## 過去の記録

### 2011年01月27日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)

#### 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
Nitsan Ben-Gal 氏 (The Weizmann Institute of Science)
Attraction at infinity: Constructing non-compact global attractors in the slowly non-dissipative realm (ENGLISH)
[ 講演概要 ]
One of the primary tools for understanding the much-studied realm of reaction-diffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to non-dissipative reaction-diffusion equations.
In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the ‘completed inertial manifold’ and ‘non-compact global attractor’, and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.

### 2011年01月26日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
p進Gross-Zagier公式は, 楕円曲線のp進L関数の微分値をHeegner点のp進高さで記述する公式である. 楕円曲線がpで通常還元をもつときは, 20年以上前にPerrin-Riouによって証明されていた. 最近, pで超特異還元をもつときにも証明できたのでそれを紹介する. この講演では特に証明の解説に重点をおいて話したい.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jong-Shenq Guo 氏 (Department of Mathematics, Tamkang University
)
Quenching Problem Arising in Micro-electro Mechanical Systems

(JAPANESE)
[ 講演概要 ]
In this talk, we shall present some recent results on quenching problems which arise in Micro-electro Mechanical Systems.
We shall also give some open problems in this research area.

#### 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

Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)
[ 講演概要 ]
The object of talk is the differentiability of implicitly defined functions which we
encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild
(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly
defined functions by reparametrizing parameters in the profile likelihood and using an approximate least
favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach
developed in Hirose (2010) which uses the differentiability of implicitly defined functions.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

### 2011年01月25日(火)

#### トポロジー火曜セミナー

16:30-17:30   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

シート数が小さい曲面結び目の自明化について (JAPANESE)
[ 講演概要 ]
A connected surface smoothly embedded in ${\\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot $F$ is homeomorphic to the $2$-sphere or the torus, then it is called an $S^2$-knot or a $T^2$-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a $1$-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an $S^2$-knot. In particular, it is known that an $S^2$-knot is trivial if and only if its sheet number is $1$, and there is no $S^2$-knot whose sheet number is $2$. In this talk, we show that there is no $S^2$-knot whose sheet number is $3$, and a $T^2$-knot is trivial if and only if its sheet number is $1$.

### 2011年01月24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 a complex analytic 3-dimensional Kleinian group theory (JAPANESE)
[ 講演概要 ]
1次元射影変換群の離散部分群はクライン群理論として複素解析的にも微分幾何学的にも長く深く研究されてきた。この理論の高次元化は、微分幾何学的には発展したが、複素解析的にはあまり進んでいないように思う。複素2次元ではうまくいかないが、ここでは複素3次元の複素解析的なクライン群理論の試みについて述べたいと思う。

### 2011年01月20日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)
[ 講演概要 ]

「$G$を普遍格子SL$_m(Z[x_1,...,x_k])$ ($m$は3以上)または斜交普遍格子Sp$_{2m}(Z[x_1,...,x_k])$ ($m$は2以上)の指数有限の部分群とする ($k$は任意の自然数). このとき, $G$から曲面(コンパクトで向きづけ可能)の写像類群への; または, 有限生成自由群の(外部)自己同型群への準同型は有限の像をもつ.」

### 2011年01月19日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Mullins方程式の本質への探求 (JAPANESE)
[ 講演概要 ]
1957年にMullinsは、蒸発-凝縮機構による固体表面の発展方程式を提案した。その方程式の定性的本質を探る事によって、どのような知見が得られるかについて議論する。具体的には、曲率と駆動力との間の関係が形態に与える影響について明らかにする。

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

Notes on estimating the probability of ruin and some generalization (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

### 2011年01月18日(火)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Claude-Alain Pillet 氏 (Univ. de Toulon et du Var)
Scattering induced current in a tight binding band (ENGLISH)

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
いつもと開始時刻がことなります
Pierre Clare 氏 (Universite Orleans and the University of Tokyo)
Connections between Noncommutative Geometry and Lie groups
representations (ENGLISH)
[ 講演概要 ]
One of the principles of Noncommutative Geometry is to study singular spaces that the tools of classical analysis like algebras of continuous functions fail to describe, replacing them by more general C*-algebras. After recalling fundamental facts about C*-algebras, Hilbert modules and group C*-algebras, we will present constructions and results aiming to understand principal series representations and Knapp-Stein theory in the noncommutative geometrical framework. Eventually we will explain the relationship between the analysis of reduced group C*-algebras and the computation of the Connes-Kasparov isomorphisms.

