## 過去の記録

### 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)
[ 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)

#### 東京無限可積分系セミナー

15:00-16:00   数理科学研究科棟(駒場) 117号室

ルート系に付随した多重ゼータ関数とベルヌーイ多項式
[ 講演概要 ]
ルート系に付随した多重ゼータ関数とは E. Witten によって導入された半単純リー代数の既約表現に関するゼータ関数を松本氏が多変数化したものである. この視点から見るとリーマンゼータ関数は A_1 型であり, Euler-Zagier 多重ゼータ関数は A_n 型で適当な変数を 0 にしたものであるといえる.

(松本耕二氏, 津村博文氏との共同研究)

### 2006年10月20日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)

[ 講演概要 ]

[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~seminar/colloquium.html

#### 東京無限可積分系セミナー

16:30-17:30   数理科学研究科棟(駒場) 118号室
Petr Kulish 氏 (Steklov Math. Inst.)
Spin systems related to Temperley - Lieb algebra

### 2006年10月19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

A unique decomposition result for HT factors with torsion free core (Popa の論文の紹介)

### 2006年10月18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
Fabrice Orgogozo 氏 (東大数理・Ecole Polytechnique de Paris) 16:30-17:30
p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique
Kim Minhyong 氏 (Purdue大学・京大数理研) 17:45-18:45
Fundamental groups and Diophantine geometry

#### 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

Fourier analysis of irregularly spaced data on R^d
[ 講演概要 ]
1970年代にはじまった時系列解析の研究は、1変量時系列からはじまり、多変量時系列、空間系列、時空間系列へと対象が拡張されてきている。近年の空間系列、時空間系列の文献を調べてみれば、時系列と同じく等間隔に観測されたデータ(regularly spaced data) を前提としている場合が多い。しかし時系列とは異なり、空間系列ではランダムに散らばった地点で観測されたデータ (irregularly spaced data)を仮定する方が、応用範囲がひろい。そこで本発表では、irregularly spaced dataによる空間相関の推定問題を扱う。具体的にはデータを周波数領域に変換してスペクトルを推定する方法を提案し、推定量が一致性、漸近正規性を持つための条件を示す。本方法による東京地価データ分析例も紹介する。本研究は、矢島美寛教授(東京大学大学院経済学研究科)との共同研究です。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/11.html

#### 代数幾何学セミナー

16:00-18:15   数理科学研究科棟(駒場) 122号室
E. Esteves 氏 (IMPA) 16:00-17:00

Jets of singular foliations and applications
to curves and their moduli spaces

F. Zak 氏 (Independent Univ. of Moscow) 17:15-18:15
Dual varieties, ramification, and Betti numbers
of projective varieties

### 2006年10月17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
Arnaud Deruelle 氏 (University of Tokyo)
Networking Seifert Fibered Surgeries on Knots (joint work with Katura Miyazaki and Kimihiko Motegi)
[ 講演概要 ]
We define a Seifert Surgery Network which consists of integral Dehn surgeries on knots yielding Seifert fiber spaces;here we allow Seifert fiber space with a fiber of index zero as degenerate cases. Then we establish some fundamental properties of the network. Using the notion of the network, we will clarify relationships among known Seifert surgeries. In particular, we demonstrate that many Seifert surgeries are closely connected to those on torus knots in Seifert Surgery Network. Our study suggests that the network enables us to make a global picture of Seifert surgeries.

### 2006年10月16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
Sebastien Boucksom 氏 (東大数理 JSPS研究員)
Differentiability of the volume of divisors and Khovanskii-Teissier inequalities

### 2006年10月12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

### 2006年10月11日(水)

#### 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

Optimal stopping problem associated with jump-diffusion processes
[ 講演概要 ]
We study an optimal stopping problem of some performance function with respect to a jump-diffusion process.

### 2006年10月10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
Elmar Vogt 氏 (Frie Universitat Berlin)
Estimating Lusternik-Schnirelmann Category for Foliations:A Survey of Available Techniques
[ 講演概要 ]
The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$.For foliated manifolds there are several notions generalizing this concept, all of them due
to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \\cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.

### 2006年10月06日(金)

#### 数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

### 2006年10月05日(木)

#### 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) 123号室

Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field
[ 講演概要 ]
We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006年09月27日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Professor Vakhtang Kokilashvili 氏 (A. Razmadze Mathematical Institute, Georgian Academy of Science)
Integral operators in the weighted Lebesgue spaces with a variable exponent
[ 講演概要 ]
We present a boundedness criteria of the maximal functions and the singular integral operators defined on Carleson curves in the weighted Lebesgue spaces with a variable exponent. There are also given the weighted estimates for the generalized singular integrals raised in the theory of generalized analytic functions of I.N.Vekua and the weighted Sobolev theorems for potentials on Carleson curves. The weight functions may be of power function type as well as oscillating type. The certain version of a Muckenhoupt-type condition for a variable exponent will be considered.

We also expect to treat two-weight problems for the classical integral operators in the variable Lebesgue spaces and to give some applications of the obtained results to the summability problems of Fourier series in two-weighted setting.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

#### 数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 123号室

The coevolution of altruism and punishment:role of the selfish punisher
[ 講演概要 ]
Punishment is an important mechanism promoting the evolution of altruism among nonrelatives. We investigate the coevolution of altruism and punitive behavior, considering four strategies: a cooperator who punishes defectors (AP), a pure cooperator (AN), a defector who punishes defectors (selfish punisher or SP), and a pure defector (SN). We especially focus on the effects of SP on the coevolution of altruism and punishment, studying both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP helps cooperators to evolve, but SP does not in the fertility model. In both models of a lattice-structured population, SP promotes the spread of AP, but AN discourages it. These results indicate that punishment is a form of spite behavior and that different models give different magnitude of advantage to spite behavior.

### 2006年09月25日(月)

#### 統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 128号室

Nonparametric testing time-homogeneity for L'evy processes
[ 講演概要 ]
First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html