## Seminar information archive

### 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.

### 2006/05/12

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

ポストゲノム時代のシステム生物学の問題について
[ Abstract ]
ヒトゲノム30億塩基対のシークエンスは解読されましたが、その遺伝暗号の意味がわかっている部分はほんの数パーセントにすぎません。DNAチップや質量分析機の発達とコンピューターの進歩により、細胞や組織で読まれている遺伝子の量や生ずるタンパク質の種類を網羅的に解析する手段ができています。これらのトランスクリプトーム解析やプロテオーム解析により多数の遺伝子あるいはタンパク質の挙動を調べることが可能になってくると、生命現象の基礎となっている調節メカニズムが単一分子の相互作用だけで説明できないのではないかと思われてきました。多数分子の挙動とそれらの相互作用をどのように解析することができるかということが、生命現象を分子から生体システムとして理解するために必要なのではないかと感じています。これまで、我々の解析で得られているデータをお示しし、現在の生命科学が直面しつつある問題点を説明できればと思います。

### 2006/05/10

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Arnak DALALYAN (Universite Paris 6, France)
Asymptotic statistical equivalence for diffusion processes II
[ Abstract ]
We consider the experiment of a continuously observed scalar diffusion process with unknown drift function. In the stationary case, we prove that this experment is locally asymptotically equivalent to a simple Gaussian white noise experiment. We also derive the rate of convergence of the Le Cam's distance and describe the Markov kernel attaining this rate of convergence. These results are obtained in collaboration with Markus Reiss.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/01.html

### 2006/05/08

#### Seminar on Geometric Complex Analysis

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

Real-analytic Levi-flats in complex tori

### 2006/04/27

#### Applied Analysis

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

#### Seminar for Mathematical Past of Asia

17:00-18:30   Room #152 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
『九数略』は,当時の代表的な政治家兼経学者、崔錫鼎(1645- 1715)が著した数学書。内容自体は伝統の実用算術のレベルを超えていないけれども、形而上学的な易学思想をもって、朝鮮の計算術と実用数学の構造を理論的に位置づけている。また数学の基本的構造自体に西洋の3数法の深い影響があることも、この数学書の特徴の1つである。

### 2006/04/26

#### Number Theory Seminar

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

Differential Operators of Rankin-Cohen-Ibukiyama Type for Automorphic Forms of Several Variables

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Arnak DALALYAN (Universite Paris 6, France)
Asymptotic statistical equivalence for diffusion processes I (JAPANESE)
[ Abstract ]
This is the first talk of a series of three talks devoted to the asymptotic statistical equivalence for diffusion processes. We will introduce the notion of Le Cam's distance between statistical experiments and will present its properties with some easy examples. Then we will show that the experiment of a discretely observed diffusion process with unknown drift is asymptoically equivalent to the experiment of continuously observed diffusion process provided that the step of discretisation is small enough (this result is due to Milstein and Nussbaum).

### 2006/04/25

#### Tuesday Seminar on Topology

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

Counting closed orbits and flow lines via Heegaard splittings
[ Abstract ]
Let K be a fibred knot in the 3-sphere. It is known that the Alexander polynomial of K is essentially equal to a Lefschetz zeta function obtained from the monodromy map of the fibre structure. In this talk, we discuss the non-fibred knot case. We introduce "monodromy matrix" by making use of Heegaard splitting for sutured manifolds of a knot K, and then observe a method of counting closed orbits and flow lines, which gives the Alexander polynomial of K. This observation is based on works of Donaldson and Mark. (joint work with Hiroshi Matsuda and Andrei Pajitnov)

#### Tuesday Seminar of Algebraic Analysis

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

[ Reference URL ]
http://agusta.ms.u-tokyo.ac.jp/seminarphotos/Matsui2006/matsui2006_1.html

### 2006/04/24

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jonas Wiklund (名古屋大学, JSPS fellow)
Monge-Ampére mass at the boundary on some domains with corner
[ Abstract ]
The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.

### 2006/04/21

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Dmitri Orlov (Steklov Institute)
Homological mirror symmetry
[ Abstract ]
Homological mirror symmetry is a relation between algebraic and symplectic sides of a geometric object. Original mirror symmetry came from physics, but homological mirror symmetry conjecture formulated by M.Kontsevich for Calabi-Yau varieties is an attempt to give a mathematical explanation of this phenomenon. We will try to describe main principles of homological mirror symmetry and the extension to a non-Calabi-Yau case.

