## Seminar information archive

Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～

#### Lectures

15:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Breaking the chain: slow versus fast pulling

**Michael Allman**(Warwick 大学)Breaking the chain: slow versus fast pulling

### 2010/01/12

#### Lie Groups and Representation Theory

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

代数的差分方程式の可解性と既約性

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka

**西岡斉治**(東京大学大学院数理科学研究科博士課程)代数的差分方程式の可解性と既約性

[ Abstract ]

差分代数の理論を使って,代数的差分方程式の代数函数解や超幾

何函数解の非存在や,存在する場合の特殊解の分類をする。

[ Reference URL ]差分代数の理論を使って,代数的差分方程式の代数函数解や超幾

何函数解の非存在や,存在する場合の特殊解の分類をする。

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka

#### Tuesday Seminar on Topology

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

Index problem for generically-wild homoclinic classes in dimension three

On a generalized suspension theorem for directed Fukaya categories

**篠原 克寿**(東京大学大学院数理科学研究科) 16:30-17:30Index problem for generically-wild homoclinic classes in dimension three

[ Abstract ]

In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.

In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.

**二木 昌宏**(東京大学大学院数理科学研究科) 17:30-18:30On a generalized suspension theorem for directed Fukaya categories

[ Abstract ]

The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz

fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a

categorification of the Milnor lattice of $W$. This is defined as the

directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to

\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of

vanishing cycles.

Recently Seidel has proved that this is stable under the suspension $W

+ u^2$ as a consequence of his foundational work on the directed

Fukaya category. We generalize his suspension theorem to the $W + u^d$

case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'

\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category

corresponding to the $A_n$-type quiver. This also generalizes a recent

work by the author with Kazushi Ueda.

The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz

fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a

categorification of the Milnor lattice of $W$. This is defined as the

directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to

\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of

vanishing cycles.

Recently Seidel has proved that this is stable under the suspension $W

+ u^2$ as a consequence of his foundational work on the directed

Fukaya category. We generalize his suspension theorem to the $W + u^d$

case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'

\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category

corresponding to the $A_n$-type quiver. This also generalizes a recent

work by the author with Kazushi Ueda.

### 2010/01/08

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

特殊関数とFuchs型常微分方程式

**大島利雄**(東京大学大学院数理科学研究科)特殊関数とFuchs型常微分方程式

[ Abstract ]

岩波全書の数学公式集III「特殊関数」の大部分はGaussの超幾何関数とその特殊化のBessel関数やLegendre多項式などで占められている。この超幾何関数についての最も重要な基本結果は1での値を与えるGaussの和公式とRiemann schemeによる特徴付けとであろう。この関数は一般超幾何関数やJordan-Pochhammer方程式へ、またHeun方程式からPainleve方程式へという解析、さらにAppell,Gelfand-青本,Heckman-Opdamによる多変数化という3つの方向の発展がある。講演ではこれらを含む統一的な理解、Riemann schemeの一般化とuniversal modelの存在定理(Deligne-Katz-Simpson問題)、接続公式(Gaussの和公式の一般化)、無限次元Kac-Moody Weyl群の作用について解説し、特異点の合流、積分表示、ベキ級数表示などについても述べたい。結果は構成的 でコンピュータ・プログラムで実現できる。

岩波全書の数学公式集III「特殊関数」の大部分はGaussの超幾何関数とその特殊化のBessel関数やLegendre多項式などで占められている。この超幾何関数についての最も重要な基本結果は1での値を与えるGaussの和公式とRiemann schemeによる特徴付けとであろう。この関数は一般超幾何関数やJordan-Pochhammer方程式へ、またHeun方程式からPainleve方程式へという解析、さらにAppell,Gelfand-青本,Heckman-Opdamによる多変数化という3つの方向の発展がある。講演ではこれらを含む統一的な理解、Riemann schemeの一般化とuniversal modelの存在定理(Deligne-Katz-Simpson問題)、接続公式(Gaussの和公式の一般化)、無限次元Kac-Moody Weyl群の作用について解説し、特異点の合流、積分表示、ベキ級数表示などについても述べたい。結果は構成的 でコンピュータ・プログラムで実現できる。

### 2010/01/07

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

**Luc Rey-Bellet**(Univ. Massachusetts)Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

#### GCOE Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

**LucRey-Bellet**(Univ. Massachusetts)Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

[ Abstract ]

Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.

Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.

