## 過去の記録

#### 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
The Dirichlet-to-Neumann map as a pseudodifferential
operator
[ 講演概要 ]
Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\\partial M$ the Dirichlet-to-Neumann operator $\\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\\Lambda_g f =(\\partial_\\nu u)|_{\\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\\laplace_g u=0$ in $M$, $u|_{\\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\\partial M$.

We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\\Lambda_g:H^{1/2}(\\partial M)\\longrightarrow H^{-1/2}(\\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 118号室
Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ 講演概要 ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

### 2008年10月10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10月06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

Lichtenbaum予想の幾何学的類似

### 2008年10月03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09月29日(月)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意下さい.
Christopher Deninger 氏 (Munster大学)
A determinant for p-adic group algebras
[ 講演概要 ]
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.

### 2008年09月22日(月)

#### 講演会

14:45-15:45   数理科学研究科棟(駒場) 122号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Invariance principle for the random conductance model
with unbounded conductances (a joint work with Martin Barlow)

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 122号室
Sergio Albeverio 氏 (Bonn 大学)
Asymptotic expansions of infinite dimensional integrals with applications (quantum mechanics, mathematical finance, biology)

### 2008年09月17日(水)

#### 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
ティータイム@コモンルーム 16:00~
Cyril Houdayer 氏 (UCLA)
Free Araki-Woods Factors and Connes's Bicentralizer Problem

### 2008年09月09日(火)

#### 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
Yves de Cornulier 氏 (CNRS, Rennes)
The space of subgroups of an abelian group

### 2008年09月08日(月)

#### Lie群論・表現論セミナー

11:00-12:00   数理科学研究科棟(駒場) 126号室
Federico Incitti 氏 (ローマ第 1 大学)
Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials
[ 講演概要 ]
Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.

In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.

I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.

This is partly based on a joint work with Francesco Brenti and Mario Marietti.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008年09月03日(水)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 002号室
Fred Weissler 氏 (University of Paris 13)
Finite time blowup of oscillating solutions to the nonlinear heat equation
[ 講演概要 ]
(This is joint work with T. Cazenave and F. Dickstein.)

We study finite time blowup properties of solutions of the nonlinear heat equation, both on $R^N$, and on a ball in $R^N$ with Dirichlet boundary conditions. We show, among other results, that the set of initial values producing global solutions is not always star-shaped around the 0 solution. This contrasts with the case where only non-negative solutions are considered.

### 2008年08月27日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
Don Zagier 氏 (Max Planck研究所)
$q$-series and modularity

### 2008年08月25日(月)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
Ronald C. King 氏 (Emeritus Professor, University of Southampton)
Affine Weyl groups, grids, coloured tableaux and characters of affine algebras
[ 講演概要 ]
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.

### 2008年08月21日(木)

#### 博士論文発表会

15:00-15:40   数理科学研究科棟(駒場) 126号室

On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)

### 2008年08月06日(水)

#### 諸分野のための数学研究会

10:30-14:00   数理科学研究科棟(駒場) 056号室

Yimin Wei氏(13:00-14:00)

Kazufumi Ito 氏 (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ 講演概要 ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei 氏 (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ 講演概要 ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

#### 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

オペレーショナルリスクと fat tail を持つ iid 確率変数の和に対する極限定理

### 2008年08月01日(金)

#### 代数学コロキウム

13:00-18:00   数理科学研究科棟(駒場) 002号室
4講演あります.また,いつもと曜日,時間,場所が異なります.
ご注意下さい.

Olivier Brinon 氏 (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell 氏 (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser 氏 (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
[ 講演概要 ]
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan 氏 (Nottingham大学) 17:00-18:00
On Iwasawa theory for abelian varieties over function fields of positive characteristic

### 2008年07月29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

Clifford代数の表現から作られる局所関数等式を満たす多項式とそれに付随する空間について(佐藤文広氏との共同研究)
[ 講演概要 ]

この講演では、概均質ベクトル空間の相対不変式ではないにもかかわらず、その複素ベキが同種の局所関数等式を満たすような多項式が、Clifford代数の表現より構成できることを報告する。

### 2008年07月28日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Lin Weng 氏 (Kyushu University)
Symmetries and the Riemann Hypothesis
[ 講演概要 ]
Associated to each pair of a reductive group
and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected
to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta,
a very different but closely related non-abelian zeta,
defined using stable lattices and a new geo-arithmetical cohomology,
will be explained.
Examples for $SL, SO, Sp$ and $G_2$ and confirmations of
(Lagarias and) Masatoshi Suzuki on the RH for zetas
associated to rank 1 and 2 groups will be presented
as well.
[ 講演参考URL ]
http://xxx.lanl.gov/abs/0803.1269

### 2008年07月26日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]
A型変形W代数の自由場表示を用いてA型Macdomald多項式のtableau表示を構成する。さらにD型変形W代数の自由場表示を用いて、第一基本ウェイトの正数倍のウェイトを持つD型Macdomald多項式のtableau表示を構成する。尚、本研究は白石潤一氏(東京大学)との共同研究である。

Entanglement Entropy in Conventional and Topological Orders
[ 講演概要 ]

(1)量子ダイマー模型におけるトポロジカル・エントロピー
トポロジカル秩序を持つ系においては、エンタングルメント・エントロピーに、背景のゲージ理論を特徴づける、負の定数項が含まれることが、Kitaevらによって予想された。我々は、Z2トポロジカル秩序を示すと考えられる量子ダイマー模型において、予想の数値的検証を行い、予想が精度よく成り立つことを示した。
Ref. S. Furukawa & G. Misguich, Phys. Rev. B 75, 214407 (2007).
(2)自発的対称性の破れとマクロスコピック・エンタングルメント

### 2008年07月24日(木)

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 122号室
Noriko Yui 氏 (Queen's University)
On the modularity of Calabi-Yau varieties over $\\mathbf{Q}$

### 2008年07月23日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
7月23日(水)は午前中の講演のみです。午後の討論会はありません。
ご注意下さい。

Andrei Constantinescu 氏 (Ecole Polytechnique)
Identification of residual stresses: problem settings and results.
[ 講演概要 ]
Identiﬁcation of residual stresses is an important task in many engineering ﬁelds such as fatigue or fracture mechanics, where their presence can signiﬁcantly increase or decrease the apparent strength of mechanical components.

The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:

1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.

2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.

3. present existing results in the identification of residual stresses for the different

#### 諸分野のための数学研究会

10:30-14:00   数理科学研究科棟(駒場) 056号室

Yimin Wei氏(13:00-14:00)

Adaptive Tikhonov Regularization for Inverse Problems
[ 講演概要 ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei 氏 (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ 講演概要 ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

### 2008年07月17日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
George Elliott 氏 (Univ. Toronto)
A canonical AF-algebra construction for rank two subgroups of R
(A new description of the Pimsner-Voiculescu embedding)