## 過去の記録

### 2006年11月09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

Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)

#### 講演会

16:20-17:50   数理科学研究科棟(駒場) 123号室
S. Bloch 氏 (シカゴ大学)
<連続講演> Graphs and motives

### 2006年11月08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
Fredric Flin 氏 (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
[ 講演概要 ]
Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### 講演会

16:20-17:50   数理科学研究科棟(駒場) 123号室
S. Bloch 氏 (シカゴ大学)
<連続講演> Graphs and motives

#### 東京幾何セミナー

14:40-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.

Counting problem in tropical geometry
[ 講演概要 ]
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.

#### 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

LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses
[ 講演概要 ]
This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

### 2006年11月07日(火)

#### 講演会

16:20-17:50   数理科学研究科棟(駒場) 123号室
11月7日(火)-11月9日(木)の連続講演です.

S. Bloch 氏 (シカゴ大学)
<連続講演> Graphs and motives

### 2006年11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
Mihai Paun 氏 (Université Henri Poincaré Nancy)
On the extension of twisted pluricanonical forms

### 2006年11月02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

Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室
Messoud Efendiev 氏 (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
[ 講演概要 ]
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.

### 2006年11月01日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 117号室
2講演です
G.Bayarmagnai 氏 (東大数理) 16:30-17:30
Essential dimension of some finite group schemes
Jacques Tilouine 氏 (パリ北大学) 17:45-18:45
Overconvergent Siegel modular forms
[ 講演概要 ]
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.

#### 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
Ilia NEGRI 氏 (Department of Management and Information Technology, University of Bergamo, Italy)
Some problems related to the estimation of the invariant measure of an ergodic diffusion.
[ 講演概要 ]
We consider a one dimensional ergodic diffusion process solution of a stochastic differential equation. We suppose that the diffusion coefficient is known whereas the drift coefficient $S$ is unknown. Our interest is the invariant measure of the process denoted as $\\mu$. We denote by $f_S$ and $F_S$ the invariant density and the invariant distribution function of $\\mu$ respectively. We present the problems of finding efficient estimators when we observe the trajectory of the diffusion in continuos time over $[0,T]$ and we study asymptotic properties of the estimators when $T$ goes to infinity.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 128号室
Tan Yongji 氏 (School of Mathematical Science, Fudan University )
A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging
[ 講演概要 ]
Spontaneous well-logging is an important technique in petroleum exploitation. The potential field is of strong discontinuity on the interface since the spontaneous potential differences. It causes difficulty in mathematical analysis and numerical computing.

New mathematical model and numerical method is designed to overcome the difficulty and good results is obtained.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006年10月31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

ルート系の部分系の分類
[ 講演概要 ]
ルート系 Ξ からルート系 Σ へのCartan整数を保つ写像の分類を考える(像は Σ の部分系と見なせる).
Σ のWeyl群(Σ の内部同型)で移りあうものを同値とみたときの分類をまず行い,

Σ の自己同型などを許すものに広げた場合の分類や像が放物型かどうかの判定も与える.
ルート系の dual pair の概念を定義し,同値類への Ξ の自己同型の作用の考察に用いる.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

#### 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

Unsmoothable group actions on elliptic surfaces
[ 講演概要 ]
Let G be a cyclic group of order 3,5 or 7.
We prove the existence of locally linear G-actions on elliptic surfaces which can not be realized by smooth actions with respect to specific smooth structures.
To prove this, we give constraints on smooth actions by using gauge theory.
In fact, we use a mod p vanishing theorem on Seiberg-Witten invariants, which was originally proved by F.Fang.
We give a geometric alternative proof of this, which enables us to extend the theorem.

### 2006年10月30日(月)

#### PDE実解析研究会

16:30-17:30   数理科学研究科棟(駒場) 128号室
Matti Lassas 氏 (Helsinki University of Technology, Institute of Mathematics)
Inverse Problems and Index Formulae for Dirac Operators
[ 講演概要 ]
We consider a selfadjoin Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M, g)$ with a nonempty boundary.

The operator $D_P$ is specified by a boundary condition $P(u|_{\\partial M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator.

We assume the existence of a chirality operator which decomposes $L2(M, V)$ into two orthogonal subspaces $X_+ \\oplus X_-$.

In the talk we consider the reconstruction of $(M, g)$, $V$, and $D_P$ from the boundary data on $\\partial M$.

The data used is either the Cauchy data, i.e. the restrictions to $\\partial M \\times R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\\times \\C4$, $M \\subset \\R3$. The presented results have been done in collaboration with Yaroslav Kurylev (Loughborough, UK).
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006年10月26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
Remi Leandre 氏 (Univ. Bourgogne)
Introduction to Brownian surfaces

### 2006年10月25日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 117号室
いつもと時間が違います

Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )
[ 講演概要 ]

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 122号室
Heinz W. Engl 氏 (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences)
Regularization of nonlinear inverse problems: mathematics, industrial application fields, new challenges
[ 講演概要 ]
Motivated by some of the industrial examples presented in the first talk, we outline the theory of regularization methods for the stable solution of nonlinear inverse problems. Then, we turn to some new problem fields of possible future industrial relevance in systems and molecular biology.

### 2006年10月24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
Marco Zunino 氏 (JSPS, University of Tokyo)
A review of crossed G-structures
[ 講演概要 ]
We present the definition of "crossed structures" as introduced by Turaev and others a few years ago. One of the original motivations in the introduction of these structures and of the related notion of a "Homotopy Quantum Field Theory" (HQFT) was the extension of Reshetikhin-Turaev invariants to the case of flat principal bundles on 3-manifolds. We resume both this aspect of the theory and other applications in both algebra and topology and we present our results on the algebraic structures involved.

#### 代数解析火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室

Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)
[ 講演参考URL ]
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html

### 2006年10月23日(月)

#### 東京幾何セミナー

14:40-18:00   数理科学研究科棟(駒場) 056号室
Naichung Conan Leung 氏 (Chinese University of Hong Kong) 14:40-16:10
Toric geometry and Mirror Symmetry
[ 講演概要 ]
We first review the geometry of toric varieties. Then we will explain the SYZ mirror symmetry conjecture and how toric geometry plays an important role here.

Xiaowei Wang 氏 (Chinese University of Hong Kong) 16:30-18:00
Balance point and stability of vector bundles over a projective manifold
[ 講演概要 ]
In this talk, we will start with some basic theory of GIT and symplectic quotient, then introduce various kind of stability of a holomorphic vector bundle over a projective manifold. As an application of the general theory, we will answer a question raised by Donaldson by showing that GIT stable vector bundle produces a sequence of balanced embedding of the underlying projective manifold to the Grassmanian.

#### 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

Classification of hypersurface simple K3 singularities -- 95 and others

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 122号室
Heinz W. Engl 氏 (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences )
Mathematical modelling and numerical simulation: from iron and steel making via inverse problems to finance
[ 講演概要 ]
We first describe the industrial mathematics structure in linz, extending from basic research via graduate education to industrial collaboration. We then present a few projetcs from our experience, ranging from aspects of iron and steel processing via mathematical simulation and optimization in car industry to robust and fast pricing methods for financial derivates. Since some of the projects involve inverse problem, we give a first introduction into this field, which will be deepened in the second talk.

### 2006年10月21日(土)

#### 東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

これらは Kerov-Kirillov-Reshetikhin (KKR)全単射により1対1対応する.

アフィン・クリスタルのエネルギー関数に一致する.

KKR全単射の明示公式を与える.

(坂本玲峰氏,山田泰彦氏との共同研究)