### 2010/01/05

#### Tuesday Seminar on Topology

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

The volume growth of hyperkaehler manifolds of type $A_{\\infty}$

**服部 広大**(東京大学大学院数理科学研究科) 16:30-17:30The volume growth of hyperkaehler manifolds of type $A_{\\infty}$

[ Abstract ]

Hyperkaehler manifolds of type $A_{\\infty}$ were constructed due to Anderson-Kronheimer-LeBrun and Goto. These manifolds are 4-demensional, noncompact and their homology groups are infinitely generated. We focus on the volume growth of these hyperkaehler metrics. Here, the volume growth is asymptotic behavior of the volume of a ball of radius $r0$ with the center fixed. There are known examples of hyperkaehler manifolds whose volume growth is $r^4$ (ALE space) or $r^3$ (Taub-NUT space). In this talk we show that there exists a hyperkaehler manifold of type $A_{\\infty}$ whose volume growth is $r^c$ for a given $3

On the Runge theorem for instantons

Hyperkaehler manifolds of type $A_{\\infty}$ were constructed due to Anderson-Kronheimer-LeBrun and Goto. These manifolds are 4-demensional, noncompact and their homology groups are infinitely generated. We focus on the volume growth of these hyperkaehler metrics. Here, the volume growth is asymptotic behavior of the volume of a ball of radius $r0$ with the center fixed. There are known examples of hyperkaehler manifolds whose volume growth is $r^4$ (ALE space) or $r^3$ (Taub-NUT space). In this talk we show that there exists a hyperkaehler manifold of type $A_{\\infty}$ whose volume growth is $r^c$ for a given $3

**松尾 信一郎**(東京大学大学院数理科学研究科) 17:30-18:30

On the Runge theorem for instantons

[ Abstract ]

A classical theorem of Runge in complex analysis asserts that a

meromorphic function on a domain in the Riemann sphere can be

approximated, over compact subsets, by rational functions, that is,

meromorphic functions on the Riemann sphere.

This theorem can be paraphrased by saying that any solution of the

Cauchy-Riemann equations on a domain in the Riemann sphere can be

approximated, over compact subsets, by global solutions.

In this talk we will present an analogous result in which the

Cauchy-Riemann equations on Riemann surfaces are replaced by the

Yang-Mills instanton equations on oriented 4-manifolds.

We will also mention that the Runge theorem for instantons can be

applied to develop Yang-Mills gauge theory on open 4-manifolds.

A classical theorem of Runge in complex analysis asserts that a

meromorphic function on a domain in the Riemann sphere can be

approximated, over compact subsets, by rational functions, that is,

meromorphic functions on the Riemann sphere.

This theorem can be paraphrased by saying that any solution of the

Cauchy-Riemann equations on a domain in the Riemann sphere can be

approximated, over compact subsets, by global solutions.

In this talk we will present an analogous result in which the

Cauchy-Riemann equations on Riemann surfaces are replaced by the

Yang-Mills instanton equations on oriented 4-manifolds.

We will also mention that the Runge theorem for instantons can be

applied to develop Yang-Mills gauge theory on open 4-manifolds.

### 2009/12/25

#### Lectures

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation

**Academician T. Sh. Kalmenov**(Research Centre of Physics and Mathematics Almaty, Kazakhstan)A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation

### 2009/12/24

#### Mathematical Biology Seminar

16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Decomposition分析:趨勢データ分析の新しい枠組とアプローチ

http://shiro_horiuchi.homestead.com/homepage.html

**堀内 四郎**(The City University of New York, Hunter College)Decomposition分析:趨勢データ分析の新しい枠組とアプローチ

[ Abstract ]

A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations.

We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifi es the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function.

A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied fl exibly to a wide variety of decomposition problems.

[ Reference URL ]A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations.

We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifi es the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function.

