## Seminar information archive

Seminar information archive ～05/26｜Today's seminar 05/27 | Future seminars 05/28～

#### Infinite Analysis Seminar Tokyo

15:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

積分変換の項を持つソリトン方程式とその解の構造について

**土谷洋平**(東大数理)積分変換の項を持つソリトン方程式とその解の構造について

[ Abstract ]

ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。

ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。

### 2006/11/17

#### Seminar on Probability and Statistics

15:00-16:10 Room #118 (Graduate School of Math. Sci. Bldg.)

Functional estimation of L'evy measure for jump-type processes

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

**清水 泰隆**(大阪大学大学院基礎工学研究科)Functional estimation of L'evy measure for jump-type processes

[ Abstract ]

Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.

[ Reference URL ]Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

### 2006/11/16

#### Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Crystalline complexes and D-modules

**Pierre Berthelot**(Rennes大学)Crystalline complexes and D-modules

#### Applied Analysis

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The large time behavior of graphical surfaces in the mean curvature flow

**奈良 光紀**(東京工業大学)The large time behavior of graphical surfaces in the mean curvature flow

[ Abstract ]

We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.

We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.

#### Operator Algebra Seminars

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

商型右余イデアルの特徴づけとポワソン境界の分類

**戸松玲治**(東大数理)商型右余イデアルの特徴づけとポワソン境界の分類

### 2006/11/15

#### Lectures

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Crystalline complexes and D-modules

**Pierre Berthelot**(Rennes大学)Crystalline complexes and D-modules

#### Mathematical Finance

17:30-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)

歪みリスク尺度の1-パラメータ族とその応用

**塚原 英敦**(成城大)歪みリスク尺度の1-パラメータ族とその応用

### 2006/11/14

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

High-codimensional knots spun about manifolds

**高瀬将道**(信州大学理学部)High-codimensional knots spun about manifolds

[ Abstract ]

The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.

The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.

The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.

The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.

### 2006/11/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds

**小野 肇**(東京工業大学)Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds

#### Algebraic Geometry Seminar

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Hom stacks and Picard stacks

**青木昌雄**(京大数理研)Hom stacks and Picard stacks

### 2006/11/10

#### Geometry Seminar

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

箙多様体のベッチ数の計算

**中島啓**(京都大学大学院理学研究科)箙多様体のベッチ数の計算

[ Abstract ]

箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.

箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.

#### Tuesday Seminar on Topology

17:40-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)

WRT invariant for Seifert manifolds and modular forms

**樋上和弘**(東京大学大学院理学系研究科 物理)WRT invariant for Seifert manifolds and modular forms

[ Abstract ]

We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.

We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.

### 2006/11/09

#### Operator Algebra Seminars

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

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

**水田有一**(東大数理)Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)

#### Lectures

16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

<連続講演> Graphs and motives

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

### 2006/11/08

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Fredric Flin**(Hokkaido University)Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### Lectures

16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

<連続講演> Graphs and motives

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

#### Geometry Seminar

14:40-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

代数多様体の退化とトロピカル幾何

Counting problem in tropical geometry

**梶原 健**(横浜国立大学大学院工学研究院応用数学) 14:40-16:10代数多様体の退化とトロピカル幾何

[ Abstract ]

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.

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.

**西納 武男**(京都大学理学研究科数学教室) 16:30-18:00Counting problem in tropical geometry

[ Abstract ]

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.

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.

#### Seminar on Probability and Statistics

16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

**蛭川 潤一**(早稲田大学)LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses

[ Abstract ]

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.

[ Reference URL ]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.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

### 2006/11/07

#### Lectures

16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

<連続講演> Graphs and motives

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

### 2006/11/06

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the extension of twisted pluricanonical forms

**Mihai Paun**(Université Henri Poincaré Nancy)On the extension of twisted pluricanonical forms

### 2006/11/02

#### Operator Algebra Seminars

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

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

**水田有一**(東大数理)Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)

#### Applied Analysis

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy

**Messoud Efendiev**(ミュンヘン工科大学)On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy

[ Abstract ]

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.

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.

### 2006/11/01

#### Number Theory Seminar

16:30-18:45 Room #117 (Graduate School of Math. Sci. Bldg.)

Essential dimension of some finite group schemes

Overconvergent Siegel modular forms

**G.Bayarmagnai**(東大数理) 16:30-17:30Essential dimension of some finite group schemes

**Jacques Tilouine**(パリ北大学) 17:45-18:45Overconvergent Siegel modular forms

[ Abstract ]

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.

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.

#### Seminar on Probability and Statistics

15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Some problems related to the estimation of the invariant measure of an ergodic diffusion.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html

**Ilia NEGRI**(Department of Management and Information Technology, University of Bergamo, Italy)Some problems related to the estimation of the invariant measure of an ergodic diffusion.

[ Abstract ]

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.

[ Reference URL ]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.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html

#### PDE Real Analysis Seminar

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Tan Yongji**(School of Mathematical Science, Fudan University )A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

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