work in numismatics and for compiling critical editions of ancient Sanskrit texts. One of the most important contributions of Kosambi to statistics is the representation of a stochastic process as an infinite linear combination of orthogonal func-tions, which is now known as Karhunen–Loeve expansion. In the 1943 paper titled “Statistics in Function Space” presented in the Journal of the Indian Mathematical Society, Kosambi presented the Proper Orthogonal Decom-position. This was done some years before Karhunen (1945) and Loeve (1948). Kosambi was also a historian of ancient India who employed the historical materialist approach in his work. He was an enthusiast of the Chinese revolution and its ideals, in addition to being a leading activist in the World Peace Movement.



Book Reviews

39July 2011, Volume 1 No 3

Kähler Geometry of Loop Spaces

Armen SergeevMathematical Society of Japan, 2010, 228 pp

This book concerns Kähler geometry and the geometric quantisation of loop spaces. The main objects are three important examples of infinite Kähler manifolds: loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassman-nians of Hilbert spaces.

It consists of five parts: Part I. Preliminary Concepts. There are six chapters in this part for reviewing all necessary background material. Chapters 1 and 2 give a quick introduction to Fréchet manifolds and Fréchet Lie groups. The readers who are familiar with the basic knowledge of differentiable manifolds can easily follow the contents. Chapter 3 contains basic facts on flag manifolds and irreducible representations of semisimple Lie groups. The central extensions and cohomology of Lie groups and Lie algebras are reviewed in Chapter 4. The Grassmannians of a Hilbert space are discussed in Chapter 5. In Chapter 6, quasiconformal maps and their basic properties are reviewed.

Part II. Loop spaces of compact Lie groups. Various geometric properties of the loop space G of a compact Lie group G are discussed, such as symplectic structure, complex structure and Kähler structure. A canonical embedding of flag manifolds of a Lie group G into G is described and the Grassmannian realisation of G is constructed. The central extensions of loop groups and loop algebras are also studied. There are three chapters (7–9) in this part.

Part III. Spaces of complex structures. This part is devoted to various spaces of complex structures on the loop groups G. It consists of two chapters. Chapter 10 is about the Virasoro group and its coadjoint orbits, and Chapter 11 is about universal Techmüller space.

Part IV. Quantisation of finite dimensional Kähler manifolds. This is a brief introduction to the geometric quantisation of finite dimensional Kähler manifolds, which consists of three chapters (12–14) concerning Dirac quantisation, Kostant–Souriau presentation and Blattner–Kostant–Sternberg quantisation.

Part V. Quantisation of loop spaces. After solving the geometric quantisation problem for the loop space of a d-dimensional vector space in Chapter 15, a geometric quantisation of the loop space G of a compact Lie group G is constructed in Chapter 16. This part provides nice representations and twister quantisation of loop groups. The study on the geometry and topology of loop spaces is motivated by the relation of these spaces and various problems in modern mathematical physics, such as string theory. This book gives a good introduction to the Kähler geometry of loop groups. Various geometric properties of the loop groups are explored in a concise way with all necessary concepts reviewed. In addition to geometers, this book could be a good reference for topologists. The geometric properties of loop groups may admit applications to the homotopy theory of loop groups. This book can be selected as a main reference in one-semester topic courses. For graduate students in geometry and topology, this book can be listed as one of basic references.

Jie WuNational University of Singapore

Markov Chains and Decision Processes for Engineers and Managers

Theodore J. SheskinCRC Press, 2010, 492 pp

Writing yet another book about Markov chains and Markov decision processes needs — without doubt — some justification. The author of the present textbook reveals his motives in the preface: most books on these topics are highly theoretical or, else, merely provide algorithms to solve particular problems,

but without explaining the intuition behind the single steps of these algorithms. This book was written with the explicit intention to embrace a bit of both ends of the spectrum.

The author introduces the basics of Markov chains, Markov chains with rewards and Markov decision

Book Reviews


processes for finite state spaces. (Keep this in mind when you come across the statement that all irreduc-ible Markov chains are recurrent!). Many standard quantities around these processes are discussed, such as stationary distributions, properties of first passage times, and expected average rewards. There is also a section on state reduction techniques and hidden Markov chains. As promised in the book’s preface, almost no proofs are given. Instead, the author often justifies a general formula by doing the corresponding calculations with quite concrete Markov chains, either considering just a few states or assuming a simplifying structure in the transition probability matrix.

With this approach, the book does, on one hand, provide the practitioner (engineer and managers) with concrete formulae to tackle specific questions involving Markov chains. On the other hand, the author tries to give the reader some insight into how these results are derived — in this case, as non-mathematicians are targeted, by means of solid heuristics, rather than mathematical proofs. These are noble motives — isn’t that exactly what we expect of a good textbook? To develop a solid piece of theory (of course not too technical, please), clearly explained and well motivated, exemplified with many, many interesting applications? As for every textbook, the author has to find the difficult balance between all these objectives, which, at the end of the day, is probably a matter of taste. I agree that it is helpful for the student to calculate the formula for the stationary distribution of a general two- or three-state Markov chain and provide some examples with explicit numbers. But how rewarding can it be to go through the reward evaluation equations for a general five-state Markov chain with rewards? Probably not as much as the name of these equations would suggest. With the availability of modern software, solving linear equations is very easy and many calculations in the book seem therefore dispensable.

So, would I use this textbook for my course on Markov chains? I will certainly take it out of my shelf should I need to provide my students with more exercises, as there are plenty of interesting hands-on examples in this book. But to explain to them the abstract concepts behind Markov chains and Markov decision processes? Maybe not.

Adrian RöllinNational University of Singapore

Roads to Infinity

John StillwellA K Peters Ltd, 2010

In 1963, Edwin E. Moise published Elementary Geom-etry from an Advanced Stand-point and his book became a classic. Roads to Infinity could well be entitled Advanced Logic from an Elementary Standpoint and deserves the same outcome. Its subtitle is actually The Mathematics of Truth and Proof, which well describes its content.

The book consists of eight short chapters. Each chapter begins with a natural mathematical question involving logic or sets and proceeds with the historical sequence of responses to that question. For example, Chapter 1 concerns Cantor’s Diagonal Argument that there can be no countable list of real numbers and deals with the existence and construction of transcendentals, with applications to the cardinality of subsets, to measur-ability of sets of reals and to unprovability. Traces of the diagonal argument recur throughout the book.

Other chapters deal with ordinals, formal systems and non-decidability, computability and large cardinal axioms. One reason I call the book “elementary” is that certain technical details, such as Gödel’s arithmetisation of predicate logic and the Proper Forcing Axiom to show independence of additional set theoretic axioms, are relegated to the references. On the other hand, the reasons for these omissions are carefully explained and a simple overview is always presented.

One of the most enjoyable features is Stillwell’s use of techniques of logic and set theory to solve real math-ematical problems, concerning properties of measur-ability and the unsolvability of the word problem for semigroups and groups. He is particularly concerned with theorems that are true, but not provable within the theory in which they are stated. For example, one result in elementary number theory is Goodstein’s Theorem: take any positive integer n and express it in complete 2-adic form, i.e. as a sum of powers of 2 in which the powers themselves are also in 2-adic form, for example,

22 134 2 2+= + . Now replace each 2 by 3, subtract 1 and write the result in 3-adic form, in this case

33 13 2+ + . Repeat the procedure, replacing 3 by 4 and so on. Although the numbers you get seem to increase

Book Reviews Book Reviews


rapidly, Goodstein’s theorem states that after finitely many steps, you reach zero. This remarkable result has an even more remarkable proof. Suppose nj is the j-adic number constructed from n at the jth step. Replace each j in nj by w , to get nj(w), a countable ordinal in Cantor Normal Form. This sequence of ordinals satisfies nj ≤ nj(w) and nj(w) > nj+1(w), because of the subtraction of 1 in moving from nj to nj+1. But there is no infinite properly descending chain of ordinals, so after finitely many steps, you get 0 ≤ nj ≤ nj(w) = 0. Warning: don’t try this at home. Stillwell points out that the least j for which 4j = 0 is 3 · 2402653211 − 1.

Another enjoyable feature is Stillwell’s uniform coverage of unprovability, undecidability and non-computability, leading naturally to the introduction of large cardinals. For example, inaccessible cardinals, which cannot be proved to exist in Zermelo–Fraenkel set theory with the axion of choice, are introduced to prove the consistency of ZFC, and so of predicate logic. Furthermore, he illustrates unprovability using natural mathematical examples such as the Paris–Harrington Theorem of combinatorics. Other examples, from graph theory, are Kruskal’s theorem that for every infinite sequence (Tk) of trees there are indices i and j such that Ti embeds in Tj, and what Stillwell calls “the hardest theorem in graph theory”, the Graph Minor Theorem, which is Kruskal’s Theorem with “tree” replaced by “finite simple graph”.

Among the many innovative features of the book is Stillwell’s decision to abandon material implication in formal predicate logic, replacing the proposition P ⇒ Q by its classical equivalent (not P or Q), and modus ponens as a rule of inference by the corresponding branching rules of Gentzen’s Natural Deduction. The advantage is that no formula appears in a proof other than one which is already a fragment of the hypothesis or the conclusion. Consequently, proofs are algo-rithmic. The disadvantage is that proofs are no longer linear, but have the form of a directed tree. Nevertheless, this proof tree is locally finite: its root is the conclusion of the theorem, each edge represents one of the rules of inference, and its leaves are tautologies of the form Pw¬P. Thus the validity of each leaf implies the validity of the root. This procedure mimics the way in which Gentzen proved the consistency of Peano arithmetic.

Another unusual feature is Stillwell’s emphasis on the “forgotten heroes” of Logic: Emil Post who anticipated both Gödel and Turing, and Gerhard Gentzen who saw how to bypass Gödel’s Incompleteness Theorems

by introducing proofs based on induction on ordinals larger than w, which enabled his proof of consistency for arithmetic and later led to consistency proofs for set theory.

The omission of complete proofs mentioned earlier and of exercises means that the book must be supplemented in order to become a textbook for a course in logic. But that is not its stated intention. Rather, it is suitable for self-study by a diligent student in mainstream mathematics and it is excellent background material for computer scientists and mathematicians in other fields. The historical notes alone are worth perusing by anyone who is interested in the development of mathematical ideas.

Phill Schultz The University of Western Australia, [email protected]

Reproduced from Gazette of Australian Mathematical Society, Vol. 38, No.1, March 2011

The 5th International Congress on Mathematical Biology Quadrennial (ICMB) was successfully held in Nanjing during June 3–6, 2011. The

conference was organised by Chinese Society for Mathematical Biology (CSMB), and was co-organised by Nanjing University of Information Science & Technology (NUIST), Nanjing University of Science & Technology (NJUST) and Jiangsu Mathematical Society (JMS). Prof. Lansun Chen (Chairman of ICMB2011, Director of CSMB, Academia Sinica, China), Prof. Avidan U. Neumann (Bar-Ilan University, Israel), Prof. Zhonglin Wu (Executive Vice Secretary-General of JMS), Prof. Qun Yin (Vice President of NJUST), Prof. Yao Wang (Honorary Chairman of ICMB2011, Vice President of NUIST) attended the conference. The opening ceremony was chaired by Prof. Yong Jiang (Chairman of Organising Committee for ICMB2011, Dean of College of Math & Physics, NUIST). Vice President Yao Wang delivered a speech of salutatory, welcoming all the participants to the ancient capital Nanjing to discuss their work on mathematical biology. Prof. Jingan Cui addressed the conference on behalf of Prof. Lansun Chen.

