## 過去の記録

### 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

#### GCOEレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam )
The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009年01月22日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

On the electron-phonon interacting system

#### GCOEレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009年01月21日(水)

#### 講演会

16:50-17:50   数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich)
The quenched critical point of a diluted disordered polymer model and the related question for the random copolymer

### 2009年01月20日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Generating function of eigenvalues of Daubechies Localization Operator
[ 講演概要 ]
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について

#### トポロジー火曜セミナー

16:30-17:30   数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム

Five dimensional $K$-contact manifolds of rank 2
[ 講演概要 ]
A $K$-contact manifold is an odd dimensional manifold $M$ with a contact form $\\alpha$ whose Reeb flow preserves a Riemannian metric on $M$. For examples, the underlying manifold with the underlying contact form of a Sasakian manifold is $K$-contact. In this talk, we will state our results on classification up to surgeries, the existence of compatible Sasakian metrics and a sufficient condition to be toric for closed $5$-dimensional $K$-contact manifolds with a $T^2$ action given by the closure of the Reeb flow, which are obtained by the application of Morse theory to the contact moment map for the $T^2$ action.

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム

Surface links which are coverings of a trivial torus knot (JAPANESE)
[ 講演概要 ]
We consider surface links which are in the form of coverings of a
trivial torus knot, which we will call torus-covering-links.
spun $T^2$-knots, turned spun $T^2$-knots, and symmetry-spun tori.
We see some properties of torus-covering-links.

### 2009年01月19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

### 2009年01月16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

### 2009年01月15日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Alin Ciuperca 氏 (Univ. Toronto)
Isomorphism of Hilbert modules over stably finite $C^*$-algebras

#### 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

On a phase field model for mode III crack growth
[ 講演概要 ]
2次元弾性体の面外変形による亀裂の進展を記述する,ある
フェイズ・フィールド・モデルについて考える.モデルの

Griffithの破壊基準をもとに,Ambrosio-Tortorelliに
よるエネルギー正則化のアイデアを用いてなされる.

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Alin Ciuperca 氏 (Univ. Toronto)
Isomorphism of Hilbert modules over stably finite $C^*$-algebras

#### Lie群論・表現論セミナー

13:30-17:20   数理科学研究科棟(駒場) 050号室

Quantization of complex manifolds
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/oshima60th200901.html

Global geometry on locally symmetric spaces — beyond the Riemannian case
[ 講演概要 ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I plan to give an exposition on the recent developments on the question about the global natures of locally non-Riemannian homogeneous spaces, with emphasis on the existence problem of compact forms, rigidity and deformation.

Classification of Fuchsian systems and their connection problem
[ 講演概要 ]
We explain a classification of Fuchsian systems on the Riemann sphere together with Katz's middle convolution, Yokoyama's extension and their relation to a Kac-Moody root system discovered by Crawley-Boevey.
Then we present a beautifully unified connection formula for the solution of the Fuchsian ordinary differential equation without moduli and apply the formula to the harmonic analysis on a symmetric space.

### 2009年01月14日(水)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]
ニューロンの興奮性の調節やシナプス可塑性において重要な役割を担っているC型タンパク質リン酸化酵素(PKC)は,その酵素活性と関連して細胞内局在が変化する性質を有する(トランスロケーション).GFP-γPKC融合タンパクを発現させたマウス小脳プルキンエ細胞において,平行線維シナプスの高頻度刺激に伴い,刺激部位近傍から樹状突起に沿ってトランスロケーションが伝播する現象が報告されている.最近,坪川は,同じ刺激条件で樹状突起内をほぼ同速度で伝播する細胞内Ca2+波が生じることを見出し,これがγPKCトランスロケーション波をリードしている可能性を指摘した.本研究では,生理学的・解剖学的知見に基づいたプルキンエ細胞の数理モデルを構築し,Ca2+波の再現を試みた.その結果に基づき,トランスロケーション伝播のメカニズムと機能的意義について考察する.