## Seminar information archive

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

### 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.

### 2009/12/11

#### 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Ⅰ

**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Ⅰ

### 2009/12/10

#### Lectures

10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (9)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (9)

#### Operator Algebra Seminars

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

Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra

**張欽**(東大数理)Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra

### 2009/12/09

#### Lectures

14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (8)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (8)

#### Seminar on Probability and Statistics

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html

**佐藤 整尚**(統計数理研究所)分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について

[ Abstract ]

近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。

[ Reference URL ]近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html

### 2009/12/08

#### Lectures

14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

冨田竹崎理論とその応用 (7)

**竹崎正道**(UCLA)冨田竹崎理論とその応用 (7)

#### GCOE Seminars

17:30-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Gaudin subalgebras and stable rational curves. (ENGLISH)

**Giovanni Felder**(ETH Zurich)Gaudin subalgebras and stable rational curves. (ENGLISH)

[ Abstract ]

We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.

We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.

### 2009/12/07

#### Kavli IPMU Komaba Seminar

17:30-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric quantization on noncompact manifolds

**Weiping Zhang**(Chern Institute of Mathematics, Nankai University)Geometric quantization on noncompact manifolds

[ Abstract ]

We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.

We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.

### 2009/12/03

#### Operator Algebra Seminars

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

Vanishing of quasi-homomorphisms and the stable commutator

lengths on special linear groups over euclidean rings

**見村万佐人**(東大数理)Vanishing of quasi-homomorphisms and the stable commutator

lengths on special linear groups over euclidean rings

### 2009/12/02

#### PDE Real Analysis Seminar

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

A hyperbolic fluid model based on Cattaneo's law

**Juergen Saal**(University of Konstanz)A hyperbolic fluid model based on Cattaneo's law

[ Abstract ]

In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).

One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.

In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).

One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.

### 2009/12/01

#### Tuesday Seminar on Topology

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

Non-Abelian Novikov homology

**Andrei Pajitnov**(Univ. de Nantes)Non-Abelian Novikov homology

[ Abstract ]

Classical construction of S.P. Novikov

associates to each circle-valued Morse map

a chain complex defined over a ring

of Laurent power series in one variable.

In this survey talk we shall explain several

results related to the construction and

properties of non-Abelian generalizations of the

Novikov complex.

Classical construction of S.P. Novikov

associates to each circle-valued Morse map

a chain complex defined over a ring

of Laurent power series in one variable.

In this survey talk we shall explain several

results related to the construction and

properties of non-Abelian generalizations of the

Novikov complex.

### 2009/11/30

#### Seminar on Geometric Complex Analysis

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

Equidistribution and Nevanlinna theory

**奥山裕介**(京都工芸繊維大学)Equidistribution and Nevanlinna theory

#### Kavli IPMU Komaba Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Chiral Algebras of (0,2) Models: Beyond Perturbation Theory

**Junya Yagi**(Rutgers University)Chiral Algebras of (0,2) Models: Beyond Perturbation Theory

[ Abstract ]

The chiral algebras of two-dimensional sigma models with (0,2)

supersymmetry are infinite-dimensional generalizations of the chiral

rings of (2,2) models. Perturbatively, they enjoy rich mathematical

structures described by sheaves of chiral differential operators.

Nonperturbatively, however, they vanish completely for certain (0,2)

models with no left-moving fermions. In this talk, I will explain how

this vanishing phenomenon takes places. The vanishing of the chiral

algebra of a (0, 2) model implies that supersymmetry is spontaneously

broken in the model, which in turn suggests that no harmonic spinors

exist on the loop space of the target space. In particular, the

elliptic genus of the model vanishes, thereby providing a physics

proof of a special case of the Hoelhn-Stolz conjecture.

The chiral algebras of two-dimensional sigma models with (0,2)

supersymmetry are infinite-dimensional generalizations of the chiral

rings of (2,2) models. Perturbatively, they enjoy rich mathematical

structures described by sheaves of chiral differential operators.

Nonperturbatively, however, they vanish completely for certain (0,2)

models with no left-moving fermions. In this talk, I will explain how

this vanishing phenomenon takes places. The vanishing of the chiral

algebra of a (0, 2) model implies that supersymmetry is spontaneously

broken in the model, which in turn suggests that no harmonic spinors

exist on the loop space of the target space. In particular, the

elliptic genus of the model vanishes, thereby providing a physics

proof of a special case of the Hoelhn-Stolz conjecture.