Many international authoritative experts from the US, Britain, Canada, Japan, Finland, Israel and South Korean were invited to give talks at the conference. There were 7 plenary addresses and 21 invited reports. The participants exchanged their work by oral reports, poster presentation and written reports. Altogether 346 international experts and scholars participated the conference, discussing the academic and social

Fifth International Congress on Mathematical Biology

concerns. 276 excellent papers were selected among numerous papers submitted to the conference. Three volumes of hardback editions of the collected papers will be published by the British World Academic Publishing Company. The conference has effectively promoted the communication between the related disciplines.

The 5th International Congress on Mathematical Biology has attracted a lot of media attention. The reporters from the Yangtse Evening Post and Modern Express have come to the conference and made relative reports about it.

Jiang YongNanjing University of Information Science and Technology, [email protected]

The group photo of all participants

The conference site



From February 27 to March 4 , 2011, the Execut ive Committee of the Interna-

tional Mathematical Union (IMU) visited Perth for their first meeting in Australia. The committee consists of a host of eminent mathematicians, pictured above with the manager of the IMU secretariat. They are, from left to right: Vasudevan Srinivas (India), Marcelo Viana (IMU Vice-President, Brazil), László Lovász (IMU Past President, Hungary), Wendelin Werner (France), Manuel de León (Spain), Cheryl Praeger (Australia), Ingrid Daubechies (IMU President, USA), Christiane Rousseau (IMU Vice-President, Canada), Martin Grötschel (IMU Secretary, Germany), Sylwia Markwardt (manager of the IMU secretariat), Alexander Mielke (IMU Treasurer, Germany), John Toland (UK) and Yiming Long (China).

Following the two-day committee meeting, a work-shop was held, with a dazzling line-up of lectures from the IMU Executive Committee. These lectures were accessible to a broad mathematically inclined audience, and were recorded via Lectopia. The presenters and titles of the talks were:

• IngridDaubechies:“Comparingsurfacesusingmasstransportation”

• LászlóLovász:“Generalquestionsaboutextremalgraphs”•ChristianeRousseau:“MathematicsofPlanetEarth”• JohnToland:“Waveswithprescribeddistributionof

vorticity”•MarceloViana:“Entropy,oldandnew”• WendelinWerner:“Randomsurfacesandfractal

carpets”

Additionally, the workshop included a forum consisting of three talks on “Mathematics: How a nation plans for the future — the Spanish, Indian and Chinese experience”, by Manuel de León, Vasudevan Srinivas and Yiming Long. These three members of the IMU each had direct experience in the organisation of the International Congress of Mathematicians in their respective countries.

On the first day of the two-day workshop, an

MathWest Workshop and IMU Meetingat The University of Western Australia

industry breakfast was sponsored by the Dean of the Faculty of Engineering, Mathematics and Computing (Professor John Dell) and the Dean of the Faculty of Education (Professor Helen Wildy). Martin Grötschel (IMU) gave an excellent presentation, “Production Factor Mathematics”, on the application of optimisa-tion methods in industry. Martin pointed out that the mathematics that sped up algorithms had actually contributed more to the solution of these problems than increases in computer speed. His talk was followed by a presentation by UWA’s Professor of Zoology and WA Chief Scientist, Professor Lyn Beazley, on the ever-increasing role of mathematics in science and industry.

Following the workshop, most of the IMU Execu-tive made a two-day trip to the south-west of Western Australia, and in particular, to Bunbury Cathedral Grammar School, where some 120 students from local schools were in attendance. Martin Grötschel spoke again about maths in the real world, from the routing of garbage collection to the electro-physiology of the heart. Martin’s presentation was followed by an interac-tive activity given by us (John Bamberg and Michael Giudici) on “The game of Nim”.

We are extremely grateful and privileged to have had the IMU Executive hold their meeting in Perth, to have been enlightened by their presentations, and to have discussed with them matters mathematical.

Reproduced from Gazette of Australia Mathematical Society, Vol. 38, No. 2, May 2011

John BambergThe University of Western Australia

Michael GiudiciThe University of Western Australia

John Bamberg and Michael Giudici



News from Australia

Australian Academy of Science Fellows

Seventeen of Australia’s leading scientists were honoured on 23 March 2011 by election to the Australian Academy of Science (see http://www.science.org.au/news/media/24march11.html). Those honoured included the following mathematical scientists.

Professor Joseph John Monaghan FAA “distinguished for his work in the development of smoothed particle hydrodynamics with broad applications in astro-physical, geophysical and engineering problems”.

Professor Ian Richard Petersen FAA FIEAust FIEEE “distinguished for his work on robust control theory with innovative advances enabling the synthesis of robust state feedback controllers using standard software tools”.

Ian Petersen is a Scientia Professor and Federation Fellow in the School of Engineering and Information Technology at the University of New South Wales (Australia Defence Force Academy). He received a Bachelor of Engineering degree in Electrical Engi-neering from the University of Melbourne in 1979 and a PhD in Electrical Engineering from the University of Rochester in 1984. From 1983 to 1985 he was a Post-doctoral Fellow at the Australian National University. In 1985 he joined the University of New South Wales at the Australian Defence Force Academy. From 2002 to 2003, he was Executive Director in Mathematics, Information and Communications for the Australian Research Council and in 2004 he was Acting Deputy Vice Chancellor (Research) for the University of New South Wales. He has served as an Associate Editor for the IEEE Transactions on Automatic Control, Systems and Control Letters, Automatica and SIAM Journal on Control and Optimisation. Currently he is an Editor for Automatica. He is a Fellow of the IEEE. His main research interests are in robust control theory, quantum control theory and stochastic control theory.

Professor Mathai Varghese FAA FAustMS “distin-guished for his work in geometric analysis involving the topology of manifolds, including the Mathai–Quillen formalism in topological field theory”.

Mathai Varghese obtained his PhD from Massachusetts Institute of Technology (MIT) in 1986 under the

supervision of the Fields Medallist Professor Daniel Quillen, and was appointed a Dickson Instructor at the University of Chicago. In 1989, he moved to the University of Adelaide, where he has been a Professor since 2006 and is currently an Australian Professorial Fellow of the Australian Research Council, and Director of the Institute for Geometry and its Applications. In 2000 he was awarded the Australian Mathematical Society Medal, in 2000–2001 he was awarded a Clay Research Fellowship and position of Visiting Scientist for a year at MIT, and in 2006 he was appointed a Senior Research Fellow for a semester at Erwin Schrödinger Institute in Vienna. From 2006 to 2009 he was Vice-President (in charge of annual conferences) of the Australian Mathematical Society and has also been a member of several national committees. Much of his research work is concerned with geometric analysis involving the topology of manifolds, and mathematical problems that originate from physics, such as topological field theories, the fractional quantum Hall effect and string theory.

Professor Aibing Yu FAA “distin-guished for his work in particle science and technology, including methods to simulate and model the motion of individual particles within large populations in flowing systems”.

Aibing Yu is a Federation Fellow and Scientia Professor in the School of Materials Science and Engineering at the University of New South Wales (UNSW). He obtained a BEng in 1982 and a MEng in 1985 from Northeastern University, China, a PhD in 1990 from the University of Wollongong and a DSc in 2007 from the University of New South Wales. He is a world-leading scientist in particle and powder technology and process engineering, and is recognised as an authority in particle packing, particulate and multiphase processing, and simulation and modelling. He has authored more than 550 publications in these areas and is currently on the editorial board of more than 10 journals. He developed and directs a world class research facility, Simulation and Modelling of Particulate Systems (SIMPAS), at UNSW. Professor Yu is the recipient of various prestigious fellowships, including a CSIRO Postdoctoral Fellowship (1990–1991), an ARC Queen Elizabeth II Fellowship (1993–1997), an Australian Professorial Fellowship (2005–2009), a Federation



Fellowship (2008–2012), and the Royal Academy of Engineering’s Distinguished Visiting Fellowship. He has also received the Josef Kapitan Award from the Iron and Steel Society, the Ian Wark Medal and Lecture from the Australian Academy of Science, and the Exxon Mobile Award from the Australian and New Zealand Federation of Chemical Engineers, and was the NSW Scientist of Year 2010 in the category of Engineering, Mathematics and Computer Science. He was elected as a Fellow of the Australian Academy of Technological Sciences and Engineering in 2004.

Winner of the 2011 J. H. Michell Medal

The J. H. Michell Medal is awarded annually by ANZIAM to at most one outstanding new researcher who has carried out distinguished research in applied and/or industrial mathematics within Australia and/or New Zealand. At the recent ANZIAM Annual Meeting, the 2011 J. H. Michell Medal was awarded to Dr Frances Kuo.

Dr Kuo completed both her Bach-elor and PhD degrees at the Univer-sity of Waikato in New Zealand. She then joined the School of Mathematics and Statistics at the University of New South Wales in 2003 as a Research Associate, before obtaining a highly competitive

UNSW Vice-Chancellor’s Research Fellow position. She followed up this distinction by winning a most prestigious ARC QEII Research Fellowship, which she holds until the end of this year, when she will take up a Senior Lectureship at UNSW.

Dr Kuo’s achievements in Applied Maths are manifold, substantial, and sustained. She is a recognised leader in the theory and applications of high-dimensional integration and approximation, quasi-Monte Carlo methods and information-based complexity, interested in applications in finance, statistics and porous media flow. She has published 29 journal articles and 3 articles in highly regarded conference series. These include 11 papers in the leading international journal in her field, the Journal of Complexity, one of which was a sole-authored paper for which she received the Information-Based Complexity Young Researcher Award.

News from China

School of Mathematical Sciences at the University of Science and Technology of China

Inauguration ceremony was held on May 19, 2011

for the formation of School of Mathematical Sciences in University of Science and Technology of China (USTC), National Center for Mathematics and Inter-disciplinary Science Hefei Branch, and Wu Wenjun Key Mathematics Laboratory of Chinese Academy of Sciences (CAS). The Department of Mathematics, the predecessor of School of Mathematical Sciences at USTC, was founded by the famous mathematician Hua Luogeng in 1958. He served as the first Chair of the department. Many scientists such as Guan Zhao-Zhi, Wu Wenjun, Feng Kang and Wang Yuan had taught there. This old department of USTC had a glorious tradition and history.

In the new era, in order to better promote the devel-opment of mathematics, the University decided to establish a new School of Mathematical Sciences based on the old Department of Mathematics. With the strong support from the Bureau of Basic Sciences, Mathematics, Physical Sciences Division of the National Natural Science Foundation, and the School of Math-ematics, National Center for Mathematics and Interdis-ciplinary Science Hefei Branch, and Wu Wenjun Key Mathematics Laboratory of CAS were formed. These marked a new milestone for mathematical sciences in USTC. The founding of these centres also provides a solid platform for a more effective support and motiva-tion to the development of Chinese mathematics.

