## Seminar information archive

Seminar information archive ～08/19｜Today's seminar 08/20 | Future seminars 08/21～

### 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

### 2006/10/31

#### Lie Groups and Representation Theory

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

ルート系の部分系の分類

http://akagi.ms.u-tokyo.ac.jp/seminar.html

**大島利雄氏**(東大数理)ルート系の部分系の分類

[ Abstract ]

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,

同値の条件をさらに Ξ の自己同型(部分系の分類に対応),Ξ の既約成分の自己同型の直積,

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.

[ Reference URL ]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,

同値の条件をさらに Ξ の自己同型(部分系の分類に対応),Ξ の既約成分の自己同型の直積,

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.

http://akagi.ms.u-tokyo.ac.jp/seminar.html

#### Tuesday Seminar on Topology

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

Unsmoothable group actions on elliptic surfaces

**中村 信裕**(東京大学大学院数理科学研究科)Unsmoothable group actions on elliptic surfaces

[ Abstract ]

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.

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.

### 2006/10/30

#### PDE Real Analysis Seminar

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

Inverse Problems and Index Formulae for Dirac Operators

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

**Matti Lassas**(Helsinki University of Technology, Institute of Mathematics)Inverse Problems and Index Formulae for Dirac Operators

[ Abstract ]

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).

[ Reference URL ]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).

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

### 2006/10/26

#### Operator Algebra Seminars

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

Introduction to Brownian surfaces

**Remi Leandre**(Univ. Bourgogne)Introduction to Brownian surfaces

### 2006/10/25

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

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

**平之内 俊郎**(九州大学)Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )

[ Abstract ]

局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).

今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.

局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).

今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.

#### Lectures

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Regularization of nonlinear inverse problems: mathematics, industrial application fields, new challenges

**Heinz W. Engl**(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

[ Abstract ]

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.

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.

### 2006/10/24

#### Tuesday Seminar on Topology

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

A review of crossed G-structures

**Marco Zunino**(JSPS, University of Tokyo)A review of crossed G-structures

[ Abstract ]

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.

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.

#### Tuesday Seminar of Algebraic Analysis

16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)

Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)

[ Reference URL ]

http://agusta.ms.u-tokyo.ac.jp/alganalysis.html

**吉野 邦生**(上智大理工)Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)

[ Reference URL ]

http://agusta.ms.u-tokyo.ac.jp/alganalysis.html

### 2006/10/23

#### Geometry Seminar

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

Toric geometry and Mirror Symmetry

Balance point and stability of vector bundles over a projective manifold

**Naichung Conan Leung**(Chinese University of Hong Kong) 14:40-16:10Toric geometry and Mirror Symmetry

[ Abstract ]

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.

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**(Chinese University of Hong Kong) 16:30-18:00Balance point and stability of vector bundles over a projective manifold

[ Abstract ]

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.

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.

#### Seminar on Geometric Complex Analysis

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

Classification of hypersurface simple K3 singularities -- 95 and others

**泊 昌孝**(日本大学文理学部)Classification of hypersurface simple K3 singularities -- 95 and others

#### Lectures

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Mathematical modelling and numerical simulation: from iron and steel making via inverse problems to finance

**Heinz W. Engl**(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

[ Abstract ]

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.

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.

### 2006/10/21

#### Infinite Analysis Seminar Tokyo

13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)

組合せベーテ仮説とタウ関数

**国場敦夫**(東大総合文化)組合せベーテ仮説とタウ関数

[ Abstract ]

組合せベーテ仮説ではベーテ根とベーテベクトルの代わりにその組合せ論的類似物として rigged configuration と highest pathを対象物とする.

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

今回のお話では rigged configuration に付随した超離散タウ関数を導入し,以下の性質,結果について(時間の許すところまで)紹介します.

アフィン・クリスタルのエネルギー関数に一致する.

超離散双線形方程式をみたす.

KKR全単射の明示公式を与える.

箱玉系の角転送行列に相当し,一般Nソリトン解を与える

周期的 highest pathでは超離散リーマンテータ関数になる.

(坂本玲峰氏,山田泰彦氏との共同研究)

組合せベーテ仮説ではベーテ根とベーテベクトルの代わりにその組合せ論的類似物として rigged configuration と highest pathを対象物とする.

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

今回のお話では rigged configuration に付随した超離散タウ関数を導入し,以下の性質,結果について(時間の許すところまで)紹介します.

アフィン・クリスタルのエネルギー関数に一致する.

超離散双線形方程式をみたす.

KKR全単射の明示公式を与える.

箱玉系の角転送行列に相当し,一般Nソリトン解を与える

周期的 highest pathでは超離散リーマンテータ関数になる.

(坂本玲峰氏,山田泰彦氏との共同研究)

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138 Next >