## 過去の記録

#### GCOEセミナー

16:15-17:00   数理科学研究科棟(駒場) 370号室
G. Yuan 氏 (Northeast Normal Univ.)
Inverse problems and observability inequalities for plate equations and Schrodinger equations.
[ 講演概要 ]
In this talk, we will present some results on inverse problems and observability inequalities for some plate and Schrodinger equaions by using several kinds of Carleman estimates.

### 2009年02月05日(木)

#### 講演会

17:00-18:30   数理科学研究科棟(駒場) 117号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Jin CHENG (程 晋) 氏 (復旦大学)
Heat transfer in composite materials with Stenfen-Boltzmann conditions and related inverse problems
[ 講演概要 ]
In this talk, we will present our recent results on the mathematical model of the heat transfer in the composite materials. The related inverse problems are discussed. The numerical results show our methods are effective.

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 118号室
GOMBODORJ BAYARMAGNAI 氏 (東京大学大学院数理科学研究科)
THE(g,K)-MODULE STRUCTURE OF PRINCIPAL SERIES AND RELATED WHITTAKER FUNCTIONS OF SU(2,2)(SU(2,2)の主系列の(g,K)-加群構造と関連するWHITTAKER関数)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 126号室

On behavior of solutions near singularities for nonlinear diffusion equations(非線形拡散方程式の特異点近くでの解の挙動)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 126号室

Inverse Problems Related with Non-symmetric Operators and Inverse Problem for One-dimensional Fractional Partial Differential Equation(非対称作用素に関する逆問題と1次元非整数階偏微分方程式に関する逆問題)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

Inverse Source Problems for diffusion Equations and Fractional Diffusion Equations(拡散方程式及び非整数階拡散方程式に対するソース項決定逆問題)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室

Analysis of error constants for linear conforming and nonconforming finite elements(適合および非適合1次有限要素の誤差定数の解析)

### 2009年02月04日(水)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室

Non-Parametric Statistics for a partial sums of iid observations: New Trials
[ 講演概要 ]
I would lke to review Alpha- quantiles and Ranks with "Empirical Distributions" defined on partial sums of iid. observations discussed in the time continuous version (Brownian Motion).. Then revisiting the formulation of classical estimand and estimators for iid observations , described for example in Fillipova's paper, I would lik,e to discuss on what we could do for our partial sums of iid observations in orde to define our non-parametric estimators and estimands. I will be talking only on the ideas, but mathematical proofs will not be provided.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/13.html

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

Black-Scholes 周りの摂動展開について(前半)/ 確率積分の離散化誤差について(後半)
[ 講演概要 ]
(前半)確率ボラティリティモデルに対して知られている, Black-Scholes モデル周りでの各種摂動展開が統一的にマルチンゲール展開の理論によって 厳密に正当化かつ一般化されることを示す. またとくに拡散過程モデルに 対しては再生法を用いてより精密な結果を与える.

(後半)確率積分の近似として, 増大停止時刻列による区間分割 Riemann 和 をとったとき, その近似誤差の漸近分布を与える. ファイナンスへの応用とし てデルタヘッジエラーを解析し, 取引費用を考慮した上で漸近的に平均2乗誤 差を最小化する戦略を定義する.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/14.html

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 002号室
GCOE 特別講演会
Bendong LOU (婁 本東) 氏 (同済大学)
Traveling waves of a curvature flow in almost periodic media
[ 講演概要 ]
In a plane media with almost periodic vertical striations, we study a curvature flow and construct two kinds of traveling waves, one having a straight line like profile and the other having a V shaped profile. For each of the first kind of traveling waves, its profile is the graph of a function whose derivative is almost periodic. For each of the second kind of traveling waves, its profile is like a pulsating cone, with tails asymptotically approach the first kind of traveling waves.
Also we consider a homogenization problem and provide an explicit formula for the homogenized traveling speed.
This is joint work with Xinfu Chen.

