## 過去の記録

#### 東京無限可積分系セミナー

13:00-15:30   数理科学研究科棟(駒場) 056号室

On recursion relation of the KP hierarchy
[ 講演概要 ]
This talk is based on an ongoing project in collaboration with Takasaki and Tsuchiya. Our goal is to reconstruct and generalise results by Eynard et al. from the standpoint of the integrable systems. Eynard, Orantin and their collaborators found "topological recursion formulae" to describe partition functions and correlation functions of the matrix models, topological string theories etc., using simple algebro-geometric data called "spectral curves". On the other hand, it is well known that the partition functions of those theories are tau functions of integrable hierarchies.
We have found that any solution of the KP hierarchy (with an asymptotic expansion parameter h) can be recovered by recursion relations from its "dispersionless" part (which corresponds to the genus zero part in topological theories) and a quantised contact transformation (which corresponds to the string equations) specifying the solution.

[ 講演概要 ]

をもち、それ以外では単純分岐点のみもつような n 次分岐被覆を考える。
このような分岐被覆の位相的同型類の個数は単純フルビッツ数と呼ばれる。
1点の代わりに2点を指定して同様に定義されるものは2重フルビッツ数である。
これらのフルビッツ数にシューア函数を乗じて総和したものはそれぞれ
KP階層および戸田階層のτ函数になることが知られている。この講演では
これらの特殊解においてラックス作用素とオルロフ・シュルマン作用素が

### 2009年07月23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
Catherine Oikonomides 氏 (慶応大理工)
Cyclic cohomology and the Novikov conjecture

### 2009年07月21日(火)

#### 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
Georgi Raikov 氏 (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ 講演概要 ]
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.

### 2009年07月18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

On some algebraic properties of CM-types of CM-fileds and their reflexs

[ 講演概要 ]

### 2009年07月17日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
Nessim Sibony 氏 (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
[ 講演概要 ]
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\\"ahler manifolds.

#### 複素解析幾何セミナー

13:45-14:45   数理科学研究科棟(駒場) 128号室
Karl Oeljeklaus 氏 (University of Provence)
Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)

#### 複素解析幾何セミナー

15:00-16:00   数理科学研究科棟(駒場) 128号室
Andrei Iordan 氏 (Univ. Paris VI)
Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds

#### 複素解析幾何セミナー

16:30-17:30   数理科学研究科棟(駒場) 002号室

Nessim Sibony 氏 (Univ. Paris Sud)
Holomorphic Dynamics In Several
Variables: equidistribution properties and statistical behavior

### 2009年07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) 056号室
Ingo Runkel 氏 (King's College London)
Algebraic structures in conformal field theory
[ 講演概要 ]
It turned out to be fruitful to isolate questions in CFT which can be formulated in a purely categorical fashion. The way left and right moving degrees of freedom can be combined to a consistent theory is an example of this, the relevant structure being a commutative symmetric Frobenius algebra. This is true independently of whether CFT is formulated via sewing of surfaces or nets of operator algebras. Another example is modular invariance, which has a surprising alternative formulation as a certain maximality condition.

#### 数理人口学・数理生物学セミナー

15:00-16:20   数理科学研究科棟(駒場) 056号室
Odo Diekmann 氏 (Mathematical Institute, Utrecht University)
The delay equation formulation of physiologically structured population models
[ 講演概要 ]
Traditionally, physiologically structured population models are formulated in terms of first order partial differential equations with non-local boundary conditions and/or transformed arguments. The stability and bifurcation theory for such equations is, in the quasi-linear case, still very immature.
The aim of this lecture is to explain that, alternatively, one can formulate such models in terms of delay equations (more precisely : renewal equations coupled to delay differential equations) without losing essential information and that for delay equations there is a well-developed local stability and bifurcation theory. As a motivating example we consider the interaction between a size-structured consumer and an unstructured resource. The lecture is based on joint work with Mats Gyllenberg and Hans Metz.

### 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 ]