A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied fl exibly to a wide variety of decomposition problems.

http://shiro_horiuchi.homestead.com/homepage.html

### 2009/12/22

#### Lie Groups and Representation Theory

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

既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**西山享**(青山学院大学)既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景

[ Abstract ]

既約 Harish-Chandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。

一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $-等質ラグランジュ部分多様体の閉包になる。

それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。)

[ Reference URL ]既約 Harish-Chandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。

一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $-等質ラグランジュ部分多様体の閉包になる。

それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。)

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Operator Algebra Seminars

14:40-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Symmetric representations of the group of diffeomorphisms of $\\mathbb R$

Topological entropy for actions of sofic groups

**谷本溶**(Univ. Roma ``Tor Vergata'') 14:40-16:10Symmetric representations of the group of diffeomorphisms of $\\mathbb R$

**David Kerr**(Texas A&M Univ.) 16:30-18:00Topological entropy for actions of sofic groups

#### Tuesday Seminar on Topology

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

Relative DG-category, mixed elliptic motives and elliptic polylog

**寺杣 友秀**(東京大学大学院数理科学研究科)Relative DG-category, mixed elliptic motives and elliptic polylog

[ Abstract ]

We consider a full subcategory of

mixed motives generated by an elliptic curve

over a field, which is called the category of

mixed elliptic motives. We introduce a DG

Hopf algebra such that the categroy of

mixed elliptic motives is equal to that of

comodules over it. For the construction, we

use the notion of relative DG-category with

respect to GL(2). As an application, we construct

an mixed elliptic motif associated to

the elliptic polylog. It is a joint work with

Kenichiro Kimura.

We consider a full subcategory of

mixed motives generated by an elliptic curve

over a field, which is called the category of

mixed elliptic motives. We introduce a DG

Hopf algebra such that the categroy of

mixed elliptic motives is equal to that of

comodules over it. For the construction, we

use the notion of relative DG-category with

respect to GL(2). As an application, we construct

an mixed elliptic motif associated to

the elliptic polylog. It is a joint work with

Kenichiro Kimura.

#### Infinite Analysis Seminar Tokyo

10:00-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)

離散周期KP方程式の簡約と、初期値問題の解の構成

Laplacian on graphs: Examples from physics

**岩尾 慎介**(東大数理) 10:00-11:00離散周期KP方程式の簡約と、初期値問題の解の構成

[ Abstract ]

様々に簡約された離散周期KP方程式に対して、スペクトル曲線を用いた逆散乱解法を考える。 このとき、簡約の種類によっては、超楕円とは限らない代数曲線が多数あらわれてくる。 本講演では、簡約周期KP方程式の初期値問題の解を構成する方法を紹介する。この方法はFayの恒等式を用いない構成的なもので、わかりやすいものである。

様々に簡約された離散周期KP方程式に対して、スペクトル曲線を用いた逆散乱解法を考える。 このとき、簡約の種類によっては、超楕円とは限らない代数曲線が多数あらわれてくる。 本講演では、簡約周期KP方程式の初期値問題の解を構成する方法を紹介する。この方法はFayの恒等式を用いない構成的なもので、わかりやすいものである。

**Y. Avishai**(Ben Gurion University) 13:00-14:00Laplacian on graphs: Examples from physics

[ Abstract ]

When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.

I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.

When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.

I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.

### 2009/12/21

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Ampleness of two-sided tilting complexes

**源 泰幸**(京都大学理学部数学教室)Ampleness of two-sided tilting complexes

[ Abstract ]

From the view point of noncommutative algebraic geometry (NCAG),

a two-sided tilting complex is an analog of a line bundle.

In this talk we introduce the notion of ampleness for two-sided

tilting complexes over finite dimensional algebras.

From the view point of NCAG, the Serre functors are considered to be

shifted canonical bundles. We show by examples that the property

of shifted canonical bundle captures some representation theoretic

property of algebras.

From the view point of noncommutative algebraic geometry (NCAG),

a two-sided tilting complex is an analog of a line bundle.

In this talk we introduce the notion of ampleness for two-sided

tilting complexes over finite dimensional algebras.

From the view point of NCAG, the Serre functors are considered to be

shifted canonical bundles. We show by examples that the property

of shifted canonical bundle captures some representation theoretic

property of algebras.

#### Seminar on Probability and Statistics

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

Absolute continuity of Ornstein-Uhlenbeck processes

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html

**Thomas Simon**(Universite de Lille 1)Absolute continuity of Ornstein-Uhlenbeck processes

[ Abstract ]

Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.

dX = AX + dB

where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.

