## 過去の記録

#### 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

### 2008年12月11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

Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras

### 2008年12月10日(水)

#### 東京幾何セミナー

14:45-18:00   数理科学研究科棟(駒場) 122号室

「今後の予定」欄には、東工大で行われるセミナーは表��

Acyclic polarizations and localization of Riemann-Roch numbers
[ 講演概要 ]

Megumi Harada 氏 (McMaster University) 16:30-18:00
The topology of symplectic and hyperkahler quotients
[ 講演概要 ]
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.

### 2008年12月09日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Bertrand Deroin 氏 (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
[ 講演概要 ]
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.

### 2008年12月08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

Critically finite holomorphic maps on projective spaces

### 2008年12月05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04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

カッツ環の作用の分類

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
いつもと開始時刻および場所が違いますのでご注意ください
Genkai Zhang 氏 (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2008年12月03日(水)

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 122号室
Freddy Delaben 氏 (ETH)
The structure of dynamic utility functions in a Brownian Filtration

[ 講演概要 ]
The penalty function for monetary dynamic utility functions
has a special form. They can be seen as potentials. In the Brownian Filtration Rao's theorem permits to give a complete description.

#### 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

Mean-periodicity and analytic properties of zeta-functions
[ 講演概要 ]
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。

### 2008年12月02日(火)

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同で開催します. またいつもと開催時刻および開催場所が違います。

[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.

The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html