## Seminar information archive

#### 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

### 2006/05/23

#### Tuesday Seminar on Topology

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

On crossed homomorphisms on symplectic mapping class groups
[ Abstract ]
We consider a symplectic manifold M. For a relation between Chern classes of M and the cohomology class of the symplectic form, we construct a crossed homomorphism on the symplectomorphism group of M with values in the cohomology group of M. We show an application of it to the flux homomorphism. Then we see that it induces a one on the symplectic mapping class group of M and show a nontrivial example of it.

### 2006/05/22

#### 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 I (Part II on May 29)
[ Abstract ]
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.

#### Seminar on Geometric Complex Analysis

15:00-16:30   Room #470 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces II

### 2006/05/20

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-15:45   Room #123 (Graduate School of Math. Sci. Bldg.)

The Koecher-Maass series for real analytic Siegel-Eisenstein series
[ Abstract ]

Standard L-functions for generic cusp forms on GSp(2)
[ Abstract ]
Whittaker模型を持つようなGSp(2)の尖点保型表現に付随するスタンダードL関数(5次のオイラー積)を、Ginzburg-Rallis-Soudry ('97)やBump-Friedberg-Ginzburg ('99)によって与えれたゼータ積分を通じて解析接続する方法について、これまでに得られた結果を紹介する。

### 2006/05/18

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Asymptotic behavior for large-time of solutions of Hamilton-Jacobi equations in n space

### 2006/05/17

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Arnak DALALYAN (Universite Paris 6, France)
Second-order efficiency in the semiparametric problem of estimating the shift of a signal

### 2006/05/16

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Laurentiu Maxim (University of Illinois at Chicago)
Fundamental groups of complements to complex hypersurfaces
[ Abstract ]
I will survey various Alexander-type invariants of hypersurface complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to affine hypersurfaces.

#### Lie Groups and Representation Theory

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

[ Abstract ]

### 2006/05/15

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Paris Sud)
Laminations with Singularities by Riemann Surfaces I (Part II on May 22)
[ Abstract ]
The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.
-Poincare metric on a hyperbolic lamination.
-Positive cycles and positive harmonic currents directed by a lamination.
-Ahlfors construction of positive harmonic currents.
-Cohomological and geometrical intersection of positive harmonic currents.