## Seminar information archive

Seminar information archive ～02/20｜Today's seminar 02/21 | Future seminars 02/22～

### 2007/08/02

#### Algebraic Geometry Seminar

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

Dynamics of automorphisms on algebraic varieties

**De-Qi Zhang**(Singapore大学)Dynamics of automorphisms on algebraic varieties

[ Abstract ]

The building blocks of automorphisms / endomorphisms of compact varieties are determined --- an algebro geometric approach towards dynamics.

The building blocks of automorphisms / endomorphisms of compact varieties are determined --- an algebro geometric approach towards dynamics.

### 2007/07/25

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

大規模ランダム行列のスペクトル理論とデータ解析への応用(Review)

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/05.html

**小林 景**(統計数理研究所, 学振特別研究員)大規模ランダム行列のスペクトル理論とデータ解析への応用(Review)

[ Abstract ]

The empirical spectral distribution of random matrices have been studied since Wigner's pioneering work on the semicircular law in the 1950's. The result says that the empirical spectral distribution of a symmetric matrix with i.i.d. random elements converges to the semicircular law as the size of the matrix becomes large. Though this result is beautiful in theory, its application has been limited to a few problems in nuclear physics and coding theory. The next breakthrough was the Marcenko-Pastur (M-P) law for the asymptotic spectral distribution of sample covariance matrices. The M-P law has found more applications, in particular high dimensional statistical data analysis, than the semicircular law.

In this talk I will first review these two significant results. Each of them has three completely different proofs. Then I will explain several other theoretical results that have mostly been studied this decade. Finally, I will present some of the applications of these results. This review is partly based on lectures on random matrices given by P. Bickel, N. El-Karoui and A. Guionnet, and also some seminars at UC Berkeley.

(# This talk is almost the same as the talk I gave at ISM on June 1.)

[ Reference URL ]The empirical spectral distribution of random matrices have been studied since Wigner's pioneering work on the semicircular law in the 1950's. The result says that the empirical spectral distribution of a symmetric matrix with i.i.d. random elements converges to the semicircular law as the size of the matrix becomes large. Though this result is beautiful in theory, its application has been limited to a few problems in nuclear physics and coding theory. The next breakthrough was the Marcenko-Pastur (M-P) law for the asymptotic spectral distribution of sample covariance matrices. The M-P law has found more applications, in particular high dimensional statistical data analysis, than the semicircular law.

In this talk I will first review these two significant results. Each of them has three completely different proofs. Then I will explain several other theoretical results that have mostly been studied this decade. Finally, I will present some of the applications of these results. This review is partly based on lectures on random matrices given by P. Bickel, N. El-Karoui and A. Guionnet, and also some seminars at UC Berkeley.

(# This talk is almost the same as the talk I gave at ISM on June 1.)

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/05.html

### 2007/07/20

#### Colloquium

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

ソリトン物理はおもしろい---スピノル型ボーズ・アインシュタイン凝縮体におけるソリトン

**和達三樹**(東京理科大学理学部物理学科)ソリトン物理はおもしろい---スピノル型ボーズ・アインシュタイン凝縮体におけるソリトン

### 2007/07/19

#### Seminar for Mathematical Past of Asia

17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)

幕末・明治初期の日本における西洋数学の導入と漢訳西洋数学書籍

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

**李 佳女華**(東京大学大学院総合文化研究科)幕末・明治初期の日本における西洋数学の導入と漢訳西洋数学書籍

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

#### Operator Algebra Seminars

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

On a class of II$_1$ factors with at most one Cartan subalgebra

**小沢登高**(東大数理)On a class of II$_1$ factors with at most one Cartan subalgebra

### 2007/07/18

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Tropical toric varieties

**梶原 健**(横浜国立大学)Tropical toric varieties

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Easy full-joint estimators of stable processes

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/04.html

**増田 弘毅**(九州大学大学院数理学研究院)Easy full-joint estimators of stable processes

[ Abstract ]

安定レヴィ過程からの高頻度観測に基づいた同時推定に関しては,尤度比確率場の漸近挙動は安易に二次項の観測情報量まで見ただけでは解明されず,最尤推定量の典型的な“良い漸近挙動”が保証されないことが分かっている.本発表では,標本メディアンおよび標本メディアンのプラグイン型統計量の漸近挙動に基づき,モデルに入る全パラメータの同時推定を可能とする計算容易な推定量の構成法を紹介し,正則な漸近共分散行列を有する漸近正規性を導出する.推定量の有限標本での挙動を数値実験で検証する.時間があれば,非対称安定レヴィ過程の場合に関して分かっている事柄についても触れる.