### 2006/04/20

#### Applied Mathematics

16:00-18:15   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Abstract ]

#### Operator Algebra Seminars

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

Compact Kac 環の極小作用の分類 I

### 2006/04/19

#### Number Theory Seminar

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

Distributions of discriminants of cubic algebras

#### Seminar on Mathematics for various disciplines

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

Oscillatory growth of a crystal controlled by interface kinetics and transport process
[ Abstract ]
Periodic texture in a crystal -such as growth banding and growth striations- are believed to be caused by oscillatory growth. The origin of oscillatory growth falls into two categories, i.e., external and internal. Since the growth rate of a crystal depends strongly on the growth conditions, periodic changes of external conditions, such as temperature, concentration, convection etc., are common reasons for explaining oscillatory growth. On the other hand, it is thought that oscillatory growth can also have an internal cause, but there is no clear understanding. In this talk we propose the hypothesis of a hysteresis behaviour of growth rate to explain the formation of periodic structures of a growing crystal without a change of external conditions. Recently, evidence for our hypothesis is observed not only in the growth of a crystal but also in the motion of steps on the surface of crystals. Possibly such self-oscillatory growth can be controlled in experiments in near future.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html

### 2006/04/18

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Vladimir Turaev (Univ. Louis Pasteur Strasbourg)
Topology of words
[ Abstract ]
There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.

#### Lie Groups and Representation Theory

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

Rankin-Cohen-伊吹山型の微分作用素について
[ Abstract ]

### 2006/04/17

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
C. Robin Graham (University of Washington)
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
[ Abstract ]
This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.

### 2006/04/15

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On the dimension of the space of Siegel Eisenstein series of weight one.
[ Abstract ]

の補空間の一部の次元を、有限群の表現論及びSatakeコンパクト化の境界の様子を調べることによって計算する方法を与える。

L-functions for $GSp(2)\\times GL(2)$: archimedean theory and applications
[ Abstract ]
$\\Pi$ を $GSp(2)$のWhittaker模型を持つ尖点保型表現で,実素点で大きい離散系列表現を生成するものとする。$\\Pi$と$\\GL(2)$の尖点保型表現$\\sigma$の組からテンソル積 L-関数が定義される。
このL-関数の関数等式を,ゼータ積分を使って証明する。

#### Infinite Analysis Seminar Tokyo

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

Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection.
[ Abstract ]
Kerov-Kirillov-Reshetikhin bijection とは、フェルミ型公式の 証明に関して 1986 年に導入された組み合わせ的な写像であり、 rigged configurations と highest paths の間の全単射を与える。 この写像を、結晶基底の組み合わせ R 行列のみを用いた代数的な 形式に書き直すことができる [1,2]。証明には、アフィン組み合わせ R 行列の構造を rigged configurations に導入することが必要となる。 これらの結果は箱玉系と呼ばれるソリトンセルオートマトンの 逆散乱形式ともなっている。

REFERENCE:
[1] A.Kuniba, M.Okado, R.Sakamoto, T.Takagi, Y.Yamada, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection" Nuclear Physics B 740 (2006) 299-327, math.QA/0601630.
[2] R.Sakamoto, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection II. Proof for sl_n case", math.QA/0601697.

ダブルアファインヘッケ代数と楕円ヘッケ代数について
[ Abstract ]
ダブルアファインヘッケ代数と楕円ヘッケ代数の比較について話します。 楕円ヘッケ代数は、マーキング付き楕円ルート系のディンキン図形から 生成元と関係式を読み取って定義される代数です。マーキング付き楕円 ルート系は、2つのアファインルート系を部分ルート系として含むので そのヘッケ代数がダブルアファインヘッケ代数と何かしらの関係がある ことは想像がつきます。ここでは、楕円ヘッケ代数がダブルアファイン ヘッケ代数の部分代数になっていること、およびダブルアファインヘッケ 代数を楕円ヘッケ代数上の加群と見たときの自由基底について説明します。

### 2006/04/13

#### Operator Algebra Seminars

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)

A construction of finite group actions on Kirchberg algebras