Chinese Scholar Elected in 2011 U.S. Industrial and Applied Mathematics Fellow

The Society for Industrial and Applied Mathematics (SIAM) named 34 academics and professionals to its 2011 Class of Fellows for their outstanding contribu-tions to applied mathematics and computational science through research in the field and service to the larger community.

Professor Ya-xiang Yuan (Chinese Academy of Sciences) is the only mathematician from China to be named as 2011 SIAM Fellow. He was honoured for his contributions to nonlinear optimisation and leadership of computational mathematics in China.

This distinguished group of individuals from wide-ranging areas was nominated by the SIAM community and will be recognised in July at the 7th International Congress on Industrial and Applied Mathematics (ICIAM 2011) in Vancouver, British Columbia.

Feimin Huang Received 2011 Young Scientist AwardOn June 17, 2011, the first “Chinese Academy of



Sciences Talent Development Activity Theme Day” was held in Beijing, 10 outstanding talented youth (under the age of 40) were awarded the 2011 Chinese Academy of Sciences Young Scientist. Professor Feimin Huang was one of them.

Demetrios Christodolou is Professor of Mathematics and Physics at Eidgenössische Technische Hoch-schule (ETH, Swiss Federal Institute of Technology) in Zurich, Swit-zerland. Born in 1952, he received his BA and PhD from Princeton University and has taught at Syra-cuse University, Courant Institute of Mathematics and Princeton University. He is a member of the American Academy of Arts and Sciences and European Academy of Sciences. His earlier awards were the Otto Hahn Medal (1981), MacArthur Fellow (1993), American Mathematical Society’s Bocher Memorial Prize (1999) and Tomalla Prize for gravity research (2008). His work on global nonlinear stability of Minkowski spacetime and the existence of “naked singularities” are significant contributions to general relativity.

Richard Streit Hamilton is Davies Professor of Mathematics at Columbia University. Born in 1943, he received his BA from Yale University and PhD from Princ-eton University and has taught at University of California at Irvine, UC at San Diego and Cornell

University. He is a member of the National Academy of Sciences and American Academy of Arts and Sciences. His earlier awards were the Oswald Veblen Prize in Geometry (1996), Clay Research Award (2003) and American Mathematical Society’s Leroy P. Steele Prize (2009). His most significant work is in differential geometry, in particular, geometric analysis. He is well known for the discovery of Ricci flow and for initiating a research program that culminated in the proof of Thurston’s Geometrisation Conjecture and solution of Poincare’s Conjecture by Grigori Perelman.

(Y. K. Leong, July 8, 2011)

News from India

Ravindran Kannan Awarded Knuth Prize 2011

The renowned mathematician and computer scientist Ravindran Kannan has been awarded the prestigious Knuth Prize for the year 2011. For the Indian math-ematical community, it is a great piece of news.

Ravindran Kannan is currently a Principal Researcher at Microsoft Research India, where he leads the

Feimin Huang, first row, fifth from the left

Feimin Huang has been working on research in equations for hyperbolic conservation laws and viscous conservation laws. He solved the isothermal gas dynamical equations (i.e., adiabatic exponent = 1), the Cauchy problem with vacuum global existence, and obtained the weak solutions to these long outstanding mathematical problems. He also obtained a new entropy condition (i.e., the energy entropy condition) on the proposed new zero-pressure flow. Furthermore, he proved the unique-ness of weak solutions on the zero-pressure flow; also verified the stability of the contact discontinuity wave in compressible Navier–Stokes equations, and improved the stability theory of the basic waves in viscous hyperbolic conservation laws.

News from Hong Kong

Shaw Prize in Mathematical Sciences 2011

Dubbed “Asia’s Nobel Prize”, the Shaw Prize was estab-lished in 2002 by the entrepreneur-philanthropist Run Run Shaw to recognise breakthroughs in astronomy, life science and medicine, and mathematical sciences with a monetary value of one million US dollars each. The names of this year’s recipients were announced in Hong Kong on June 7, 2011 and the prize giving ceremony scheduled for September 28, 2011. The prize in mathematical sciences is awarded in equal shares to Demetrios Christodolou and Richard Streit Hamilton “for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology”.



algorithms research group. He is also the first adjunct faculty of the Computer Science and Automation Department of the Indian Institute of Science. Before joining Microsoft, he was the William K. Lanman Jr. Professor of Computer Science and

Professor of Applied Mathematics at Yale University. He has also taught at Massachusetts Institute of Technology (MIT) and Carnegie Mellon University (CMU). The Association for Computing Machinery’s (ACM) Special Interest Group on Algorithms and Computation Theory (SIGACT) will present its 2011 Knuth Prize to Ravi Kannan for developing influential algorithmic techniques aimed at solving long-standing computational problems.

Ravi Kannan did his B.Tech at Indian Institutes of Tech-nology (IIT), Bombay and PhD at Cornell University. His research interests include Algorithms, Theoretical Computer Science and Discrete Mathematics as well as Optimisation. His work is mainly focused on efficient algorithms for problems of a mathematical (often geometric) flavour that arise in Computer Science. He has worked on algorithms for integer programming and the geometry of numbers, random walks in n-space, randomised algorithms for linear algebra and learning algorithms for convex sets.

The Knuth Prize was first awarded in 1996. It is awarded every one and a half years by ACM SIGACT and the IEEE Computer Society’s Technical Committee on the Mathematical Foundations of Computing. The prize includes an award of US$5000. Prizes are awarded in alternation at the ACM Symposium on Theory of Computing and at the IEEE Symposium on Foundations of Computer Science, which are both among the most prestigious conferences in theoretical computer science.

In contrast with the Gödel Prize, which recognises outstanding papers, the Knuth Prize is awarded to individuals for their overall impact in the field.

News from Japan

Alliance for Breakthrough Between Mathematics and Sciences

The Alliance for Breakthrough between Mathematics and Sciences was established in 2007 by the Japan Science and Technology Agency (JST) as part of the Core Research for Evolutional Science and Technology

(CREST) program. It is directed by Yasumasa Nishiura at the Research Institute for Electronic Science (RIES), Hokkaido University. The first aim of this alliance is to demonstrate and maximise the potential of mathematics as a “connective knowledge” in society, by applying the voluminous mathematical assets accumulated so far to some of the most difficult challenges encountered today. The second aim is to employ mathematics as a core component in the formation of a “language of mutual understanding” for all humanity.

As research initiatives of the alliance, the Precursory Research for Embryonic Science and Technology (PREST) program provides grants for individual research projects by young researchers started in 2007. Following this is the CREST program for team based research in 2008. More than 30 PREST research projects and 13 CREST projects are already under way. These projects address a number of areas in materials science, life sciences, environmental sciences, information and communications, transport, finance and medicine, with projects such as “A mathematical challenge to a new phase of material science” (Team leader: Prof. Motoko Kotani), “Innovations in controlling hyper redundant and flexible systems inspired by biological locomotion” (Team leader: Prof. Ryo Kobayashi) and “Harmony of Gröbner bases and the modern industrial society” (Team leader: Prof. Takayuki Hibi) being selected for CREST grants.

The detailed information can be found in the alliance webpage: www.math.jst.go.jp.

The CREST Project: A Mathematical Challenge to a New Phase of Material Science, Based on Discrete Geometric Analysis

The development of high-performance materials serves the purpose of improving the well-being of human-society. Now that we observe and design nano-scale systems for material development, demands for a new mathematical theory to describe nano-scale phenomena are increasing. Supported by the Japan Science and Technology Agency (JST) under the program “Breakthrough by Mathematical Science Researches towards the Resolution of Issues with High Social Needs”, the present project started from October 1, 2008 with a mutually beneficial partner-ship between mathematics and material science. Our research project aims to meet these demands and to develop new mathematical models. This would enable us to design new compounds and yield their



prescribed functional properties. In the future, this research team is expected to develop the research core of “mathematical materials sciences” with high integration of mathematical science, information science, physical chemistry, chemical physics, and materials science.

The project is directed by Motoko Kotani at Math-ematical Institute, Graduate School of Science, Tohoku University. Refer to the project webpage for details:http://www.mathmate.tohoku.ac.jp/english/index.html

The 9th Takagi Lectures Held in Kyoto on June 4

The Takagi Lectures are research survey lectures of the highest level, by the finest contemporary mathemati-cians, which are held twice a year in Japan. The lectures bear the name of Prof. Teiji Takagi (1875–1960), the creator of Class Field Theory and the founder of the Japanese School of Modern Mathematics. He served as one of the first Fields Medal Committee Members together with G. D. Birkhoff, E. Cartan, C. Carathéo-dory, and F. Severi in 1936. The videos of the lectures are available on the Internet.http://www.ms.utokyo.ac.jp/~toshi/takagi_video/

The 9th Takagi Lectures were led by the two distin-guished speakers, Simon Brendle (Stanford) and Carlos E. Kenig (Chicago) at the Research Institute for Mathematical Science (RIMS) Kyoto on June 4, 2011, where both held lectures on subjects intended for a wide range of mathematicians. Prof. Brendle spoke on “Evolution equations in Riemannian geometry”, while Prof. Kenig discussed “Critical nonlinear dispersive equations: Global existence, scattering, blow-up and universal profiles”.

The lecture notes will be published by the Japanese Journal of Mathematics (JJM).http://www.ms.u-tokyo.ac.jp/~toshi/takagi/

The 3rd MSJ–SI “Development of Galois–Teich-müller Theory and Anabelian Geometry”

MSJ–Seasonal Institute has been held annually by MSJ since 2008. Each year, the topic of the workshop is chosen by MSJ and leading mathematicians in that area from all over the world are invited accordingly. MSJ especially emphasises on the importance of interac-tion with Asian mathematicians and the invitation of promising young Asian students.

The 3rd MSJ–SI Meeting “Development of Galois–Teichmüller Theory and Anabelian Geometry” was held at the Research Institute for Mathematical Science (RIMS), Kyoto University, during the period October 25–30, 2010 as a joint MSJ–RIMS project, where 25 lectures were presented covering introductory survey talks as well as advanced research announcements. It was organised by Hiroaki Nakamura (chair), Florian Pop, Leila Schneps and Akio Tamagawa. There were 107 participants (38 from overseas, 21 graduate students). The conference was accompanied by a satellite meeting, “Galois theoretic arithmetic geometry’’ held at International Institute for Advanced Studies and Keihanna Plaza Hotel in Kyoto suburb during October 19–24, 2010 as one of the RIMS-Camp-Style Seminars. Proceedings volume collecting contributions from both meetings will be published as “Galois–Teichmüller Theory and Arithmetic Geometry” in Advanced Studies in Pure Mathematics (ASPM) series of the Mathematical Society of Japan.

Noriko Mizoguchi Awarded the 31st Saruhashi Prize

The 31st Saruhashi Prize was awarded to Dr. Noriko Mizoguchi, associate professor at Tokyo Gakugei University. Dr. Mizoguchi is internationally well known for her outstanding contributions to “Asymptotic analysis of the blow up phenomena”.