[ Reference URL ]Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.

dX = AX + dB

where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html

### 2009/12/18

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)

数理科学をビジネスに - 最適化とデータマイニングの周辺でⅡ

**山下 浩**(数理システム代表取締役)数理科学をビジネスに - 最適化とデータマイニングの周辺でⅡ

#### Colloquium

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Dixmierの相似問題

**小澤登高**(東京大学大学院数理科学研究科)Dixmierの相似問題

[ Abstract ]

群のユニタリ表現に関しては美しい理論があるが, ユニタリでない無限次元表現はまったくとらえがたい対象である. そこで, 群のヒルベルト空間上の表現がいつユニタリ表現と相似(共役ともいう)になるかを問うのがDixmierの相似問題である. この問題は従順性という概念と深い関わりを持ち, 従って群の従順性の代数的な特徴づけを問うたvon Neumannの問題とも関わっている. von Neumannの問題は, 1980年代に否定的に解かれたものの, 近年の測度論的群論の発展により予想外の展開を見た. 講演では, これらのストーリ ーと測度論的群論の相似問題への応用(Monod氏との共同研究)を話す予定である. 予備知識はほとんど仮定しないので, 学部生にも聞きに来てもらいたい.

群のユニタリ表現に関しては美しい理論があるが, ユニタリでない無限次元表現はまったくとらえがたい対象である. そこで, 群のヒルベルト空間上の表現がいつユニタリ表現と相似(共役ともいう)になるかを問うのがDixmierの相似問題である. この問題は従順性という概念と深い関わりを持ち, 従って群の従順性の代数的な特徴づけを問うたvon Neumannの問題とも関わっている. von Neumannの問題は, 1980年代に否定的に解かれたものの, 近年の測度論的群論の発展により予想外の展開を見た. 講演では, これらのストーリ ーと測度論的群論の相似問題への応用(Monod氏との共同研究)を話す予定である. 予備知識はほとんど仮定しないので, 学部生にも聞きに来てもらいたい.

### 2009/12/17

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Almost commuting unitaries and ${\\mathbb{Z}}^2$-action

**佐藤康彦**(北海道大理)Almost commuting unitaries and ${\\mathbb{Z}}^2$-action

#### Seminar on Geometric Complex Analysis

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

Hyperbolicity of cycle spaces and automorphism groups of flag domains

**Alan Huckleberry**(Ruhr-Universität Bochum)Hyperbolicity of cycle spaces and automorphism groups of flag domains

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

A Liouville theorem for a semilinear heat equation with no gradient structure

**Hatem Zaag**(CNRS / パリ北大学)A Liouville theorem for a semilinear heat equation with no gradient structure

[ Abstract ]

We prove a Liouville Theorem for entire solutions of a vector

valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.

We prove a Liouville Theorem for entire solutions of a vector

valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.

### 2009/12/16

#### Seminar on Probability and Statistics

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

ecent results on volatility change point analysis for discretely sampled stochastic differential equations

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html

**Stefano Maria Iacus**(Department of Economics, Business and Statistics, University of Milan, Italy)ecent results on volatility change point analysis for discretely sampled stochastic differential equations

[ Abstract ]

In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.

Join work with Prof. Nakahiro Yoshida.

[ Reference URL ]In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.

Join work with Prof. Nakahiro Yoshida.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html

### 2009/12/15

#### Lie Groups and Representation Theory

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Open Problems in Discrete Geometric Analysis

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada

**砂田利一氏**(明治大学理工学部)Open Problems in Discrete Geometric Analysis

[ Abstract ]

Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.

[ Reference URL ]Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Open Problems in Discrete Geometric Analysis

**砂田 利一**(明治大学)Open Problems in Discrete Geometric Analysis

[ Abstract ]

Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.

Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.

### 2009/12/14

#### Seminar on Probability and Statistics

14:00-15:10 Room #128 (Graduate School of Math. Sci. Bldg.)

On the stability of contingent claimes in incomplet models under statistical estimations.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html

**L. VOSTRIKOVA**(LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)On the stability of contingent claimes in incomplet models under statistical estimations.

[ Abstract ]

In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.

[ Reference URL ]In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html

#### Algebraic Geometry Seminar

14:40-16:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Invariants of Fano varieties via quantum D-module

**Sergey Galkin**(IPMU)Invariants of Fano varieties via quantum D-module

[ Abstract ]

We will introduce and compute Apery characteristic

class and Frobenius genera - invariants of Fano variety derived from

it's Gromov-Witten invariants. Then we will show how to compute them

and relate with other invariants.

We will introduce and compute Apery characteristic

class and Frobenius genera - invariants of Fano variety derived from

it's Gromov-Witten invariants. Then we will show how to compute them

and relate with other invariants.

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