## 過去の記録

### 2009年12月25日(金)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 370号室
Academician T. Sh. Kalmenov 氏 (Research Centre of Physics and Mathematics Almaty, Kazakhstan)
A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation

### 2009年12月24日(木)

#### 数理人口学・数理生物学セミナー

16:00-17:30   数理科学研究科棟(駒場) 123号室

Decomposition分析:趨勢データ分析の新しい枠組とアプローチ
[ 講演概要 ]
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.
[ 講演参考URL ]

### 2009年12月22日(火)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

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。)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 作用素環セミナー

14:40-18:00   数理科学研究科棟(駒場) 128号室

Symmetric representations of the group of diffeomorphisms of $\\mathbb R$
David Kerr 氏 (Texas A&M Univ.) 16:30-18:00
Topological entropy for actions of sofic groups

#### 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

Relative DG-category, mixed elliptic motives and elliptic polylog
[ 講演概要 ]
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.

#### 東京無限可積分系セミナー

10:00-14:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

Y. Avishai 氏 (Ben Gurion University) 13:00-14:00
Laplacian on graphs: Examples from physics
[ 講演概要 ]
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.