## Seminar information archive

### 2009/09/07

#### Operator Algebra Seminars

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Marek Bozejko (University of Wroclaw)
Generalized Gaussian field, theta function of Jacobi and functor of second quantization

### 2009/09/01

#### Algebraic Geometry Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Matthias Schuett (Leibniz University Hannover)
Arithmetic of K3 surfaces
[ Abstract ]
This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.
We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.

### 2009/08/12

#### Lie Groups and Representation Theory

10:00-16:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Sigurdur Helgason (MIT) 10:00-11:00
Fulton G. Gonzalez (Tufts University) 11:20-12:20
Multitemporal Wave Equations: Mean Value Solutins
Angela Pasquale (Universite Metz) 14:00-15:00
Analytic continuation of the resolvent of the Laplacian in the Euclidean settings
[ Abstract ]
We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Henrik Schlichtkrull (University of Copenhagen) 15:30-16:30
Decay of smooth vectors for regular representations
[ Abstract ]
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)

### 2009/08/07

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Fabien Trihan (Nottingham大学)
On the $p$-parity conjecture in the function field case
[ Abstract ]
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).

### 2009/07/30

#### GCOE lecture series

11:00-15:45   Room #002 (Graduate School of Math. Sci. Bldg.)

Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅤ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅥ
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

### 2009/07/29

#### GCOE lecture series

11:00-17:15   Room #002 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
KdV方程式をはじめとする長波長近似の非線形分散型方程式は,水面波の運動やプラズマ中のイオンの運動を記述することで知られている. KdV方程式のソリトン解は安定的に伝播することが知られていたが,近年変分法に基づいたアプローチで非可積分系のモデルの場合にもソリトン解とよく似た解が安定的に存在することが証明された.第1回目の講演ではに変分原理に基づいた安定性の結果について概説し,次にFermi-Pasta-Ulam格子やある種の流体のbidirectional modelなど変分原理から安定性がうまく説明できないモデルの場合について述べる.
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅢ
Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅣ

シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅡ
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

### 2009/07/28

#### GCOE lecture series

13:30-17:15   Room #002 (Graduate School of Math. Sci. Bldg.)
Frank Merle (Cergy Pontoise 大学/IHES) 13:30-14:30
Dynamics of solitons in non-integrable systemsⅠ
[ Abstract ]

Frank Merle (Cergy Pontoise 大学/IHES) 14:45-15:45
Dynamics of solitons in non-integrable systemsⅡ

シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅠ
[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

### 2009/07/27

#### thesis presentations

14:00-15:15   Room #123 (Graduate School of Math. Sci. Bldg.)

『Five dimensional K-contact Manifolds of rank 2(階数2の5次元K接触多様体について)』

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Misha Verbitsky (ITEP Moscow/IPMU)
Mapping class group for hyperkaehler manifolds
[ Abstract ]
A mapping class group is a group of orientation-preserving
diffeomorphisms up to isotopy. I explain how to compute a
mapping class group of a hyperkaehler manifold. It is
commensurable to an arithmetic lattice in a Lie group
$SO(n-3,3)$. This makes it possible to state and prove a
new version of Torelli theorem.

### 2009/07/24

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Carlos Simpson (CNRS, University of Nice)
Differential equations and the topology of algebraic varieties
[ Abstract ]
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of shape'' and nonabelian cohomology.

#### Infinite Analysis Seminar Tokyo

13:00-15:30   Room #056 (Graduate School of Math. Sci. Bldg.)

On recursion relation of the KP hierarchy
[ Abstract ]
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.

[ Abstract ]

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

### 2009/07/23

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Catherine Oikonomides (慶応大理工)
Cyclic cohomology and the Novikov conjecture

### 2009/07/21

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ Abstract ]
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.

### 2009/07/18

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

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

[ Abstract ]

### 2009/07/17

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Universite Paris-Sud)
Holomorphic dynamics in several variables: equidistribution problems and statistical properties
[ Abstract ]
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.

#### Seminar on Geometric Complex Analysis

13:45-14:45   Room #128 (Graduate School of Math. Sci. Bldg.)
Karl Oeljeklaus (University of Provence)
Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)

#### Seminar on Geometric Complex Analysis

15:00-16:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Andrei Iordan (Univ. Paris VI)
Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds

#### Seminar on Geometric Complex Analysis

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Nessim Sibony (Univ. Paris Sud)
Holomorphic Dynamics In Several
Variables: equidistribution properties and statistical behavior

### 2009/07/16

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ingo Runkel (King's College London)
Algebraic structures in conformal field theory
[ Abstract ]
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.

#### Mathematical Biology Seminar

15:00-16:20   Room #056 (Graduate School of Math. Sci. Bldg.)
Odo Diekmann (Mathematical Institute, Utrecht University)
The delay equation formulation of physiologically structured population models
[ Abstract ]
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.

### 2009/07/14

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
[ Abstract ]
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.

### 2009/07/13

#### Algebraic Geometry Seminar

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

Seshadri constants on rational surfaces with anticanonical pencils

[ Abstract ]

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。

### 2009/07/09

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数物連携宇宙研究機構)
Examples of groups of intermediate rank

### 2009/07/06

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)

On the CR Hamiltonian flows
[ Abstract ]
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".

#### Algebraic Geometry Seminar

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

アーベル曲面上の安定層とフーリエ向井変換について
[ Abstract ]

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.