Dr. Mizoguchi’s main area of interest is asymptotic analysis of the blow up phenomena of nonlinear diffusion equations. She developed various methods in asymptotic analysis to study the behaviour of solutions at blow up points, and successfully settled many unsolved

problems. She showed that semilinear heat equations with supercritical exponent have no self-similar solu-tions. She found a condition under which solutions can be continued beyond a blow up point, which enabled her to construct solutions with infinitely many blow up points. Her results concerning the speed of blow up of solutions are remarkable as well. For example, she showed that the blow up speed is algebraic in time when the equation has supercritical exponent.

The Saruhashi Prize is one of the most prestigious Japanese awards in science, covered by major newspa-pers and other media. Since 1981, the prize has been awarded annually to a Japanese female researcher who made outstanding contributions to natural science. The past laureates from mathematics are: Dr. Mariko Yasugi, Dr. Shihoko Ishii and Dr. Motoko Kotani.

The prize was founded by Dr. Katsuko Saruhashi (1920–2007), a geochemist, who discovered that the Pacific Ocean releases CO2 twice as much as it absorbs through the meticulous measurement of CO2 contained in seawater. She also conducted pioneering researches in the 1950s on the diffusion of radioactive debris from atomic bomb tests.

Takuro Mochizuki Awarded the Japan Academy Prize

Dr. Takuro Mochizuki was awarded the Japan Academy Prize by the Japan Academy. Dr. Mochizuki, an associate professor at the Research Institute for Math-ematical Sciences, Kyoto University is recognised for his outstanding contributions to “Study on pure twistor D-modules”. He is the 2006 MSJ Spring winner and the 6th JSPS prize awardee.

Hirosi Iritani and Yoshitaka Kida Will be Awarded the Young Scientists’ Prize

Dr. Hirosi Iritani and Dr. Yoshitaka Kida will be awarded the Young Scientists’ Prize of Commenda-tion for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology, FY2011. Dr. Iritani, an associate professor at the

Graduate School of Science, Kyoto University, and Dr. Kida, a GCOE program-specific associate professor at the Graduate School of Science, Kyoto University, are recognised for their outstanding contributions respectively to “Study on quantum cohomology” and to “Study on discrete groups and measure equivalence”.

News from Korea

The Korean Mathematical Society Successfully Hosted 2011 KMS Spring Conference at Korea University, Seoul

2011 Korean Mathemat-ical Society (KMS) Spring Conference was held on April 30, 2011 at Korea University in Seoul, Korea. The aim of the 2011 KMS Spring Conference was to bring together researchers working in many different areas of Mathematics to foster exchange of new ideas and to promote

collaborations.

Plenary speaker was Shui-Nee Chow (Georgia Institute of Technology) and there was a special lecture by the President of National Research Foundation of Korea, Se-Jung Oh. Other notable invitees included Lucian Beznea (Institute of Mathematics of the Romanian Academy), Xuding Zhu (Zhejiang Normal University), Sangho Kum (Chungbuk National University), Sung Ho Park (Hankuk University of Foreign Studies), Kyung-Ah Shim (National Institute for Mathematical Sciences), Chan Woo Yang (Korea University), Young Tak Oh (Sogang University), Seonhee Lim (Seoul National University), Jongmin Han (Kyung Hee Univer-sity), and Sunwook Hwang (Soongsil University). In addition, there was an invited lecture by Soonsik Kwon (KAIST), the winner of 2010 Sangsan Prize for Young Mathematicians.

There were total 181 presentations in 8 special sessions and poster sessions including plenary and invited presentations.

2011 Korean Mathematical Society Paper Awards

Prof. Jung Hee Cheon of Seoul National University and



Professor Jong-Sheng Guo received his PhD degree from the University of Minnesota in 1989. He is currently a Professor in the Mathematics Department of Tamkang University, Taipei. His main research interests are formation of singularity, wave phenomena, free boundary problem, and mathematical biology.

Professor Chia-Fu Yu received his PhD degree from the University of Pennsylvania in 1999. He is currently a Research Fellow in the Institute of Mathematics, Academia Sinica, Taipei. His main research interests are arithmetic of moduli spaces of abelian varieties, geometry Shimura varieties, the interaction of theory of automorphic representations with arithmetic geometry.

News from Thailand

First Thailand Mathematics Contest Awards Presen-tation

Mr. Chinnaworn Boonyakiat, the Minister of Education, presided over the presentat ion of the medals and trophies by Mr. Kasem Watanachai, the Privy Councilor, to the winners of the First Thailand Mathematics Contest. The event took place on April 30, 2011 at the Auditorium of Siam University. The winners of this contest will be the representatives of Thailand in the International Mathematics Contest which will take place in Singapore soon.

The Minister informed all in attendance that students talented in mathematics had tried very hard to win this contest at inter-nat ional level . The Minister also reiterated the fact that the Ministry of Education recognises the importance of learning and

teaching science and mathematics. As such, the Institute for the Promotion of Teaching Science and Mathematics (IPST) has been established in order to further develop the potential of Thai students in these areas. In addition, Her Royal Highness Princess Maha Chakri Sirindhorn has gracefully accepted the posts as the President of the Promotion of Academics Olympiads and Development of Science Education Foundation.

Jae-Hoon Kwon of University of Seoul received 2011 KMS Paper Awards in recognition of their outstanding papers, “Discrete logarithm problems with auxiliary inputs, J. Cryptology 23 (2010), 457–476” by Cheon and “Rational semistandard tableaux and character formula for the Lie superalgebra , Adv. Math. 217 (2008), 713–739” by Kwon.

Korea ranks the 1st in the 23rd Asian Pacific Math-ematics Olympiad

Every year, APMO is to be held in the afternoon of the second Monday of March for participating countries in the North and South Americas, and in the morning of the second Tuesday of March for participating countries on the Western Pacific and Asia. Each country sends top ten individual high scores to the Senior Coordinating Country (Japan this year), then SCC announces the result of each country.

This year Korea ranks the 1st among 34 participating countries, with 1 gold medals, 2 silver medals, 4 bronze medals, and 3 Honourable Mentions scoring total of 289 points out of possible 350 points.

News from Taiwan

The 1st Hsu Chen-Jung Lecture Series On October 17–18, 2011

The Hsu Chen-Jung Lecture Series, endowed by Hsu’s family, is spon-sored by the Mathematical Society of Republic of China and the Insti-tute of Mathematics, Academia

Sinica. The first speaker is Professor Kenji Fukaya, a renowned mathematician from Kyoto University, Japan. The title of his talks is Lagrangian Floer Homology and Mirror Symmetry.

Jong-Sheng Guo and Chia-Fu Yu Awarded 2011 Outstanding Research Awards Sponsored by the National Science Council of Taiwan

Prof. Jung Hee Cheon and Jae-Hoon Kwon



The Ministry has been lending its support and will continue to do so in various areas of science and mathematics, such as the adjustment of related curriculum, the continued improvement of the standard of teachers, as well as the upgrading of 12 of Princess Chulabhorn’ Colleges nationwide into regional science schools.

Other News

Gove: How Asia Can Teach Us a Lesson on Math-ematics

Mathematics teaching in schools should be overhauled, with the introduction of Asian-style daily teaching and a focus on fundamentals, the UK Education Secretary Michael Gove has suggested recently.

He has signalled a return to academic rigour in the maths curriculum amid concerns that the UK is lagging behind other countries. He suggested daily maths lessons and regular tests are to be adopted, inspired by the system in Singapore, with the possible return of “numeracy hour” – a Labour initiative scrapped two years ago. Under his proposals, lessons for primary school children are to focus on fractions and the building blocks of algebra. And those in secondary school will study advanced calculus and statistics — currently the preserve of A-level students. Mr Gove also suggested that within a decade all children should study maths in some form up to the age of 18 — which will be the school leaving age from 2015.

The proposals come amid concerns that half the adult population lacks “basic maths skills”.

English schools are slipping down international league tables in the subject while countries such as Singapore, Japan, China and Korea steam ahead. At the age of 15, pupils in China are around two academic years ahead of British counterparts in the subject.

Primary pupils need to be taught maths every day to prepare them for secondary school, Mr Gove says.

In a speech to the Royal Society yesterday, Mr Gove said: “If we are to keep pace with our competitors, we need fundamental, radical reform in the curriculum, in teaching, and in the way we use technology in the classroom. Unless we dramatically improve our performance, the grim arithmetic of globalisation will leave us all poorer.”

Mr Gove will publish details of reforms following the national curriculum review.

Dame Athene Donald, chairman of the Royal Society Education Committee, welcomed his proposals. She said: “The UK has a proud track record of achievement in science and engineering, with the most productive research base among leading economies.”

“However, we need to place science and innovation at the heart of the UK’s long-term strategy for economic growth if we are to remain competitive, and at the apex of this must be inspiring the next generation of scientists, mathematicians and engineers.”

“The Education Secretary’s recognition that more students should be studying mathematics and for longer is particularly welcome.”

Currently, mathematics is compulsory up to the age of 16. Only around 13 percent of pupils, some 85,000, take it at A or AS-level each year.

Source: Daily News (June 30, 2011)



Conference CALENDAR


Conferences in Asia Pacific Region

JULY 2011

1 – 3 Jul 2011The 4th Congress of the Turkic World Mathematical Society (TWMS)Baku, Azerbaijanhttp://www.twmsc2011.com/

1 – 5 Jul 2011International Conference on Mathematical Control Theory and MechanicsSuzdal, Russiahttp://agora.guru.ru/display.php?conf=mctm2011

3 – 6 Jul 2011The 2nd IMS Asia Pacific Rim MeetingsTokyo, Japanhttp://www.sonic-city.or.jp/modules/english/

3 – 7 Jul 2011AAMT–MERGA Conference 2011: Mathematics: Traditions and New PracticesAlice Spring, Australiahttp://www.aamt.edu.au/conferences/AAMT-MERGA-conference

4 – 8 Jul 20112011 Taiwan International Conference on Geometry (Special Lagrangians and Related Topics)Taipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=111

4 – 8 Jul 2011Econometric Society Australasian Meeting,Adelaide, Australiahttp://www.alloccasionsgroup.com/ESAM2011

4 – 8 Jul 2011Workshop on The Arithmetic Geometry of Shimura Varieties and Rapoport-Zink SpacesKyoto, japanhttp://www.math.kyoto-u.ac.jp/~tetsushi/workshop201107/

4 – 10 Jul 2011ICTA 2011 — International Conference on Topology and Its ApplicationsIslamabed, Pakistanhttp://ww2.ciit.edu.pk/icta/

6 – 8 Jul 2011ICMFE 2011 — International Conference on Mathematical Finance and EconomicsIstanbul, Turkeyhttp://www.mat.itu.edu.tr/icmfe2011/icmfe2011.html

6 – 8 July 2011Integer Programming Down Under: Theory, Algorithms and ApplicationsNew Castle, Australiahttp://www.amsi.org.au/index.php/past-events/628-integer-programming-down-under-theory-algorithms-and-applications

