## 過去の記録

#### 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.

### 2009年01月13日(火)

#### 講演会

10:30-11:30   数理科学研究科棟(駒場) 002号室
この講義で単位は出ません。

Gieri Simonett 氏 (Vanderbilt University, USA)
Analytic semigroups, maximal regularity and nonlinear parabolic problems
[ 講演参考URL ]
http://www.math.sci.hokudai.ac.jp/sympo/090113/index.html

#### 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

Compactification of the homeomorphism group of a graph
[ 講演概要 ]
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\\Gamma$ with countably many components,
the homeomorphism group $\\mathcal{H}(\\Gamma)$
and its identity component $\\mathcal{H}_+(\\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\\overline{\\mathcal{H}}(\\Gamma)$ and
$\\overline{\\mathcal{H}}_+(\\Gamma)$ of these groups and describe the
topological type of the pair $(\\overline{\\mathcal{H}}_+(\\Gamma), \\mathcal{H}_+(\\Gamma))$
using the data of $\\Gamma$. I will also discuss the topological structure of
$\\overline{\\mathcal{H}}(\\Gamma)$ where $\\Gamma$ is the circle.

### 2009年01月12日(月)

#### 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

[ 講演概要 ]

#### 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
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)

### 2009年01月09日(金)

#### GCOEレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 123号室
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.

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

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations

[ 講演概要 ]
The condition number of a matrix is commonly used for investigating the
stability of solutions to linear algebraic systems. Recent meshless
techniques for solving PDEs have been known to give rise to
ill-conditioned matrices, yet are still able to produce results that are
close to machine accuracy. In this work, we consider the method of
fundamental solutions (MFS), which is known to solve, with extremely high
accuracy, certain
partial differential equations, namely those for which a fundamental
solution is known. To investigate the applicability of the MFS, either when
the boundary is not analytic or when the boundary data is not harmonic, we
examine the relationship between its accuracy and the effective condition
number.

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
[ 講演概要 ]
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.

### 2009年01月08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
Stefaan Vaes 氏 (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors

#### 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
Stefaan Vaes 氏 (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors

#### 諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 056号室
※今回は開催日、開催時間共に通常と異なりますことをご了承下さい。

Calibration problems for Black-Scholes American Options under the GMMY process
[ 講演概要 ]
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.

#### GCOEレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 123号室

Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications

[ 講演概要 ]
Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.

We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009年01月06日(火)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 123号室

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)
[ 講演概要 ]

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

#### 講演会

14:00-15:30   数理科学研究科棟(駒場) 123号室

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)
[ 講演概要 ]

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

### 2009年01月05日(月)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 123号室

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)
[ 講演概要 ]

・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

### 2008年12月26日(金)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

On Siegel Eisenstein series of degree two and weight 2
[ 講演概要 ]
Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。

### 2008年12月19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

### 2008年12月18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
Benoit Collins 氏 (東大数理/Ottawa 大学)
Some geometric and probabilistic properties of the free quantum group $A_o(n)$

### 2008年12月17日(水)

#### 統計数学セミナー

13:40-14:50   数理科学研究科棟(駒場) 002号室
Ilia Negri 氏 (University of Bergamo, Italy)
Goodness of fit tests for ergodic diffusions by discrete sampling schemes
[ 講演概要 ]
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct two kinds of tests based on different types of discrete observations, namely, the data observed discretely in time or in space. We prove that the limit distribution of our tests is the supremum of the standard Brownian motion, and thus our tests are asymptotically distribution free. We also show that our tests are consistent under any fixed alternatives.

joint with Yoichi Nishiyama (Inst. Statist. Math.)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/09.html

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室
Stefano Maria Iacus 氏 (Universita degli Studi di Milano, Italy)
Divergences Test Statistics for Discretely Observed Diffusion Processes
[ 講演概要 ]
In this paper we propose the use of $\\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.

joint work with A. De Gregorio
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 002号室
Nicolas Privault 氏 (City University of Hong Kong)
Stein estimation of Poisson process intensities
[ 講演概要 ]
In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html

### 2008年12月12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

ガスタービン翼の伝熱について