## Seminar information archive

### 2007/02/22

#### Lectures

10:30-12:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Stan Osher (UCLA)
The level set method, multivalued solutions and image science
[ Abstract ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.

#### Lectures

13:00-15:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ Abstract ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.

The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.

### 2007/02/21

#### Lectures

10:30-12:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Stan Osher (UCLA)
The level set method, multivalued solutions and image science
[ Abstract ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.

#### Lectures

13:30-15:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ Abstract ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.

The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.

### 2007/02/20

#### Lectures

10:30-17:20   Room #123 (Graduate School of Math. Sci. Bldg.)
Erwin Bolthausen (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments

Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)

Interacting Brownian motions related to Ginibre random point field

#### Tuesday Seminar of Analysis

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Patrick G¥'erard (パリ南大学)
On the dynamics of the Gross-Pitaevskii equation

### 2007/02/17

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

Finite-dimensional representations of the small quantum algebras
[ Abstract ]

そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。
さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、
De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、
それぞれ表現論が異なる。
また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と

どちらの表現論においても重要な役割を果たしている。

●小型量子代数が、非制限型量子代数のある商代数と同型になることを、

●A, B, C, D, G型の小型量子代数の有限次元既約表現を、
Schnizer表現の部分表現として構成する。
●A型の小型ループ量子代数のevaluation表現の性質を調べる。
Seok-Jin Kang (Seoul National University) 15:00-16:00
Combinatorics of Young walls and crystal bases
[ Abstract ]
We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.

### 2007/02/16

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

トポロジーと私の思い出
[ Abstract ]

ことになります。それから「多様体のトポロジー」の分野で研究を
してきましたが、この40年間にトポロジーもずいぶん変化した
ように思います。自分の思い出話を交えて、その変化の様子をお話
できればと思います。私的な観点のものですので、それほど大所

#### Applied Analysis

15:00-16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ratnasingham SHIVAJI (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
[ Abstract ]
We study the existence of multiple positive solutions to systems of the form

-\\Delta u = \\lambda f(v)
-\\Delta v = \\lambda g(u)

in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.

### 2007/02/01

#### Lectures

15:00-16:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Lassi Paivarinta (Helsinki University of Technology, Finland)
On Calderon's inverse conductivity problem in the plane.

#### Lectures

16:15-17:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Nuuti Huyvonen (Helsinki University of Technology,
Finland)
Locating transparent cavities in optical absorption and scattering
tomography

### 2007/01/31

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #123 (Graduate School of Math. Sci. Bldg.)

ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――
[ Abstract ]

ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。

このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### Number Theory Seminar

15:15-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Dennis Eriksson (東大数理/Paris) 15:15-16:15
Towards a proof of a metrized Deligne-Riemann-Roch theorem

CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)
Frans Oort (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

A Sequential Unit Root Test
[ Abstract ]
It is well known that conventional unit root tests such as Dickey=Fuller and its variants do not have good power properties when sample size is not large. Lai and Siegmund (1983, AS) proved that OLS estimator of the AR(1) coefficient is asymptotically normally distributed in a sequential framework even if the time series has a unit root unlike the OLS estimator under a standard sampling scheme. We pursue this direction to propose a unit root test under a sequential sampling. The proposed test uses not only the OLS estimator of the AR(1) coefficient, which is asymptotically normal, but also the stopping time to construct the critical region, anticipating a better power property. We obtain analytic expressions of the joint distribution of the two statistics as well as its marginals under the null. We also consider the distribution of the statistics under local alternatives. The properties of the stopping time, to the best of our knowledge, have not been studied in the unit root literature. We calculate its expectation and variance.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html

### 2007/01/30

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
John F. Duncan (Harvard University)
Elliptic genera and some finite groups
[ Abstract ]
Recent developments in the representation theory of sporadic groups
suggest new formulations of moonshine' in which Jacobi forms take on the
role played by modular forms in the monstrous case. On the other hand,
Jacobi forms arise naturally in the study of elliptic genera. We review
the use of vertex algebra as a tool for constructing the elliptic genus of
a suitable vector bundle, and illustrate connections between this and
vertex algebraic representations of certain sporadic simple groups.

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Jerome Le Rousseau (Laboratoire d'Analyse Topologie Probabilit\'es
Universit\'e de Provence / CNRS)
Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates
[ Abstract ]
We shall review the different concepts of controllability for parabolic equations and a fix-point method to achieve null-controllability of classes of semilinear equations. It is mainly based on observability inequalities and a precise knowledge of the observability constant. These inequalities are obtained by means of global Carleman estimates. We shall review their derivations and how they can be obtained in the case of non-smooth coefficients. We shall also present some open questions.
Part of this work is in collaboration with Assia Benabdallah and Yves Dermenjian (also from Universit\\'e de Provence).

#### Infinite Analysis Seminar Tokyo

14:00-15:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Michael Lashkevich (Landau Institute)
Scaling limits for the SOS models and bosonization
[ Abstract ]
Two different scaling limits in the SOS models are considered. The scaling limits of the bosonic construction for form factors provide form factors of some classes of operators in the scaling SOS/RSOS models and the sine-Gordon model.

### 2007/01/29

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Radial cluster set of a bounded holomorphic map in the unit ball of C^n

### 2007/01/27

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

マイクロクラスターの特異なダイナミクス
[ Abstract ]

[ Abstract ]

この問題にアプローチするために、キリロフ・レシェティヒン加群$W_s^{(r)}$ (以下略してKR加群)を研究したい。これはアフィンリー環のディンキン図形の頂点$0$を除く頂点の番号$r$と、任意の正整数$s$の組によってパラメトライズされる。KR加群に関して、`フェルミ型公式''に起源をもつ以下の予想がある。尚, 現在までにこの予想の反例は見つかっていない。

さらに$s$が$t_r:=max(1,2/(\\alpha_r \\vert \\alpha_r))$の倍数ならば、KR加群$W_s^{(r)}$の結晶基底$B^{r,s}$は、レベル$s/t_r$の完全結晶である。ただし, $(\\cdot \\vert \\cdot)$はウェイト格子上の標準線形形式。」

### 2007/01/26

#### Algebraic Geometry Seminar

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Professor Frans Oort
(Department of Mathematics
University of Utrecht
)
Irreducibility of strata and leaves in the moduli space of
abelian varieties I (a survey of results)

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems

### 2007/01/25

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Michael TRIBELSKY (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset

#### Operator Algebra Seminars

15:15-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

The Pimsner-Voiculescu AF-embedding of the irrational rotation $C^*$-algebra and its subalgebra

A Note on Weak Amenability