[ Reference URL ]安定レヴィ過程からの高頻度観測に基づいた同時推定に関しては,尤度比確率場の漸近挙動は安易に二次項の観測情報量まで見ただけでは解明されず,最尤推定量の典型的な“良い漸近挙動”が保証されないことが分かっている.本発表では,標本メディアンおよび標本メディアンのプラグイン型統計量の漸近挙動に基づき,モデルに入る全パラメータの同時推定を可能とする計算容易な推定量の構成法を紹介し,正則な漸近共分散行列を有する漸近正規性を導出する.推定量の有限標本での挙動を数値実験で検証する.時間があれば,非対称安定レヴィ過程の場合に関して分かっている事柄についても触れる.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/04.html

### 2007/07/17

#### Tuesday Seminar on Topology

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

Orbifold Cohomology of Wreath Product Orbifolds and

Cohomological HyperKahler Resolution Conjecture

**松村 朝雄**(東京大学大学院数理科学研究科)Orbifold Cohomology of Wreath Product Orbifolds and

Cohomological HyperKahler Resolution Conjecture

[ Abstract ]

Chen-Ruan orbifold cohomology ring was introduced in 2000 as

the degree zero genus zero orbifold Gromov-Witten invariants with

three marked points. We will review its construction in the case of

global quotient orbifolds, following Fantechi-Gottsche and

Jarvis-Kaufmann-Kimura. We will describe the orbifold cohomology of

wreath product orbifolds and explain its application to Ruan's

cohomological hyperKahler resolution conjecture.

Chen-Ruan orbifold cohomology ring was introduced in 2000 as

the degree zero genus zero orbifold Gromov-Witten invariants with

three marked points. We will review its construction in the case of

global quotient orbifolds, following Fantechi-Gottsche and

Jarvis-Kaufmann-Kimura. We will describe the orbifold cohomology of

wreath product orbifolds and explain its application to Ruan's

cohomological hyperKahler resolution conjecture.

### 2007/07/12

#### Operator Algebra Seminars

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

Normalizers of MASAs and irreducible subfactors

**酒匂宏樹**(東大数理)Normalizers of MASAs and irreducible subfactors

### 2007/07/11

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Algebraic cycles on products of elliptic curves over p-adic fields

**Andreas Rosenschon**(University of Alberta)Algebraic cycles on products of elliptic curves over p-adic fields

### 2007/07/10

#### Tuesday Seminar on Topology

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

Combable functions, quasimorphisms, and the central limit theorem

(joint with Koji Fujiwara)

**Danny C. Calegari**(California Institute of Technology)Combable functions, quasimorphisms, and the central limit theorem

(joint with Koji Fujiwara)

[ Abstract ]

Quasimorphisms on groups are dual to stable commutator length,

and detect extremal phenomena in topology and dynamics. In typical groups

(even in a free group) stable commutator length is very difficult to

calculate, because the space of quasimorphisms is too large to study

directly without adding more structure.

In this talk, we show that a large class of quasimorphisms - the so-called

"counting quasimorphisms" on word-hyperbolic groups - can be effectively

described using simple machines called finite state automata. From this,

and from the ergodic theory of finite directed graphs, one can deduce a

number of properties about the statistical distribution of the values of a

counting quasimorphism on elements of the group.

Quasimorphisms on groups are dual to stable commutator length,

and detect extremal phenomena in topology and dynamics. In typical groups

(even in a free group) stable commutator length is very difficult to

calculate, because the space of quasimorphisms is too large to study

directly without adding more structure.

In this talk, we show that a large class of quasimorphisms - the so-called

"counting quasimorphisms" on word-hyperbolic groups - can be effectively

described using simple machines called finite state automata. From this,

and from the ergodic theory of finite directed graphs, one can deduce a

number of properties about the statistical distribution of the values of a

counting quasimorphism on elements of the group.