7 July 2011TIMS Special Day on Positive CharacteristicTaipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=126

8 – 9 Jul 2011Conference in Honor of the 60th Birthday of Chang-Shou LinTaipei, Taiwanhttp://www.cts.ntu.edu.tw/indexmain.cfm?mainbody=indexmain_news_detail.cfm&uuid=20FC2F27-155D-0064-068058C4D979F705&viewmode=en

8 – 11 Jul 2011IMS–China International Conference on Statistics and Probability 2011Xi An, Chinahttp://www.stat.umn.edu/~statconf/imschina2011/

8 – 13 Jul 2011Symposium on Theoretical and Mathematical PhysicsSt. Petersburg, Russiahttp://www.pdmi.ras.ru/EIMI/2011/STMP/index.html

10 – 13 Jul 2011ICWAPR 2011 — International Conference on Wavelet Analysis and Pattern RecognitionGuilin, Chinahttp://www.icmlc.com

10 – 15 Jul 2011IFORS 2011 — Conference for the International Federation of Operational Research SocietiesMelbourne, Australiahttp://www.ifors2011.org/

10 – 15 Jul 2011PME35 — 35th Conference of the International Group for the Psychology of Mathematics EducationAnkara, Turkeyhttp://www.arber.com.tr/pme35.org/index.php/home

10 – 16 Jul 2011International Conference on Analysis and Its ApplicationsAligarh, Indiahttp://www.amu.ac.in/conference/icaa2011/

10 – 16 Jul 2011International Conference on Rings and Algebras in Honour of Professor Pjek-Hwee LeeTaipei, Taiwanhttp://moonstone.math.ncku.edu.tw/2011AlgConference/index.html

11 – 13 Jul 2011 ISSME 2011 — International Seminar in Science and Mathematics EducationJohor, Malaysiahttp://www.ppsmj.com/issme2011

11 – 13 Jul 2011NDT 2011 — 3rd International Conference on Networked Digital TechnologiesMacau, Chinahttp://www.dirf.org/ndt

11 – 13 Jul 2011UMTAS 2011 — Universiti Malaysia Terengganu 10th International Annual SymposiumTerengganu, Malaysiahttp://umtas.umt.edu.my/

11 – 14 July 2011KIAS Summer School on Several Complex VariablesYang yang, Koreahttp://workshop.kias.re.kr/SCV2011/

11 – 15 Jul 2011A Conference in Honor of the 70th Birthday of S. R. Srinivasa Varadhan Taipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=119

11 Jul – 5 Aug 2011Summer School on Applied MathematicsBeijing, Chinahttp://www.math.pku.edu.cn/misc/amtl/sumschool.htm

12 – 15 Jul 2011Australasian Applied Statistics ConferenceNorth Queensland, Australiahttp://aasc2011.science.qld.gov.au/

12 – 15 Jul 2011The 6th SEAMS–GMU 2011 International Conference on Mathematics and Its ApplicationsYogyakarta, Indonesiahttp://seams2011.fmipa.ugm.ac.id/index.htm

15 – 16 Jul 2011International Conference on Education Technology and ComputerChangChun, Chinahttp://www.icetc.org/

Conference CALENDAR Conference CALENDAR


18 – 22 Jul 2011Geometry & Topology Down Under — A Conference in Honour of Hyam RubinsteinMelbourne, Australiahttp://www.maths.uq.edu.au/~tillmann/hyamfest/

18 – 22 Jul 2011Workshop on Non-abelian Class Field TheoryPohang, Koreahttp://math.postech.ac.kr/~minhyong/nacftws.htm

18 – 29 Jul 2011CIMPA–UNESCO–MICINN–Indonesia Research School on Nonlinear Computational GeometryYogyakarta, Indonesiahttp:www.cimpa-icpam.org/spip.php?article313

18 Jul – 5 Aug 2011Computational Prospects of Infinity II: WorkshopsSingaporehttp://www2.ims.nus.edu.sg/Programs/011aiic/index.php

20 – 26 Jul 201112th National Lie Algebra MeetingHuzhou, Chinahttp://www.cms.org.cn/cms/#

20 – 26 Jul 2011The 12th Lie Algebra National ConferenceZhejiang, Chinahttp://www.cms.org.cn/cms/2011active.pdf

21 – 23 Jul 2011ICMSA 2011 — The 7th International Conference on Mathematics, Statistics and its ApplicationsBangkok, Thailandhttp://icmsa2011.nida.ac.th

22 – 24 Jul 2011ACC 2011 — International Conference on Advances in Computing and CommunicationsKochi, Indiahttp://www.acc-rajagiri.org

24 – 26 Jul 2011WCMS’11 — 2011 World Congress on Mathematics and StatisticsCairo, Egypthttp://infomesr.org/en/scientific-research/conferences/2011-conferences/48-wcms11

25 – 27 Jul 2011ASONAM 2011 — The 2011 International Conference on Advances in Social Networks Analysis and MiningKaohsiung, Taiwanhttp://asonam.im.nuk.edu.tw

25 – 27 Jul 2011MASCOTS 2011 — The 19th Annual Meeting of the IEEE International Symposium on Modelling, Analysis and Simulation of Computer and Telecommunication SystemsSingaporehttp://pdcc.ntu.edu.sg/mascots2011

25 – 29 Jul 2011Infinite Analysis 11 — Frontier of IntegrabilityTokyo, Japanhttp://sites.google.com/site/infiniteanalysis2011/

25 – 29 July 2011KIAS Summer School on Derived CategoriesGangwando, Koreahttp://workshop.kias.re.kr/SSDC2011/

25 – 29 July 2011TIMS 2011 Summer School on Number TheoryTaipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=127

27 – 29 Jul 2011ICCAM 2011 — International Conference on Computer and Applied MathematicsSingaporehttp://www.ourglocal.com/event/?eventid=4932

27 – 29 Jul 2011ICMMS 2011 — International Conference on Mathematics and Mathematical SciencesSingaporehttp://landrd.com2011/icmms-2011-international-conference-on-mathemati-2/

28 – 30 Jul 2011ICSFA 2011 — International Conference on Special Functions & Their ApplicationsJodhpur, Indiahttp://www.ssfaindia.webs.com/conf.htm

29 – 31 Jul 2011PMC 2011 — 12th International Pure Mathematics ConferenceIslamabad, Pakistanhttp://www.pmc.org.pk/

31 Jul – 5 Aug 2011ISIT 2011 — IEEE International Symposium on Information TheorySt Petersburg, Russiahttp://www.isit2011.org/

AUGUST 2011

1 – 12 Aug 2011CIMPA–UNESCO–MICINN–Indonesia Research School on Geometric Representation TheoryBandung, Indonesiahttp:www.cimpa-icpam.org/spip.php?article309

3 – 5 Aug 201118th Computational Fluid Dynamics Conference in TaiwanYilan, Taiwanhttp://18thcfd.iam.ntu.edu.tw/index.php

8 – 10 Aug 2011IC3 2011 — 4th International Conference on Contemporary ComputingNoida, Indiahttp://www.jiit.ac.in/jiit/ic3

8 – 12 Aug 20116th Pacific Rim Conference on Complex GeometryGyeongju, Koreahttp://workshop.kias.re.kr/PRCCG2011/

8 – 12 Aug 2011The 9th KAIST Geometric Topology FairDaejeon, Koreahttp://mathsci.kaist.ac.kr/~shkim/gtfair/gtfair/Welcome.html

11 – 13 Aug 2011EMC 2011 — The 6th International Conference on Embedded and Multimedia Computing Enshi, Chinahttp://grid.hust.edu.cn/EMC2011/

11 – 13 Aug 2011HumanCom 2011 — The 4th International Conference on Human-centric ComputingEnshi, Chinahttp://grid.hust.edu.cn/HumanCom2011/

15 – 16 Aug 2011Annual International Conference on Quantum and Molecular Computing and CommunicationsSingapore http://www.qmcomputing.org/

15 – 19 Aug 2011International Workship on Recent Advances in Biomedical ImagingShanghai, Chinahttp://ins.sjtu.edu.cn/programs/2011/ws_rabi/default.html

15 – 19 Aug 2011The Physics and Mathematics of General Relativity Summer CampTaipei, Taiwanhttp://math.cts.ntu.edu.tw/indexmain.cfm?mainbody=indexmain_news_detail.cfm&uuid=E0B26FAD-155D-0064-0680971F0F3220E2&viewmode=zh-tw

15 – 26 Aug 2011Geometry. Control. Economics.Astrakhan, Russiahttp://conf.d-omega.org/eng/

16 – 19 Aug 2011The Arithmetic of Function Fields and Related Topics Gyeongju, Koreahttp://mathsci.kaist.ac.kr/asarc/bbs/filebox/conference/number/regist.html

20 – 22 Aug 2011IIASCT 2011 — International Conference on Industrial Applications of Soft Computing TechniquesBhubaneswar, Orissa, Indiahttp://www.iiasct.info

22 – 24 Aug 20114th Workshop on Advanced Numerical Methods for Partial Differential Equation AnalysisSt. Petersburg, Russiahttp://www.pdmi.ras.ru/EIMI/2011/wanm/

22 – 24 Aug 2011COIA 2011 — The 3rd International Conference on Control and Optimisation with Industrial ApplicationsAnkara, Turkeyhttp://www.ee.bilkent.edu.tr/~coia2011

Conference CALENDAR


22 – 24 Aug 2011The 36th Sapporo Symposium on Partial Differential EquationsHokkaido, Japanhttp://www.math.sci.hokudai.ac.jp/sympo/sapporo/program_en.html

22 – 26 Aug 2011The Pan Asian Number Theory (PANT) ConferencesBeijing, Chinahttp://www.mcm.ac.cn/activities/pant2011/register.aspx

24 – 26 Aug 2011CSE 2011 — The 14th IEEE International Conference on Computational Science and Engineering Dalian, Chinahttp://ncc.dlut.edu.cn/~cse11/

24 – 26 Aug 2011International Conference on Applied Mathematics and Mathematical EngineeringTokyo, Japanhttp://www.waset.org/conferences/2011/japan/icamme/

24 – 26 Aug 2011International Conference on Applied Physics and Mathematical EngineeringTokyo, Japanhttp://www.waset.org/conferences/2011/japan/icapme/

24 – 26 Aug 2011International Conference on Distributed and Grid ComputingTokyo, Japanhttp://www.waset.org/conferences/2011/japan/icdgc/

24 – 26 Aug 2011ISPAN 2011 — The 11th International Symposium on Pervasive Systems, Algorithms and Networks Dalian, Chinahttp://ncc.dlut.edu.cn/ISPAN2011/

26 – 27 Aug 2011IHMSC 2011 — Intelligent Human Machine Systems and CyberneticsHangzhou, Chinahttp://ihmsc.zju.edu.cn/index.html

28 – 31 Aug 20112011 New Zealand Statistical Association (NSZA) ConferenceAuckland, New Zealandhttp://www.nzsa2011.org.nz/index.php

29 Aug – 1 Sep 2011One Forum, Two Cities: Aspect of Nonlinear PDEsTaipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=128

