## 過去の記録

### 2006年06月27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
Cedric Tarquini 氏 (Ecole Nomale Superieure of Lyon)
Lorentzian foliations on 3-manifolds
[ 講演概要 ]
a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)

The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.

The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.

We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.

### 2006年06月26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

Toward construction of Green current for modular cycles in modular varieties

### 2006年06月23日(金)

#### 談話会・数理科学講演会

17:00-18:00   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:30～17:00(コモンルーム)
Robert Gompf 氏 (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
[ 講演概要 ]
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.

### 2006年06月22日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
Detlev Buchholz 氏 (Univ. Göttingen)
Integrable models and operator algebras
[ 講演概要 ]
Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional local nets of von Neumann algebras describing an interacting massive particle with factorizing scattering matrix. This novel approach is based on structural results in algebraic quantum field theory concerning the modular structure of such theories. It is thus complementary to the older methods of constructive quantum field theory and settles some longstanding questions in the context of integrable models (form-factor program). In this talk, a survey is given on basic ideas, results and perspectives of this promising new approach.

### 2006年06月21日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

Malliavin calculus applied to mathematical finance and a new formulation of the intgration-by-parts
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/05.html

### 2006年06月19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

Deformations and smoothing of (generalized) holomorphic symplectic structures

### 2006年06月15日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室
6月15日は,集中講義と重なるため,開始時間を遅らせます.
Mark Bowen 氏 (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
[ 講演概要 ]
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.

### 2006年06月14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
Qing-Ming Cheng 氏 (Saga University)
Bounds on eigenvalues of Dirichlet aplacian
[ 講演概要 ]
In this talk, I shall consider the eigenvalue problem of the Dirichlet Laplacian. I shall mention the Weyl asymptotic formula,
Polya conjecture and its partial solution. Furthermore, I shall talk about Bochner-Kac problem.
For universal inequalities for eigenvalues, I shall consider
conjectures of Payne, Polya and Weinberger and their development. In the final, I shall talk the universal bounds for eigenvalues as main part of my talk, which is my recent joint work with rofessor Yang.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006年06月13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

A note on C1-moves
[ 講演概要 ]

#### 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 ]

(1) 各λに対する $M_Θ(λ)$ の最小多項式の明示公式
(2) $M_Θ(λ)= M(λ)/I_Θ(λ)M(λ)$ が成り立つためのλの 必要十分条件

が得られた(これらは大島により g = gln の場合には既に得られている).セミナーでは(2)を示すための q(F) の各成分の Harish-Chandra 準同型像の計算法を主に説明する.

### 2006年06月12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

The Rumin complex and Hamiltonian mechanism
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf

### 2006年06月10日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室
Boris Feigin 氏 (Landau Institute for Theoretical Physics) 13:30-14:30
"Critical" level for Vertex Algebras
[ 講演概要 ]
In the talk I present the construction of "VOA" on a critical level using fermionic screenings.Then I discuss the geometric background behind such algebras and applications - Langlands correspondence and related things

[ 講演概要 ]

### 2006年06月07日(水)

#### 東京無限可積分系セミナー

14:00-15:00   数理科学研究科棟(駒場) 270号室
6月6日(火), 7日(水)の両日で行われます。
Youjin Zhang 氏 (Tsinghua Univ.)
On deformations of bihamiltonian structures of hydrodynamic type
[ 講演概要 ]
I will talk about the properties of deformations bihamiltonian structures of hydrodynamic type and the related integrable hierarchies, and the problem of classification of such deformations.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

On phase boundary motion by surface diffusion with triple junction
[ 講演概要 ]
The phase boundary motion by a geometrical evolution law in a bounded domain is studied in this talk. We consider the surface diffusion flow equation, which has the gradient flow structure with respect to $H^{-1}$-inner product and the area-preserving property. This equation was derived by Mullins to model the motion of interfaces in the case that the motion of interfaces is governed purely by mass diffusion within the interfaces. We study the three-phase problem with triple junction in a bounded domain and analyze the stability of the stationary solutions for this problem.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/022.html

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

Hecke-Siegel's pull back formula for the Epstein zeta function with spherical

#### 応用解析セミナー

16:00-18:00   数理科学研究科棟(駒場) 002号室
Marek FILA 氏 (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation

### 2006年06月06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

Thurston's inequality for a foliation with Reeb components
[ 講演概要 ]
The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.

#### 東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 117号室
6月6日(火), 7日(水)の両日で行われます。
Leon Takhtajan 氏 (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
[ 講演概要 ]
We extend our previous work on local index theorem for families of $\\bar\\partial$-operators on punctured Riemann surfaces (Comm. Math. Phys. 137 (1991), 399-426) and for families of $\\bar\\partial$-operators on endomorphism bundles of stable vector bundles over a compact Riemann surface (Math. USSR Izvestia 35 (1990), 83-100) to the case of stable parabolic vector bundles over a Riemann surface. The result is an explicit formula for the first Chern form of the canonical line bundle to the moduli space stable parabolic bundles with the Quillen's type metric. The derivation uses Mehta-Seshadri theorem and spectral theory of automorphic functions on the Lobatchevsky plane with the unitary representation. This is a joint work with P. Zograf.

### 2006年06月05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
Wolfram Bauer 氏 (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf

### 2006年05月31日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

Bhattacharyya inequality for quantum state estimation II
[ 講演概要 ]

(1) g(θ)=θ^2に対するUMVUEは存在してS型Bhattacharyya下限を達成する. その推定量は, 物理系にスクイジングと呼ばれる操作を施した後の個数測定によって与えられる.
(2) g(θ)=θ^3に対するUMVUEは, 生成消滅作用素の多項式の形では存在しない.
(3) g(θ)が正則, 或いは反正則, ならば, ヘテロダイン測定によってUMVUEが与えられ, それぞれR型, L型のBhattacharyya下限を達成する.
(4) g(θ)が実数値ならば, ある測定によりUMVUEが与えられ, R型, L型両方の下限を達成する.

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/04.html

### 2006年05月30日(火)

#### 代数解析火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室

Fuchs 型偏微分方程式の超分布解に対する割算定理について

#### 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

[ 講演概要 ]

### 2006年05月29日(月)

#### 数理人口学・数理生物学セミナー

16:00-17:00   数理科学研究科棟(駒場) 056号室

#### 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
Marco Brunella 氏 (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II

#### 複素解析幾何セミナー

13:30-15:00   数理科学研究科棟(駒場) 128号室

Hodge theory with bounds and its application to foliations