## 過去の記録

### 2009年07月14日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム

The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
[ 講演概要 ]
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.

### 2009年07月13日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Seshadri constants on rational surfaces with anticanonical pencils

[ 講演概要 ]

この不変量を調べることでしばしば幾何的な情報が得られる。

が得られた。

### 2009年07月09日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Mikael Pichot 氏 (東大数物連携宇宙研究機構)
Examples of groups of intermediate rank

### 2009年07月06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) 126号室

On the CR Hamiltonian flows
[ 講演概要 ]
The deformation theory of CR structures was initiated by Kuranishi and the versal family of CR structures were constructed by Garfied, Lee and myself "in the sense of Kuranishi". Miyajima also discussed the versal family by the completely different method. While, our method relies on the contact geometry(this suggest that there is a deep relation between Hamiltonian geometry and CR structures). Today, I report that our family is also versal "in the sense of CR Hamiltonian flows".

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

アーベル曲面上の安定層とフーリエ向井変換について
[ 講演概要 ]

アーベル曲面上には半等質層と呼ばれる半安定層があり, その分類, 構成方法やコホモロジーが完全に知られている. アーベル曲面のフーリエ向井対は半等質層のモジュライ空間であることも知られている.

また安定層のフーリエ変換における振舞いの記述において, 算術群や整数係数2次形式が重要な役割を果たすことも分かる. この事と先に述べた表示の存在から, 安定層のモジュライとアーベル曲面上の点のヒルベルトスキームとの間の双有理変換が明示的に構成できる.
アーベル曲面のフーリエ向井変換のフォーマリズムはK3曲面の変換と共通する部分も少なくない. 講演ではそうした点にも触れつつ, 今回の結果とその証明の概要を解説したい.

### 2009年07月02日(木)

#### 作用素環セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室

Dixmier's Similarity Problem ---Littlewood and Forests--- (一般の数学者向け)

### 2009年07月01日(水)

#### 講演会

15:30-17:00   数理科学研究科棟(駒場) 470号室

ASEPおよびzero-range processの分配関数

### 2009年06月30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

Torsion volume forms and twisted Alexander functions on
character varieties of knots

[ 講演概要 ]
Using non-acyclic Reidemeister torsion, we can canonically
construct a complex volume form on each component of the
lowest dimension of the $SL_2(\\mathbb{C})$-character
This volume form enjoys a certain compatibility with the
following natural transformations on the variety.
Two of them are involutions which come from the algebraic
structure of $SL_2(\\mathbb{C})$ and the other is the
action by the outer automorphism group of the link group.
Moreover, in the case of knots these results deduce a kind
of symmetry of the $SU_2$-twisted Alexander functions
which are globally described via the volume form.

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Ivana Alexandrova 氏 (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
[ 講演概要 ]
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.

### 2009年06月29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) 126号室

VII型曲面上の反自己双対双エルミート構造の存在について

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Moduli on the projective plane and the wall-crossing
[ 講演概要 ]

を用いることにより、ある有限次元代数の半安定表現のモジュライ空間
として構成する。階数が2以下の場合、表現の安定性条件を変化させること
により、壁越え現象としてのflip の記述を得る。

### 2009年06月25日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Infrared divergence of scalar quantum field model on pseudo Riemann manifold

### 2009年06月24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
Vincent Maillot 氏 (Paris第7大学) 16:30-17:30
New algebraicity results for analytic torsion
Richard Hain 氏 (Duke大学) 17:45-18:45
On the Section Conjecture for the universal curve over function fields

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Winston Ou 氏 (Scripps College / currently visiting assistant professor at Keio University)
Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights
[ 講演概要 ]
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\\infty$, and then present a few related problems.

#### 講演会

15:30-17:00   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

### 2009年06月23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 Meyer functions for projective varieties and their applications
[ 講演概要 ]
Meyer function is a kind of secondary invariant related to the signature
of surface bundles over surfaces. In this talk I will show there exist uniquely the Meyer function
for each smooth projective variety.
Our function is a class function on the fundamental group of some open algebraic variety.
I will also talk about its application to local signature for fibered 4-manifolds

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Group actions on affine cones
[ 講演概要 ]
The action of the additive group scheme C_+ on normal affine varieties is one of main subjects in affine algebraic geometry for a long time. In this talk, we shall mainly consider the problem about the existence of C_+-actions on affine cones, more precisely, the question:

"Determine the affine cones over smooth projective varieties admitting a (non-trivial) C_+-action ".

This question has an interest from a point of view of singularities. Indeed, a normal Cohen-Macaulay affine variety admitting an action by C_+ has at most rational singularities due to the result of H. Flenner and M. Zaidenberg. In the case of dimension 2, any affine cone over the projective line P^1 has a cyclic quotient singularity, and we can see that it admits, in fact, a C_+-action. Meanwhile, in case of dimension 3, i.e., affine cones over rational surfaces, the situation becomes more subtle.

One of the main results is concerned with a criterion for the existence of a C_+-action on affine cones (of any dimension) in terms of a cylinderlike open subset on the base variety. By making use of it, it is shown that, for any rational surface Y, we can take a suitable embedding of Y in such a way that the associated affine cone admits an action of C_+. Furthermore we are able to confirm that an affine cone over an anticanonically embedded del Pezzo surface of degree greater than or equal to 4 also admits such an action.

Nevertheless, our final purpose to decide whether or not there does exist a C_+-action on the fermat cubic: x^3+y^3+z^3+u^3 =0 in C^4, which is the affine cone over an anticanonically embedded cubic surface, say Y_3, is not yet accomplished. But, we can obtain certain informations about a linear pencil of rational curves on Y_3 arising from a C_+-action which seem to be useful in order to deny an existence of an action of C_+.

### 2009年06月22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) 126号室

### 2009年06月20日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

Fourier coefficients of Arakawa lifting and some degree eight L-function

[ 講演概要 ]

この講演では「荒川リフト」という内部形式上のカスプ形式に対し、そのフーリエ係数とある次数8の保型L関数の中心値との明示的な関係について最近得られた結果を紹介する。(村瀬篤氏との共同研究)

#### 東京無限可積分系セミナー

11:00-12:00   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

る1次元格子上の確率過程がある。今回はその多成分の場合を考える。系の時間

Perk-Schultz模型のハミルトニアンの特殊な場合と等価である。講演者らは各粒

### 2009年06月18日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

The super Virasoro algebra and noncommutative geometry

### 2009年06月17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

Variational problems for anisotropic surface energies
[ 講演概要 ]
A surface energy is anisotropic if it depends on the direction of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing a fixed volume is called the Wulff shape. We will discuss the characterization of the Wulff shape, the uniqueness and stability of solutions to variational problems for anisotropic surface energy with several boundary conditions.

### 2009年06月16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 abelianization of the level 2 mapping class group
[ 講演概要 ]
The level d mapping class group is a finite index subgroup of the mapping class group of an orientable closed surface. For d greater than or equal to 3, the abelianization of this group is equal to the first homology group of the moduli space of nonsingular curves with level d structure.
In this talk, we determine the abelianization of the level d mapping class group for d=2 and odd d. For even d greater than 2, we also determine it up to a cyclic group of order 2.

### 2009年06月15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) 126号室

A unicity theorem and Erdös' problem for polarized semi-abelian varieties (joint with P. Corvaja)

#### 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
The Schur-Szeg\\"o composition of the degree $n$ polynomials $P:=\\sum_{j=0}^na_jx^j$ and $Q:=\\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$) is representable as a Schur-Szeg\\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\\sigma_1$, $\\ldots$, $\\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$