## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

### 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

https://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.

https://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

https://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.

https://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

https://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.

https://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.

https://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.

https://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

https://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。

https://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.

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