### 2007/07/09

#### Seminar on Geometric Complex Analysis

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

Geometry of hyperkahler quotients

**今野宏**(東京大学)Geometry of hyperkahler quotients

### 2007/07/06

#### Seminar on Probability and Statistics

15:00-16:10 Room #122 (Graduate School of Math. Sci. Bldg.)

Estimating multidimensional densities through the Malliavin-Thalmaier formula

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/03.html

**Arturo KOHATSU-HIGA**(大阪大学大学院基礎工学研究科)Estimating multidimensional densities through the Malliavin-Thalmaier formula

[ Abstract ]

TBA

[ Reference URL ]TBA

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/03.html

### 2007/07/05

#### Operator Algebra Seminars

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

Factorization in $C^*$-Algebras

**Rolf Dyre Svegstrup**(東大数理)Factorization in $C^*$-Algebras

### 2007/07/04

#### PDE Real Analysis Seminar

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

The Lipschitz truncation method

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

**Lars Diening**(Universitat Freiburg)The Lipschitz truncation method

[ Abstract ]

We study the existence of weak solutions to the incompressible $p$-Navier Stokes equations. This system can be used to describe the flow of honey, ketchup, blood, suspensions, polymers, and glaciers. We are interested in small values of $p$, where the method of monotone operators fails. We establish weak solutions by means of the Lipschitz truncation technique, where Sobolev Functions are approximated by Lipschitz functions in a special way. We apply the technique also to electrorheological fluids, where the exponent $p$ depends on the electric field.

[ Reference URL ]We study the existence of weak solutions to the incompressible $p$-Navier Stokes equations. This system can be used to describe the flow of honey, ketchup, blood, suspensions, polymers, and glaciers. We are interested in small values of $p$, where the method of monotone operators fails. We establish weak solutions by means of the Lipschitz truncation technique, where Sobolev Functions are approximated by Lipschitz functions in a special way. We apply the technique also to electrorheological fluids, where the exponent $p$ depends on the electric field.

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

#### Geometry Seminar

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

A Special Lagrangian Fibration in the TAUB-NUT Space

Symmetries in generalized complex geometry

**野田尚廣**(名古屋大学大学院多元数理科学研究科) 14:40-16:10A Special Lagrangian Fibration in the TAUB-NUT Space

[ Abstract ]

この講演では, Taub-NUT space における special Lagrangian fibration の具体的構成について述べるつもりである.Taub-NUT space は複素多様体としては二次元複素空間であるが,計量が通常と異なり完備で非平坦なリッチ平坦計量をもつ Hyper-Kahler 多様体として特徴づけられる.この空間の special Lagrangian fibration が,Ionel-Min Oo の手法を用いることで具体的に構成できることを見る.

この講演では, Taub-NUT space における special Lagrangian fibration の具体的構成について述べるつもりである.Taub-NUT space は複素多様体としては二次元複素空間であるが,計量が通常と異なり完備で非平坦なリッチ平坦計量をもつ Hyper-Kahler 多様体として特徴づけられる.この空間の special Lagrangian fibration が,Ionel-Min Oo の手法を用いることで具体的に構成できることを見る.

**新田泰文**(大阪大学大学院理学研究科) 16:30-18:00Symmetries in generalized complex geometry

[ Abstract ]

一般化された複素構造という新しい幾何構造についてお話しします.これは複素構造とシンプレクティック構造を自然に含む非常に大きな枠組みで Hitchin が導入し,Gualtieri らによって複素幾何学的,シンプレクティック幾何学的な視点から盛んに研究されています.本講演では一般化された複素多様体への群作用について,シンプレクティック幾何的立場から解説いたします.一般化された複素多様体への Hamiltonian action という概念を導入し,その群作用に関する簡約定理や,一般化された運動量写像に関する凸性について説明します.