### 2009/11/27

#### Lecture Series on Mathematical Sciences in Soceity

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

金融リスク管理と数理(実践)

**池森俊文氏(高野 康 氏)**(みずほ第一フィナンシャルテクノロジー(株))金融リスク管理と数理(実践)

#### Seminar on Probability and Statistics

13:40-14:50 Room #128 (Graduate School of Math. Sci. Bldg.)

非線形時系列モデルのイノベーション密度の推定

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html

**加藤 賢悟**(広島大学大学院理学研究科数学専攻)非線形時系列モデルのイノベーション密度の推定

[ Abstract ]

In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.

[ Reference URL ]In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html

### 2009/11/26

#### Applied Analysis

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

L^p 粘性解の弱ハルナック不等式の最近の進展

**小池 茂昭**(埼玉大学・理学部数学科)L^p 粘性解の弱ハルナック不等式の最近の進展

[ Abstract ]

Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.

しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.

本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.

Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.

しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.

本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.

### 2009/11/25

#### PDE Real Analysis Seminar

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

Recent results on weak and strong solutions of the Navier-Stokes equations

**Hermann Sohr**(University Paderborn)Recent results on weak and strong solutions of the Navier-Stokes equations

[ Abstract ]

Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.

This condition is not only sufficient

- there are several well-known sufficient conditions in this context

- but also necessary, and yields therefore the largest possible class of such strong solutions.

As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.

Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.

This condition is not only sufficient

- there are several well-known sufficient conditions in this context

- but also necessary, and yields therefore the largest possible class of such strong solutions.

As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.

### 2009/11/24

#### Tuesday Seminar of Analysis

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

Analytic Properties of Eigen Values of Daubechies Localization Operator

**吉野 邦生**(東京都市大学)Analytic Properties of Eigen Values of Daubechies Localization Operator

[ Abstract ]

1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、

(2)ドーベシー局在化作用素のシンボルの再現公式、

(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示

等について述べる。

1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、

(2)ドーベシー局在化作用素のシンボルの再現公式、

(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示

等について述べる。

#### Tuesday Seminar on Topology

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

A topological approach to left orderable groups

**Adam Clay**(University of British Columbia)A topological approach to left orderable groups

[ Abstract ]

A group G is said to be left orderable if there is a strict

total ordering of its elements such that gin G. Left orderable groups have been useful in solving many problems in topology, and now we find that topology is returning the favour: the set of all left orderings of a group is denoted by LO(G), and it admits a natural topology, under which LO(G) becomes a compact topological

space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.

For example, the space of left orderings of the braid group B_n for n>2

contains isolated points (yet it is uncountable), while the space of left

orderings of the fundamental group of the Klein bottle is finite.

Twice in recent years, the space of left orderings has been used very

successfully to solve difficult open problems from the field of left

orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the

newest understanding of this connection, and highlight some potential

applications of further advances.

A group G is said to be left orderable if there is a strict

total ordering of its elements such that g

space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.

For example, the space of left orderings of the braid group B_n for n>2

contains isolated points (yet it is uncountable), while the space of left

orderings of the fundamental group of the Klein bottle is finite.

Twice in recent years, the space of left orderings has been used very

successfully to solve difficult open problems from the field of left

orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the

newest understanding of this connection, and highlight some potential

applications of further advances.

### 2009/11/20

#### Lecture Series on Mathematical Sciences in Soceity

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

金融リスク管理と数理(概論)

**池森俊文**(みずほ第一フィナンシャルテクノロジー(株)取締役社長)金融リスク管理と数理(概論)

#### Colloquium

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

On solving fully nonlinear elliptic Partial Differential Equations

**Louis Nirenberg**

(New York University)On solving fully nonlinear elliptic Partial Differential Equations

[ Abstract ]

The talk will present some results in recent work by R.Harvey and B. Lawson: Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 (2009), 396-443. It concerns solving boundary value problems for elliptic equations of the form F(D'2u) = 0. They find generalized solutions which are merely continuous . The talk will be expository. No knowledge of Partial Differential Equations will be necessary.

The talk will present some results in recent work by R.Harvey and B. Lawson: Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 (2009), 396-443. It concerns solving boundary value problems for elliptic equations of the form F(D'2u) = 0. They find generalized solutions which are merely continuous . The talk will be expository. No knowledge of Partial Differential Equations will be necessary.

### 2009/11/19

#### Lectures

15:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

数論的D加群の特性サイクルと分岐理論

**阿部知行**(東京大学大学院数理科学研究科)数論的D加群の特性サイクルと分岐理論

### 2009/11/18

#### Lectures

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The stochastic Burgers equation and its discretization

**Herbert Spohn**(ミュンヘン工科大学・九州大学)The stochastic Burgers equation and its discretization

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