## Seminar information archive

### 2006/06/19

#### Seminar on Geometric Complex Analysis

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

Deformations and smoothing of (generalized) holomorphic symplectic structures

### 2006/06/15

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Mark Bowen (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
[ Abstract ]
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.

### 2006/06/14

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Qing-Ming Cheng (Saga University)
Bounds on eigenvalues of Dirichlet aplacian
[ Abstract ]
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.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006/06/13

#### Tuesday Seminar on Topology

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

A note on C1-moves
[ Abstract ]

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

(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.

### 2006/06/12

#### Seminar on Geometric Complex Analysis

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

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

### 2006/06/10

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Boris Feigin (Landau Institute for Theoretical Physics) 13:30-14:30
"Critical" level for Vertex Algebras
[ Abstract ]
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

[ Abstract ]

### 2006/06/07

#### Infinite Analysis Seminar Tokyo

14:00-15:00   Room #270 (Graduate School of Math. Sci. Bldg.)
Youjin Zhang (Tsinghua Univ.)
On deformations of bihamiltonian structures of hydrodynamic type
[ Abstract ]
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 Real Analysis Seminar

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

On phase boundary motion by surface diffusion with triple junction
[ Abstract ]
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.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/022.html

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

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

#### Applied Analysis

16:00-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Marek FILA (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation

### 2006/06/06

#### Tuesday Seminar on Topology

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

Thurston's inequality for a foliation with Reeb components
[ Abstract ]
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.

#### Infinite Analysis Seminar Tokyo

13:30-14:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Leon Takhtajan (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
[ Abstract ]
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.

### 2006/06/05

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Wolfram Bauer (東京理科大)
Integral formulas for infinite dimensional domains with arbitrary boundary
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf

### 2006/05/31

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

Bhattacharyya inequality for quantum state estimation II
[ Abstract ]

(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.

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/04.html

### 2006/05/30

#### Tuesday Seminar of Algebraic Analysis

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)

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

#### Tuesday Seminar on Topology

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

[ Abstract ]

### 2006/05/29

#### Mathematical Biology Seminar

16:00-17:00   Room #056 (Graduate School of Math. Sci. Bldg.)

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Marco Brunella (Bourgogne)
Uniformisation of Holomorphic Foliations by Curves II

#### Seminar on Geometric Complex Analysis

13:30-15:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Hodge theory with bounds and its application to foliations

### 2006/05/27

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
インスタントン軌道により記述される1次元系のトンネル効果とは対照的に、多数の複素経路が関与することが非可積分系のトンネル効果の特徴である。
(1)簡単な離散写像系(エノン写像)においては,この複素軌道はジュリア集合と密接な関係があること、
(2)トンネル軌道の選別に,完全WKB解析の手法(特に高階微分方程式に対する)が有効であること、
などを示す。

[ Abstract ]
Six-vertex 模型は数理的には量子群、物質としては量子 XXZ スピン鎖に関連し、 Yang-Baxter 関係式によって対角化される可解模型の典型例である。この模型に現れるフラクタル構造、特に graph-directed IFS フラクタルについて議論し、確率過程その他との関連に言及する。

### 2006/05/25

#### Operator Algebra Seminars

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)

カントール極小$Z^d$系のコホモロジー

#### Seminar for Mathematical Past of Asia

17:00-18:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

### 2006/05/24

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

Bhattacharyya inequality for quantum state estimation I
[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/03.html

#### Number Theory Seminar

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Kai Köehler (Düesseldorf 大学) 16:30-17:30
Quaternionic analytic torsion and arithmetic geometry
Thomas Geisser (南カリフォルニア大学) 17:45-18:45
Duality via cycle complexes