### 2011年01月17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
Dano Kim 氏 (KIAS)
L^2 methods and Skoda division theorems (ENGLISH)
[ 講演概要 ]
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.

#### 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

Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)
[ 講演概要 ]
In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

### 2011年01月13日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Robert Coquereaux 氏 (CNRS/CPT)
Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)

### 2011年01月12日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 056号室
Zhonghua Li 氏 (東京大学大学院数理科学研究科) 16:30-17:30
On regularized double shuffle relation for multiple zeta values (ENGLISH)
[ 講演概要 ]
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki 氏 (North Carolina University) 17:45-18:45
Spines with View Toward Modular Forms (ENGLISH)
[ 講演概要 ]
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.

### 2011年01月11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

The Chas-Sullivan conjecture for a surface of infinite genus (JAPANESE)
[ 講演概要 ]

\\Sigma_{\\infty,1} を境界成分 1 の向きづけられたコンパクト曲面の

の中心が定数ループで張られることを証明する。閉曲面についての

することで証明される。時間が許せば、線型コード図式の空間上の
Lie 代数の構造についても議論したい。

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Raphael Ponge 氏 (Univ. Tokyo)
Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

https://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

### 2010年12月22日(水)

#### GCOEセミナー

11:00-12:00   数理科学研究科棟(駒場) 570号室
Mourad Bellassoued 氏 (Faculté des Sciences de Bizerte)
Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)
[ 講演概要 ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

「ゼータ関数の貼り合わせ」の手法を用いて加藤、Mahesh Kakde 及び

Alfred Weiss も異なる定式化の下で主予想が成立する例を構成している)。

なお、総実代数体の非可換岩澤主予想は、2010年に
Ritter-Weiss 及び Kakde によって一般の場合にも

### 2010年12月21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

Some relation between the Weyl module and the crystal basis of the tensor product of fudamental representations (ENGLISH)
[ 講演概要 ]
The Lie algebra defined by the tensor product of a simple Lie algebra and a polynomial ring is called the current algebra, and the Weyl module is defined by a finite dimensional module of the current algebra having some universal property.
The fundamental representation is a irreducible, finite dimensional, level zero integrable representation of the quantized affine algebra, and it is known that this module has a crystal basis.
If the simple Lie algebra is of ADE type, Fourier and Littelamnn has shown that the Weyl module is isomorphic to a module called the Demazure module.
Using this fact, we can easily see that the (\\mathbb{Z}-graded) characters of the Weyl module and the crystal basis of the tensor product of fundamental representations coincides.
In my talk, I will introduce the generalization of this result in the non-simply laced case.
In this case, the result of Fourier and Littelmann does not necessarily true, but we can show the characters of two objects also coincide in this case.
This fact is shown using the Demazure modules and its crystal basis'' called the Demazure crystals.

### 2010年12月20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

ホップ曲面の擬凸状領域について (JAPANESE)
[ 講演概要 ]
2つの複素数a, b (1<|a|\\le|b|)に関するホップ曲面をHとする. Hの実解析的滑らかな境界を持つ擬凸状領域Dのロバン函数 ¥Lambda[z,w] は多重劣調和近似函数であることを示し, 上田の予想について述べる.

#### 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

On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)
[ 講演概要 ]
I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)

### 2010年12月16日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Marco Merkli 氏 (Memorial Univ. Newfoundland)
Evolution of Quantum Dynamical Systems (ENGLISH)