SEPTEMBER 2011

1 – 30 Sep 2011Automata Theory and ApplicationsSingaporehttp://www2.ims.nus.edu.sg/Programs/011auto/index.php

1 Sep – 31 Dec 2011Mathematical Theory and Stimulation of Phase TransitionsBeijing, Chinahttp://www.bicmr.org/conference/mtspt/

5 – 6 Sep 2011NTA 2011 — International Conference on Mathematics: Number Theory and ApplicationTunisiahttp://www.ourglocal.com/event/?eventid=7805

5 – 10 Sep 2011International Conference: Toric Topology and Automorphic Functions Khabarovsk, Russiahttp://www.iam.khv.ru/ttaf-2011/the1st_announcement.htm

6 – 8 Sep 2011GRAVISMA 2011 — Computer Graphics, Vision and MathematicsOstrava, Czech Republichttp://gravisma.zcu.cz/

6 – 8 Sep 2011MOL 12 2011 — 12th Meeting on Mathematics of LanguageNara, Japanhttp://sites.google.com/site/mol12nara/

6 – 9 Sep 2011Front Propagation, Biological Problems and Related Topics: Viscosity Solution Methods for Asymptotic AnalysisHokkaido, Japanhttp://www.math.sci.hokudai.ac.jp/sympo/110906/index_en

7 – 8 Sep 2011The 3rd International Workshop on Internet Survey Methods — “Expansion of the Internet Survey and a Paradigm Shift for Statistical Production”Daejeon, South Korea http://kostat.go.kr/portal/korea/index.action

7 – 9 Sep 2011Algebraic and Geometric Models for Spaces and Related TopicsKyoto, Japanhttp://marine.shinshu-u.ac.jp/~kuri/symposium11_RIMS/Home.html

7 – 9 Sep 2011BI 2011 — International Conference on Brain InformaticsLanzhou, Chinahttp://wi-consortium.org/conferences/amtbi11/

7 – 9 Sep 2011International Conference on Nonlinear Mathematics for Uncertainty and Its ApplicationsBeijing, Chinahttp://www.caas.org.cn/NLMUA2011/

8 – 10 Sep 2011National Workshop on Biostatistics: Application of Computational Statistics in Medicine & BiologyKharagpur, Indiahttp://www.iitkgp.ac.in/news/showannouncedescr.php?newsid=551

8 – 11 Sep 2011ITCDM 2011 — 2nd India–Taiwan Conference on Discrete MathematicsCoimbatore, Tamil Nadu, Indiahttp://engineering.amrita.edu/cb/depts/maths/itcdm

12 – 21 Sep 2011The 4th MSJ–SI — Non-linear Dynamics in Partial Differential EquationsFukuoka, Japanhttp://www2.math.kyushu-u.ac.jp/~tohru/msjsi11/

13 Sep 2011P2S2 — 4th International Workshop on Parallel Programming Models and Systems Software for High-End Computing Taipei, Taiwanhttp://www.mcs.anl.gov/events/workshops/p2s2/2011/

13 – 16 Sep 2011AWASN’11 — The 2011 International Workshop on Applications of Wireless Ad Hoc and Sensor NetworksTaipei, Taiwanhttp://wasn.csie.ncu.edu.tw/AWASN11.htm

13 – 16 Sep 2011CloudSec 2011 — The 3rd International Workshop on Security in Cloud Computing (Sept 13-16 2011, Taipei, Taiwan)http://bingweb.binghamton.edu/~ychen/CloudSec2011.htm

13 – 16 Sep 2011EMS 2011 — The 2011 International Workshop on Embedded Multicore SystemsTaipei, Taiwanhttp://esw.cs.nthu.edu.tw/icpp_ems/icpp_ems.htm

13 – 16 Sep 2011ITCSA-2011 — The 2011 International Workshop on IT Converged Services and ApplicationsTaipei, Taiwanhttp://ftrai.org/itcsa2011/index.php

13 – 16 Sep 2011PSTI 2011 — The 2nd International Workshop on Parallel Software Tools and Tool Infrastructures Taipei, Taiwanhttp://www.psti-workshop.org/



13 – 16 Sep 2011SRMPDS’11 — The 7th International Workshop on Scheduling and Resource Management for Parallel and Distributed SystemsTaipei, Taiwanhttp://www.mcs.anl.gov/~kettimut/srmpds/

14 – 15 Sep 2011ARTCom 2011 — 3rd International Conference on Advances in Recent Technologies in Communication andComputingBangalore, Indiahttp://artcom.engineersnetwork.org/2011/

14 – 16 Sep 2011CCIS 2011 — International Conference on Cloud Computing and Intelligence SystemsBeijing, Chinahttp://conference.bupt.edu.cn/ccis2011

15 – 17 Sep 20118th All-Russian Scientific Conference “Mathematical Modeling and Boundary-Value Problems”, Dedicated to 75 Anniversary of Yu. SamarinSamara, Russiahttp://www.mmikz.ru/

17 – 21 Sep 2011Ubicomp’11 — The 13th International Conference on Ubiquitous ComputingBeijing, Chinahttp://www.ubicomp.org/ubicomp2011

18 – 20 Sep 2011Minisymposium on Mathematics in Material ScienceBeijing, Chinahttp://lsec.cc.ac.cn/~mmms/

19 – 23 Sep 2011ATCM 2011 — The 16th Asian Technology Conference in MathematicsBolu, Turkeyhttp://atcm2011.org/

19 – 23 Sep 2011The Geometry of Differential EquationsCanberra, Australiahttp://www.amsi.org.au/index.php/past-events/653-the-geometry-of-differential-equations

20 – 22 Sep 2011KIAS Workshop on Periods and ModuliSeoul, Koreahttp://workshop.kias.re.kr/WPM2011/?Home

21 – 23 Sep 2011SUComS 2011 — The 2nd International Conference on Security-enriched Urban Computing and Smart Grids Hualien, Taiwanhttp://sucoms2011.ndhu.edu.tw/

26 – 29 Sep 2011Australian Mathematical Society Conference 2011Wollongong, Australiahttp://www.uow.edu.au/informatics/maths/news/austms/index.html

26 – 29 Sep 2011The 5th Sino–Japan Optimisation MeetingBeijing, Chinahttp://lsec.cc.ac.cn/~sjom/index.htm

27 Sep 20112011 MSJ Autumn MeetingMatsumoto, Japanhttp://mathsoc.jp/en/meeting/shinshu11sept/

28 – 29 Sep 20113rd Wellington Workshop in Probability and Mathematical StatisticsWellington, New Zealandhttp://msor.victoria.ac.nz/Events/WWPMS2011/

28 – 30 Sep 2011International Conference on Applied Mathematics and Computer SciencesSingaporehttp://www.waset.org/conferences/2011/singapore/icamcs/

28 – 30 Sep 2011International Conference on Applied Mathematics, Mechanics and PhysicsSingaporehttp://www.waset.org/conferences/2011/singapore/icammp/

28 – 30 Sep 2011International Conference on Sensor Networks, Information, and Ubiquitous ComputingSingaporehttp://www.waset.org/conferences/2011/singapore/icsniuc/

28 Sep – 1 Oct 2011The Mathematical Society of Japan Autumn Meeting 2011Matsumoto, Japanhttp://mathsoc.jp/meeting/

OCTOBER 2011

3 – 7 Oct 2011Geometric Structures on Complex ManifoldsMoscow, Russiahttp://bogomolov-lab.ru/GS/

3 – 7 Oct 2011VI-th Ufa International Mathematical Conference “Complex Analysis and Differential Equations”, Dedicated to the 70th Anniversary of Valentin V. NapalkovUfa, Russiahttp://ufaconf.info/

9 – 14 Oct 2011ESWeek 2011 — Embedded Systems WeekTaipei, Taiwanhttp://www.esweek.org

10 – 14 Oct 2011GCP-2011 — Kolmogorov readings. General Control Problems and Their ApplicationsTambov, Russiahttp://www.tambovopu2011.narod.ru/

11 – 14 Oct 2011Mal’tsev MeetingNovosibirsk, Russiahttp://www.math.nsc.ru/conference/malmeet/11/index.html

12 – 13 Oct 2011ICOMSc — International Conference on Mathematics and ScienceEast Java, Indonesiahttp://icomsc.its.ac.id/

14 – 17 Oct 2011The 10th International Symposium on Distributed Computing and Applications to Business Engineering and SciencesWuxi, Chinahttp://dcabes2011.jiangnan.edu.cn/

18 – 21 Oct 2011ISRM 2011 — 12th ISRM International Conference on Rock MechanicsBeijing, Chinahttp://www.isrm2011.com/

19 – 21 Oct 20112011 4th International Workshop on Advanced Computational IntelligenceWuhan, Chinahttp://www.iwaci.org

19 – 21 Oct 2011Celebration of Mathematical Sciences, in Commemoration of the Centennial of the Birth of Shiing-Shen ChenTaipei, Taiwanhttp://www.math.sinica.edu.tw/www/file_upload/conference/201110_ssc/index.html

19 – 23 Oct 2011ICS-13 — The 13th International Congress of StereologyBeijing, Chinahttp://www.ics13beijing.org/

21 – 22 Oct 2011MATHTED’s Biennial Conference 2011Olongapo City, Philippineshttp://mathtedphil.org/

22 – 24 Oct 2011ICREM5 — The 5th International Conference on Research and Education in MathematicsBandung, Indonesiahttp://www.math.itb.ac.id/~nanang/topic.html

22 – 25 Oct 2011Cross-Strait Conference on Integrable Systems and Related TopicsChangshu, Chinahttp://www.cms.org.cn/cms/2011active.pdf

24 – 26 Oct 2011IEEE BIBE 2011 — The 11th IEEE International Conference on Bioinformatics and Bioengineering Taichung, Taiwanhttp://bibe2011.asia.edu.tw/

24 – 28 Oct 2011Chern Centennial ConferenceTianjin, Chinahttp://www.nim.nankai.edu.cn/activites/conferences/Chern-Centennial-20111024/index.htm

Conference CALENDAR


25 – 28 Oct 2011RIMS Program 2011: Operator Algebras and Mathematical PhysicsKyoto, Japanhttp://www.ms.u-tokyo.ac.jp/~yasuyuki/op2011.htm

26 – 28 Oct 2011International Conference on Computer and Applied MathematicsBali, Indonesiahttp://www.waset.org/conferences/2011/bali/iccam/

26 – 28 Oct 2011International Conference on Mathematics and Mathematical SciencesBali, Indonesiahttp://www.waset.org/conferences/2011/bali/icmms/

28 – 30 Oct 20112011 International Conference on Applied and Engineering Mathematics Shanghai, Chinahttp://www.engii.org/cet2011/AEM2011.aspx

28 – 30 Oct 2011International Conference on Computational Biology and Bioinformatics (CBB)Shanghai, Chinahttp://www.engii.org/cet2011/CBB2011.aspx

21 – 24 Oct 2011IWCFTA 2010 — 2010 International Workshop on Chaos-Fractals Theories and ApplicationsHangzhou, Chinahttp://www.chaos-fractal.cn/

NOVEMBER 2011

1 – 3 Nov 2011International Seminar on the Application of Science and MathematicsKuala Lumpur, Malaysiahttp://uhsb.uthm.edu.my/isasm2011/index.html