一般化された複素構造という新しい幾何構造についてお話しします.これは複素構造とシンプレクティック構造を自然に含む非常に大きな枠組みで Hitchin が導入し,Gualtieri らによって複素幾何学的,シンプレクティック幾何学的な視点から盛んに研究されています.本講演では一般化された複素多様体への群作用について,シンプレクティック幾何的立場から解説いたします.一般化された複素多様体への Hamiltonian action という概念を導入し,その群作用に関する簡約定理や,一般化された運動量写像に関する凸性について説明します.

### 2007/07/03

#### Tuesday Seminar on Topology

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

Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation

(joint work with Mitsuhiko Takasawa)

**金 英子**(東京工業大学情報理工学研究科)Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation

(joint work with Mitsuhiko Takasawa)

[ Abstract ]

We concern two invariants of pseudo-Anosov mapping classes.

One is the dilatation of pseudo--Anosov maps and the other is the volume

of mapping tori. To study how two invariants are related, fixing a surface

we represent a mapping class by using the standard generator set and compute

these two for all pseudo--Anosov mapping classes with up to some word length.

In the talk, we observe two properties:

(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to

the volume is bounded from below by some positive constant which only

depends on the surface.

(2) The conjugacy class having the minimal dilatation reaches the minimal volume.

On the observation (1), in case of the mapping class group of a once--punctured

torus, we give a concrete lower bound of the ratio.

We concern two invariants of pseudo-Anosov mapping classes.

One is the dilatation of pseudo--Anosov maps and the other is the volume

of mapping tori. To study how two invariants are related, fixing a surface

we represent a mapping class by using the standard generator set and compute

these two for all pseudo--Anosov mapping classes with up to some word length.

In the talk, we observe two properties:

(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to

the volume is bounded from below by some positive constant which only

depends on the surface.

(2) The conjugacy class having the minimal dilatation reaches the minimal volume.

On the observation (1), in case of the mapping class group of a once--punctured

torus, we give a concrete lower bound of the ratio.

### 2007/07/02

#### Seminar on Geometric Complex Analysis

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

On the Meyer function for theta divisors

**飯田修一**(東大数理)On the Meyer function for theta divisors

### 2007/06/29

#### Lie Groups and Representation Theory

15:30-17:45 Room #122 (Graduate School of Math. Sci. Bldg.)

On the theory of Bessel functions associated with root systems

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

**Salem Ben Said**(Nancy大)On the theory of Bessel functions associated with root systems

[ Abstract ]

The theory of spherical functions on Riemannian symmetric spaces G/K and on non-compactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of Heckman-Opdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to non-compactly causal symmetric spaces.

[ Reference URL ]The theory of spherical functions on Riemannian symmetric spaces G/K and on non-compactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of Heckman-Opdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to non-compactly causal symmetric spaces.

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

### 2007/06/28

#### Operator Algebra Seminars

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

A new construction of causal nets of operator algebras

**谷本溶**(東大数理)A new construction of causal nets of operator algebras

### 2007/06/27

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Empirical likelihood method for time series analysis

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html

**小方 浩明**(早稲田大学, 国際教養学部)Empirical likelihood method for time series analysis

[ Abstract ]

For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.

[ Reference URL ]For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

The conjecture of Birch and Swinnerton-Dyer is misleading

**Stephen Lichtenbaum**(Brown University)The conjecture of Birch and Swinnerton-Dyer is misleading

[ Abstract ]

All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these

points should be given by the sum and difference of the ranks of

corresponding finitely generated abelian groups.

All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these

points should be given by the sum and difference of the ranks of

corresponding finitely generated abelian groups.

#### Mathematical Finance

17:30-19:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Selection and Performance Analysis of Asia-Pacific Hedge Funds

**山本 匡**(東京大)Selection and Performance Analysis of Asia-Pacific Hedge Funds

### 2007/06/25

#### Seminar on Geometric Complex Analysis

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

Weil-Petersson 計量とTakhtajan-Zograf 計量の漸近挙動

**小櫃邦夫**(鹿児島大学)Weil-Petersson 計量とTakhtajan-Zograf 計量の漸近挙動

### 2007/06/22

#### Algebraic Geometry Seminar

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

Projective varieties with nef anti-canonical divisors

**Qi Zhang**(Missouri大学)Projective varieties with nef anti-canonical divisors

[ Abstract ]

Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.

Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.

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