## 過去の記録

### 2009年12月21日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

Ampleness of two-sided tilting complexes
[ 講演概要 ]
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.

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Thomas Simon 氏 (Universite de Lille 1)
Absolute continuity of Ornstein-Uhlenbeck processes
[ 講演概要 ]
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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html

### 2009年12月18日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)

Dixmierの相似問題
[ 講演概要 ]

### 2009年12月17日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

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

#### 複素解析幾何セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

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

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Hatem Zaag 氏 (CNRS / パリ北大学)
A Liouville theorem for a semilinear heat equation with no gradient structure
[ 講演概要 ]
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年12月16日(水)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Stefano Maria Iacus 氏 (Department of Economics, Business and Statistics, University of Milan, Italy)
ecent results on volatility change point analysis for discretely sampled stochastic differential equations
[ 講演概要 ]
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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html

### 2009年12月15日(火)

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同です。この週に砂田利一氏の集中講義が行われます

Open Problems in Discrete Geometric Analysis
[ 講演概要 ]
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.
[ 講演参考URL ]

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム

Open Problems in Discrete Geometric Analysis
[ 講演概要 ]
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年12月14日(月)

#### 統計数学セミナー

14:00-15:10   数理科学研究科棟(駒場) 128号室
L. VOSTRIKOVA 氏 (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
On the stability of contingent claimes in incomplet models under statistical estimations.
[ 講演概要 ]
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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html

#### 代数幾何学セミナー

14:40-16:10   数理科学研究科棟(駒場) 126号室
いつもと時間帯が異なります。ご注意ください。
Sergey Galkin 氏 (IPMU)
Invariants of Fano varieties via quantum D-module
[ 講演概要 ]
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年12月11日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

### 2009年12月10日(木)

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

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

### 2009年12月09日(水)

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 128号室

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html

### 2009年12月08日(火)

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 128号室

#### GCOEセミナー

17:30-19:00   数理科学研究科棟(駒場) 002号室
Giovanni Felder 氏 (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
[ 講演概要 ]
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年12月07日(月)

#### Kavli IPMU Komaba Seminar

17:30-19:00   数理科学研究科棟(駒場) 002号室
Weiping Zhang 氏 (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
[ 講演概要 ]
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年12月03日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings

### 2009年12月02日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Juergen Saal 氏 (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
[ 講演概要 ]
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年12月01日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes)
Non-Abelian Novikov homology
[ 講演概要 ]
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年11月30日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Equidistribution and Nevanlinna theory

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Junya Yagi 氏 (Rutgers University)
Chiral Algebras of (0,2) Models: Beyond Perturbation Theory
[ 講演概要 ]
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.