1 – 5 Nov 2011ICSOAA2011 — 3rd Conference of Settat on Operator Algebras and ApplicationsSettat, Moroccohttp://www.math.ist.utl.pt/~elharti/3rd/settat2011.htm

2 – 6 Nov 2011MaThCryst Workshop on Mathematical CrystallographyManila, Philippineshttp://www.crystallography.fr/mathcryst/manila2011.php

3 – 5 Nov 2011DAHITO 2011 — Conference on Algebra, Geometry and TopologyThai Nguyen City, Vietnamhttp://www.vms.org.vn/conf/DaHiTo2011.htm

7 – 11 Nov 2011The 8th International Conference on Numerical Optimisation and Numerical Linear AlgebraXiamen, Chinahttp://lsec.cc.ac.cn/~icnonla/index.htm

10 – 11 Nov 2011AUCC 2011 — Australian Control ConferenceMelbourne, Australiahttp://www.aucc.org.au/

13 – 16 Nov 2011Chinese Mathematical Society Annual Conference 2011 and the China Council of the 11th Congress of MathematicsSichuan, Chinahttp://www.cms.org.cn/cms/#

13 – 16 Nov 2011The 11th National Congress of the Chinese Mathematical SocietyChengdu, Chinahttp://www.cms.org.cn/cms/#

14 – 17 Nov 2011The International Conference on Applied Sciences, Mathematics and Humanities 2011Negeri Sembilan, Malaysiahttp://www.nsembilan.uitm.edu.my/index.php/icasmh/

15 – 17 Nov 2011CoSMEd 2011 — 4th International Conference on Science and Mathematics EducationPenang, Malaysia http://www.recsam.edu.my/cosmed

16 – 18 Nov 2011FCST 2011 — The 6th International Conference on Frontier of Computer Science and Technology Changsha, China http://trust.csu.edu.cn/conference/fcst2011/

19 – 21 Nov 2011International Conference on Analysis and Its ApplicationsAligarh, Indiahttp://www.amu.ac.in/conference/icaa2011/

19 – 23 Nov 2011International Workshop on Advanced Computational Intelligence and Intelligent InformationSuzhou, Chinahttp://www.ewh.ieee.org/soc./eds/imw/

22 – 23 Nov 2011ICSD–IV — 4th International Conference for Science and DevelopmentGaza Strip, Palestinehttp://www.iugaza.edu.ps/en/Confereces/ConferencePages.aspx?PageID=0&ConfId=246

27 Nov – 2 Dec 2011Volcanic DELTA 2011 — 7th DELTA Conference on Teaching and Learning of Undergraduate Mathematics and StatisticsRotorua, New Zealandhttp://www.delta2011.co.nz/delta2011/

28 – 30 Nov 20112011 1st Asian Conference on Pattern RecognitionBeijing, Chinahttp://www.acpr2011.org

DECEMBER 2011

1 – 3 Dec 2011CIMMACS’11 — The 10th WSEAS International Conference on Computational Intelligence, Man-MachineSystems and CyberneticsJakarta, Indonesiahttp://www.wseas.us/conferences/2011/jakarta/cimmacs/

1 – 5 Dec 2011The 10th Pacific Rim Geometry Conference 2011 Osaka–FukuokaOsaka, Japanhttp://www.sci.osaka-cu.ac.jp/~ohnita/2011/PRG2011Osaka-Fukuoka_e.html

5 – 8 Dec 2011The 4th National Conference on Computational MathematicsGuangzhou, Chinahttp://www.cms.org.cn/cms/2011active.pdf

5 – 9 Dec 201135ACCMCC — The 35th Australasian Conference on Combinatorial Mathematics & Combinatorial ComputingMelbourne, Australiahttp://users.monash.edu.au/~accmcc/

5 – 9 Dec 2011AMSI Summer Symposium in BioinformaticsMelbourne, Australiahttp://www.amsi.org.au/index.php/events/652-bioinfosummer-2011

5 – 9 Dec 2011SCPDE11 — The 4th International Conference on Scientific Computing and Partial Differential EquationsHong Kong, Chinahttp://www.math.hkbu.edu.hk/SCPDE11/

5 – 9 Dec 2011The 4th East Asia Conference on Algebraic TopologyTokyo, Japanhttp://pantodon.shinshu-u.ac.jp/conferences/EACAT4/

7 – 9 Dec 2011ISPACS 2011 — 19th International Symposium on Intelligent Signal Processing and Communication SystemsChiangmai, Thailandhttp://www.ispacs2011.org

7 – 9 Dec 2011The 10th Pacific Rim Geometry Conference 2011 Osaka–FukuokaFukuoka, Japanhttp://www.sci.osaka-cu.ac.jp/~ohnita/2011/PRG2011Osaka-Fukuoka_e.html

9 – 11 Dec 2011Congress of Mathematical Operations in ChinaTaoyuan County, Taiwanhttp://tms.math.ntu.edu.tw/webpage/newspaper/newspaper_20110311.pdf



9 – 11 Dec 2011CiSE 2011 — International Conference on Computational Intelligence and Software EngineeringWuhan, Chinahttp://www.ciseng.org/2011/

12 – 15 Dec 2011APSCC 2011 — The 6th IEEE Asia-Pacific Services Computing Conference Jeju, Koreahttp://www.ftrai.org/apscc2011

12 – 16 Dec 2011MODSIM 2011 — International Congress on Modelling and SimulationPerth, Australiahttp://www.mssanz.org.au/modsim2011/

14 – 16 December 2011IICAI 2011 — 5th Indian International Conference on Artificial IntelligenceTumkur, Indiahttp://www.iiconference.org

14 – 18 Dec 2011International Conference on Integral and Convex Geometry Analysis and Related TopicsTianjin, Chinahttp://www.nim.nankai.edu.cn/activites/conferences/hy20111217/index.htm

15 – 20 Dec 201112th Asian Logic ConferenceWellington, New Zealandhttp://msor.victoria.ac.nz/Events/ALC2011

16 – 19 Dec 2011Joint Meeting of The 2011 Taipei International Statistical Symposium and 7th Conference of the Asian Regional Section of IASTaipei, Taiwanhttp://joint2011.stat.sinica.edu.tw/

17 – 18 Dec 20111st International Conference on Mathematical Sciences and ApplicationsDelhi, Indiahttp://ijmsa.yolasite.com/conference-announcement.php

17 – 19 Dec 2011ICMA-MU’11 — International Conference in Mathematics and ApplicationsBangkok, Thailandhttp://www.sc.mahidol.ac.th/cem/ICMA2011/index.html

18 – 20 Dec 2011MSAST 2011 — The 5th International Conference of IMBIC on “Mathematical Sciences for Advancement of Science and Technology”Kolkata, Indiahttp://www.ams.org/meetings/calendar/2011_dec18-20_kolkata.html

21 – 23 Dec 2011International Conference on Applied Mathematics and Engineering MathematicsPhuket, Thailandhttp://www.waset.org/conferences/2011/phuket/icamem/

21 – 23 Dec 2011International Conference on Computational Mathematics, Statistics and Data EngineeringPhuket, Thailandhttp://www.waset.org/conferences/2011/phuket/iccmsde/

22 – 24 Dec 2011The 17th Biennial Mathematics Conference of Bangladesh Mathematical SocietySavar, Bangladeshhttp://bdmathsociety.org/?q=node/16

28 – 30 Dec 2011Statistical Concepts and Methods for the Modern WorldColombo, Sri Lankahttp://www.maths.usyd.edu.au/u/shelton/SLSC2011/

28 – 31 Dec 2011International Conference on Advances in Probability and Statistics — Theory and Applications: A Celebration of N. Balakrishnan’s 30 years of Contributions to StatisticsHong Kong, Chinahttp://faculty.smu.edu/ngh/icaps2011.html

29 – 30 Dec 2011ICAPM 2011 — 2011 International Conference on Applied Physics and MathematicsChennai, Indiahttp://www.icapm.org/cfp.htm

JANUARY 2012

3 – 11 Jan 2012International Colloquium on Automorphic Representations and L-FunctionsMumbai, Indiahttp://www.math.tifr.res.in/~ic2012/

9 – 13 Jan 2012Conference on Von Neumann Algebras and Related TopicsKyoto, Japanhttp://www.ms.u-tokyo.ac.jp/~yasuyuki/vn2012.htm

9 Jan – 3 Feb 2012AMSI Summer School 2012Sydney, Australiahttp://www.amsi.org.au/index.php/events/691-amsi-summer-school-2012

16 Jan 2012ANALCO12 — Analytic Algorithmics and CombinatoricsKyoto, Japanhttp://www.siam.org/meetings/analco12/

16 – 19 January 2012East Asia Number Theory Conference (EANTC)Taipei, Taiwanhttp://www.tims.ntu.edu.tw/workshop/Default/index.php?WID=125

17 – 19 Jan 2012SODA12 — ACM–SIAM Symposium on Discrete AlgorithmsKyoto, Japanhttp://www.siam.org/meetings/da12/

29 – 31 Jan 2012ICMCSSE 2012 — International Conference on Mathematical, Computational and Statistical Sciences, and EngineeringDubai, UAEhttp://www.waset.org/conferences/2012/dubai/icmcsse/

30 Jan – 2 Feb 2012SICPRO 2012 — 9th International Conference “System Identification and Control Problems”Moscow, Russiahttp://www.sicpro.org

FEBRUARY 2012

9 – 10 Feb 2012Conference on Computer Science & Computational Mathematics CCSCM 2012Malacca, Malaysiahttp://www.ccscm.net

13 – 17 Feb 2012MCQMC 2012 — 10th International Conference on Monte Carlo and Quasi–Monte Carlo Methods in Scientific ComputingSydney, Australiahttp://www.mcqmc2012.unsw.edu.au

22 – 24 Feb 2012ICCMSDE 2012 — International Conference on Computational Mathematics, Statistics and Data EngineeringPenang, Malaysiahttp://www.waset.org/conferences/2012/penang/iccmsde/

MARCH 2012

1 – 3 Mar 2012The 5th International Conference on Science and Mathematics Education in Developing CountriesPhnom Penh, Cambodiahttp://www.cambmathsociety.org/conferen1-3-March-2012.htm

5 – 9 Mar 20125th International Conference on High Performance Scientific ComputingHanoi, Vietnamhttp://hpsc.iwr.uni-heidelberg.de/HPSCHanoi2012/

11 – 13 Mar 2012ICAMEM 2012 — International Conference on Applied Mathematics and Engineering MathematicsBangkok, Thailandhttp://www.waset.org/conferences/2012/bangkok/icamem/

12 – 16 Mar 2012International Number Theory Conference in Memory of Alf van der PoortenNewcastle, Australiahttp://www.amsi.org.au/index.php/past-events/669-international-number-theory-conference-in-memory-of-alf-van-der-poorten

Conference CALENDAR


25 – 30 Mar 2012ICASSP 2012 — 37th IEEE International Conference on Acoustics, Speech, and Signal ProcessingKyoto, Japanhttp://www.icassp2012.com