#### 統計数学セミナー

13:40-14:50   数理科学研究科棟(駒場) 128号室
Stefano Maria Iacus 氏 (Universita degli Studi di Milano)
Applications of Iterated Function Systems to Inference and Simulation
[ 講演概要 ]
The Iterated Function Systems (IFSs) were born in mid eighties as applications of the theory of discrete dynamical systems and as useful tools for buildings fractals and other similar sets or to produce image compression algorithms. The fundamental result on which the IFS method is based is the Banach contraction theorem because IFSs are defined as operators with some contractive property. In practical applications the crucial point is to solve the inverse problem: given an element f in some metric space (S,d), find a contraction T:S -> S that admits a unique fixed point p such that d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the fixed point p can be identified with the operator T, but in most cases T is an approximation of the target f and T takes linear forms. We present applications of the IFS technique to the problem of estimation of distribution and density functions and to the simulation of L2 stochastic processes.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html

### 2009年02月03日(火)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Gombodorj Bayarmagnai 氏 (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
[ 講演概要 ]
In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009年02月02日(月)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich)
On a perceptron version of the Generalized Random Energy Model

### 2009年01月30日(金)

#### GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 370号室
F. Cakoni 氏 (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
[ 講演概要 ]
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.

#### GCOEセミナー

15:10-16:10   数理科学研究科棟(駒場) 370号室
Lucie Baudouin 氏 (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
[ 講演概要 ]
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).

### 2009年01月29日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method
[ 講演概要 ]
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.

### 2009年01月28日(水)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 122号室

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
Pierre Colmez 氏 (École polytechnique)
On the p-adic local Langlands correspondence

### 2009年01月27日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム

Lagrangian Floer homology and quasi homomorphism
from the group of Hamiltonian diffeomorphism

[ 講演概要 ]
Entov-Polterovich constructed quasi homomorphism
from the group of Hamiltonian diffeomorphisms using
spectral invariant due to Oh etc.
In this talk I will explain a way to study this
quasi homomorphism by using Lagrangian Floer homology.
I will also explain its generalization to use quantum
cohomology with bulk deformation.
When applied to the case of toric manifold, it
gives an example where (infinitely) many quasi homomorphism
exists.
(Joint work with Oh-Ohta-Ono).

### 2009年01月26日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

#### GCOEレクチャーズ

17:15-18:15   数理科学研究科棟(駒場) 470号室

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講
[ 講演概要 ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 470号室
Vilmos Komornik 氏 (University of Strasbourg)
Ingham-Beurling type inequalities
[ 講演概要 ]
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.

### 2009年01月24日(土)

#### 東京無限可積分系セミナー

11:00-16:00   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]
Young図形における hook formula は、組合せ論的には、その Young 図形の standar
d tableau の総数を数え上げる公式である。R. P. Stanley は reverse plane parti
tion のなす母関数を考えることにより、この公式をq-hook formula に拡張し、E. R
. Gansner はそれをさらに多変数に一般化した。

n の hook formula の証明も与える。

Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$
[ 講演概要 ]
Motivated by a connection between representation theory of
the degenerate affine Hecke algebra of type A and
Lie theory associated with $A^{(1)}_{p-1}$, we determine the complete
set of representatives of the orbits for the Weyl group action on
the set of weights of level 2 integrable highest weight representations of $\\widehat{\\mathfrak{sl}}_p$.
Applying a crystal technique, we show that Catalan numbers appear in their weight multiplicities.

Here "a crystal technique" means a result based on a joint work with S.Ariki and V.Kreiman,
which (as an application of the Littelmann's path model) combinatorially characterize
the connected component (usually called Kleshchev bipartition in the representation theoretic context)
$B(\\Lambda_0+\\Lambda_s)\\subseteq B(\\Lambda_0)\\otimes B(\\Lambda_s)$ in the tensor product.

On a dimer model with impurities
[ 講演概要 ]
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the boundary, which we set as a conjecture. We first show that there is a bijection between the set of dimer coverings on
$G$ and the set of spanning forests on two graphs which are made from $G$, with configuration of impurities satisfying a pairing condition, and this bijection can be regarded as a extension of the Temperley bijection. We consider local move consisting of two operations, and by using the bijection mentioned above, we prove local move connectedness. Finally, we prove that the above conjecture is true,
in some spacial cases.

### 2009年01月23日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 128号室