26 – 29 Mar 2012MSJ Spring Meeting 2012Tokyo, Japanhttp://mathsoc.jp/meeting/

JUNE 2012

3 – 5 Jun 2012ICMG 2012 — 2012 International Conference on Mathematics and GeosciencesBeijing, Chinahttp://www.ourglocal.com/event/?eventid=8584

4 – 8 Jun 2012Arithmetic Geometry Week in TokyoTokyo, Japanhttp://www.ms.u-tokyo.ac.jp/~t-saito/conf/agwtodai/agwtodai.html

6 – 8 Jun 20122012 KIAS–POSTECH Workshop — Number Theory “L-functions”Pohang, Koreahttp://math.postech.ac.kr/new/conferences/view/191

19 – 22 Jun 20127th World Congress of Bachelier Finance SocietySydney, Australiahttp://www.bfs2012.com

JULY 2012

1 – 4 Jul 2012The 2nd Institute of Mathematical Statistics Asia Pacific Rim MeetingTsukuba, Japanhttp://www.ims-aprm2011.org/

8 – 15 Jul 2012ICME-12 — The 12th International Congress on Mathematical EducationSeoul, Koreahttp://www.icme12.org/

9 – 12 Jul 20128th World Congress in Probability and StatisticsIstanbul, Turkeyhttp://www.worldcong2012.org/

9 – 13 Jul 2012MTNS 2012 — 20th International Symposium on Mathematical Theory of Networks and SystemsMelbourne, Australiahttp://mtns2012.eng.unimelb.edu.au/

9 – 14 Jul 20128th World Congress in Probability and StatisticsIstanbul, Turkeyhttp://www.vvsor.nl/en/pages/Calendar/9thofjuli2012/1309/AyazmaderesiCadKaradutSokNo7/8thWorldCongressinProbabilityandStatistics

15–18 Jul 201211th Australia - New Zealand Conference on Geomechanics (ANZ 2012)Melbourne, Australiahttp://www.anz2010.com.au/index.php

16 – 20 Jul 2012HPM 2012 History and Pedagogy of Mathematics, The HPM Satellite Meeting of ICME-12Daejeon, Koreahttp://www.hpm2012.org/

18 – 22 Jul 2012PME36 — 36th Annual Meeting of the International Group for the Psychology of Mathematics EducationTaipei, Taiwanhttp://www.tame.tw/pme36/show_content.php?content_id=25

30 Jul – 3 Aug 201224th International Conference on Formal Power Series and Algebraic CombinatoricsNagoya, Japanhttp://www.math.nagoya-u.ac.jp/fpsac12/index.html

AUGUST 2012

16 – 18 Aug 2012International Conference on “Fluid Mechanics, Graph Theory and Differential Geometry” Bangalore, Karnataka, Indiahttp://www.christuniversity.in/Mathematics/deptresources.php?division=Deanery%20of%20Sciences&dept=12&sid=144#ac

20 – 24 Aug 2012SMF–VMS Congres De Commun Mathematiques — Coordination Meeting of the School of Legal AccountingHue, Vietnamhttp://www.vms.org.vn/conf/SMF-VMS_3Colors.htm

SEPTEMBER 2012

17 Sep 2012MSJ–KMS Joint Meeting 2012Fukuoka, Japanhttp://mathsoc.jp/en/

12 – 14 Sep 2012ICAPM 2012 — International Conference on Applied Physics and MathematicsSingapore, Singaporehttp://www.waset.org/conferences/2012/singapore/icapm/

18 – 21 Sep 2012MSJ Autumn Meeting 2012Fukuoka, Japanhttp://mathsoc.jp/en/pamph/current/spring_autumn.html

OCTOBER 2012

15 – 19 Oct 2012Multiscale Materials Modeling (MMM) 2012 ConferenceSingaporehttp://www.mrs.org.sg/mmm2012/

24 – 26 Oct 2012ICAMCS 2012 — International Conference on Applied Mathematics and Computer SciencesIndonesia, Balihttp://www.waset.org/conferences/2012/bali/icamcs/

24 – 26 Oct 2012ICAMMP 2012 — International Conference on Applied Mathematics, Mechanics and PhysicsIndonesia, Balihttp://www.waset.org/conferences/2012/bali/icammp/

NOVEMBER 2012

11 – 15 Nov 2012ICPR 2012 — The 21st International Conference on Pattern RecognitionTsukuba, Japanhttp://www.icpr2012.org

DECEMBER 2012

1 – 31 Dec 2012COLING 2012 — 24th International Conference on Computational LinguisticsMumbai, Indiahttp://www.coling2012-iitb.org

AUGUST 2014

13 – 21 Aug 2014International Congress of Mathematicians 2014Seoul, Koreahttp://www.icm2014.org/

Conference CALENDAR

Australian Mathematical Society

President: P. G. Taylor Address: Department of Mathematics and

Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

Email: [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] Tel.: +880 17 11 86 47 25http://bdmathsociety.org/

Cambodian Mathematical Society

President: Chan Roath Address: Khemarak University, Phnom Penh Center Block DEmail: [email protected].: (855) 642 68 68 (855) 11 69 70 38http://www.cambmathsociety.org/

Chinese Mathematical Society

President: Zhiming MaAddress: Zhongguan Road East No. 55, Beijing 100080, ChinaEmail: [email protected].: 0086 62562362http://www.cms.org.cn/cms/

Hong Kong Mathematical Society

President: Tao Tang Director of Joint Research Institute for Applied Mathematics, Department of Mathematics, The Hong Kong Baptist University

Address: Department of Mathematics, The Hong Kong Baptist University, FSC1102, Fong Shu Chuen Building, Kowloon Tong, Hong Kong Email: [email protected] Tel.: 852 3411 5148 Fax: 852 3411 5811 http://www.hkms.org.hk/

Mathematical Societies in India:

The Allahabad Mathematical ScocietyPresident: D. P. GuptaAddress: 10, C S P Singh Marg, Allahabad - 211001,UP, IndiaEmail: [email protected]://www.amsallahabad.org/

Calcutta Mathematical SocietyPresident: B. K. Lahiri Kalyani UniversityAddress: 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 India

Email: [email protected]://www.indianmathsociety.org.in/

Ramanujan Mathematical SocietyPresident: M. S. RaghunathanAddress: School of Mathematics, Tata Institute of Fundamental

Research, Homi Bhaba Road, Colaba, Mumbai, IndiaEmail: [email protected]://www.ramanujanmathsociety.org/

Mathematical Societies in Asia Pacific Region



Vijnana Parishad of IndiaPresident: V. P. SaxenaContact: R.C. Singh Chandel Secretary, Vijnana Parishad of India D.V. Postgraduate College, Orai - 285001, UP, IndiaEmail: [email protected].: + 91 11 27495877http://vijnanaparishadofindia.org/

Indonesian Mathematical Society

President: WidodoAddress: Fakultas MIPA Universitas Gadjah Mada, Yogyakarta, IndonesiaEmail: [email protected] http://www.indoms-center.org

Israel Mathematical Union

President: Louis H. RowenAddress: Israel Mathematical Union, Department of Mathematics, Bar Ilan University, Ramat Gan 52900, Israel Email: [email protected].: +972 3 531 8284 Fax: +972 9 7418016 http://www.imu.org.il/

The Mathematical Society of Japan

President: Takashi TsuboiAddress: Taitou 1-34-8 Taito-ku, Tokyo110-0016, JapanEmail: [email protected] Tel.: + 81 03 3835 3483http://mathsoc.jp/en/

The Korean Mathematical Society

President: Dong Youp Suh KAIST Address: The Korean Mathematical Society, Korea Science and Technology Center 202, 635-4, Yeoksam-dong, Kangnam-gu, Seoul 135-703, KoreaEmail: dysuh@ math.kaist.ac.kr [email protected] http://www.kms.or.kr/eng/

Malaysian Mathematical Sciences Society

President: Mohd Salmi Md. Noorani Address: School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600, Selangor D. Ehsan, MalaysiaEmail: [email protected] Tel.: +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 TuladharAddress: Nepal Mathematical Society, Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, NepalEmail: [email protected].: 9841 639131 00977 1 2041603 (Res)http://www.nms.org.np/

New Zealand Mathematical Society

President: Charles SempleContact: Alex James SecretaryAddress: Department of Mathematics and

Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New ZealandEmail: [email protected]://nzmathsoc.org.nz/

Pakistan Mathematical Society

President: Qaiser Mushtag Department of Mathematics, Quaid-i-Azam University, Islamabad Contact: Dr. Muhammad Aslam General SecretaryAddress: Department of Mathematics, Qauid-i-Azam University, Islamabad, PakistanEmail: [email protected] Fax: 92 51 4448509http://pakms.org.pk/



Mathematical Society of the Philippines

President: Jumela F. Sarmiento Ateneo de Manila University Address: Mathematical Society of the Philippines, c/o Department of Mathematics, University of the Philippines, Diliman, Quezon City, 1101, PhilippinesEmail: [email protected]: 632 920 1009http://www.mathsocietyphil.org/

Mathematical Societies in Russia:

Moscow Mathematical Society President: S. Novikov Contact: John O'Connor Prof Edmund RobertsonAddress: Landau Institute for Theoretical

Physics, Russian Academy of Sciences, Kosygina 2 1, 1 7 940 Moscow GSP-1, Russia Email: [email protected] [email protected]://mms.math-net.ru/

St. Petersburg Mathematical SocietyPresident: Yu. V. MatiyasevichAddress: St. Petersburg Mathematical Society, Fontanka 27, St. Petersburg, 191023, RussiaEmail: [email protected] Tel.: +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 ZhuAddress: Department of Mathematics, National

University of Singapore, 2 Science Drive 2, Singapore 117543

Email: [email protected].: +65 6516 6400http://sms.math.nus.edu.sg/

Southeast Asian Mathematical Society

President: Fidel NemenzoAddress: Institute of Mathematics, University of the Philippines, Diliman, QC, PhilippinesEmail: [email protected]://www.seams-math.org/

The Mathematical Society of the Republic of China

President: Sze-Bi Hsu Department of Mathematics, National

Tsing Hua University Address: No. 101, Section 2, Kuang-Fu Road, Hsinchu, 30013, R.O.C., TaiwanEmail: [email protected] Tel.: +886 3 571 5131 ext. 31052 Fax: +886 3 572 3888http://tms.math.ntu.edu.tw/

Mathematical Association of Thailand

President: Rajit VadhanasindhuContact: Utomporn Phalavonk SecretaryAddress: c/o Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandEmail: [email protected]: 66-2-252-7980Fax: 66-2-252-7980http://www.math.or.th/mat/

Vietnam Mathematical Society

President: Le Tuan HoaAddress: Institute of Mathematics, VAST 18 Hoang Quoc Vietnam, Hanoi,

VietnamEmail: [email protected]://www.vms.org.vn/english/vms_e.htm



MICA (P) 094/02/2011

Documents

Asia Pacific Mathematics Newsletter - Australian ... Pacific Mathematics Newsletter July 2011 Volume 1 Number 3 Behind the Great Wave at Kanagawa Institute for Mathematical Sciences,