## Seminar information archive

### 2007/10/09

#### Tuesday Seminar on Topology

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

Classification of codimension-one locally free actions of the affine group of the real line.
[ Abstract ]
By GA, we denote the group of affine and orientation-preserving transformations
of the real line. In this talk, I will report on classification of locally free action of
GA on closed three manifolds, which I obtained recently. In 1979, E.Ghys proved
that if such an action preserves a volume, then it is smoothly conjugate to a homogeneous action. However, it was unknown whether non-homogeneous action exists. As a consequence of the classification, we will see that the unit tangent bundle of a closed surface of higher genus admits a finite-parameter family of
non-homogeneous actions.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (Reims University and University of Tokyo)
Rankin-Cohen brackets and covariant quantization
[ Abstract ]
The particular geometric structure of causal symmetric spaces permits the definition of a covariant quantization of these homogeneous manifolds.
Composition formulae (#-products) of quantizad operators give rise to a new interpretation of Rankin-Cohen brackets and allow to connect them with the branching laws of tensor products of holomorphic discrete series representations.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007/10/04

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Gandalf Lechner (Erwin Schroedinger Institute)
Local nets of von Neumann algebras and modular theory

### 2007/10/02

#### Lie Groups and Representation Theory

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

Invariant integral operators on affine G-varieties and their kernels
[ Abstract ]
We consider certain invariant integral operators on a smooth affine variety M carrying the action of a reductive algebraic group G, and assume that G acts on M with an open orbit. Then M is isomorphic to a homogeneous vector bundle, and can locally be described via the theory of prehomogenous vector spaces. We then study the Schwartz kernels of the considered operators, and give a description of their singularities using the calculus of b-pseudodifferential operators developed by Melrose. In particular, the restrictions of the kernels to the diagonal can be described in terms of local zeta functions.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007/09/28

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Irreducible unitary representations and automorphic forms

[ Abstract ]
Unitary representations of adelic groups in the spaces of automorphic forms are big source of important irreducible unitary representations of classical groups over local fields.

We shall present classifications of some classes of irreducible unitary representations (older, as well as quite new), describe
isolated unitary representations among them, and discuss which of them can be obtained from spaces of automorphic forms.

### 2007/09/26

#### Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Grigory Mikhalkin (Toronto大学)
Floor diagrams and enumeration of tropical curves
[ Abstract ]
The enumerative problems considered in this talk are finding the number of curves in projective spaces (over complex, real and tropical numbers) of given genus and degree constrained by certain incidence conditions (e.g. passing via points or lines). Floor diagrams are a combinatorial tool that reduces an enumerative problem in dimension n to the corresponding problem n dimension n-1. Floor diagrams give a constructive (and rather efficient) way to find all tropical curves for a given enumerative problem. And once we have a tropical solution of the problem we can use it to solve the corresponding problems over the complex and real numbers.

### 2007/09/19

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Gereon Quick (Universitaet Muenster)
Etale cobordism
[ Abstract ]
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.

### 2007/09/15

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

Siegl principal series Whittaker functions on $Sp(2,\\mathbf{R})$
(部屋は056室)
[ Abstract ]
2次シンプレクティック群のSiegel極大放物型部分群から誘導された一般型主系列表現に対するWhittaker関数の級数表示と積分表示を与えることを目的とし,Whittaker関数の満たす微分評定式を与え,その解の構成に向けて現在進めている研究の方針を述べる.
(部屋は,冷房効く056室に変更です)

A higher rank version of Abel-Jacobi's theorem (Room 056)
[ Abstract ]

(部屋は117号室です)

### 2007/09/12

#### Algebraic Geometry Seminar

15:00-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
E. Lau (Univ. of Bielefeld) 15:00-15:45
Classification of p-divisible groups by displays and duality
T. Zink (Univ. of Bielefeld) 16:00-16:45
Applications of the theory of displays
E. Looijenga (Univ. of Utrecht) 17:00-18:00
Presentation of mapping class groups from algebraic geometry
[ Abstract ]
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.

#### Number Theory Seminar

15:00-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
E. Lau (Univ. of Bielefeld) 15:00-15:45
Classification of p-divisible groups by displays and duality
T. Zink (Univ. of Bielefeld) 16:00-16:45
Applications of the theory of displays
E. Looijenga (Univ. of Utrecht) 17:00-18:00
Presentation of mapping class groups from algebraic geometry
[ Abstract ]
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.

### 2007/09/05

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Reinhard Farwig (Darmstadt University of Technology)
Reguarity of Weak Solutions to the Navier-Stokes System beyond Serrin's Criterion
[ Abstract ]
Consider a weak instationary solution $u(x,t)$ of the Navier-Stokes equations in a domain $\\Omega \\subset \\mathbb{R}^3$ in the sense of Leray-Hopf. As is well-known, $u$ is is unique and regular if $u\\in L^s(0,T;L^q(\\Omega))$ satisfies the {\\it strong energy inequality} and $s,q$ satisfy Serrin's condition $\\frac{2}{s} + \\frac{3}{q}=1$, $s>2,\\, q>3$. Now consider $u$ such that $$u\\in L^r(0,T;L^q(\\Omega))\\quad \\mbox{ where }\\quad \\frac{2}{r} + \\frac{3}{q}>1$$ and has a sufficiently small norm in $L^r(0,T;L^q(\\Omega))$. Then we will prove that $u$ is regular. Similar results of local rather than global type in space will be proved provided that $u$ satisfies the {\\it localized energy inequality}. Finally H\\"older continuity of the kinetic energy in time will imply regularity.

The proofs use local in time regularity results which are based on the {\\it theory of very weak solutions} and on uniqueness arguments for weak solutions.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2007/08/29

#### Algebraic Geometry Seminar

17:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Valery Alexeev (Georgia大学)
Computations on the moduli spaces of weighted log pairs

### 2007/08/27

#### Number Theory Seminar

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Steven Zucker (Johns Hopkins大学)
The reductive Borel-Serre motive

### 2007/08/02

#### Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
De-Qi Zhang (Singapore大学)
Dynamics of automorphisms on algebraic varieties
[ Abstract ]
The building blocks of automorphisms / endomorphisms of compact varieties are determined --- an algebro geometric approach towards dynamics.

### 2007/07/25

#### Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
The empirical spectral distribution of random matrices have been studied since Wigner's pioneering work on the semicircular law in the 1950's. The result says that the empirical spectral distribution of a symmetric matrix with i.i.d. random elements converges to the semicircular law as the size of the matrix becomes large. Though this result is beautiful in theory, its application has been limited to a few problems in nuclear physics and coding theory. The next breakthrough was the Marcenko-Pastur (M-P) law for the asymptotic spectral distribution of sample covariance matrices. The M-P law has found more applications, in particular high dimensional statistical data analysis, than the semicircular law.

In this talk I will first review these two significant results. Each of them has three completely different proofs. Then I will explain several other theoretical results that have mostly been studied this decade. Finally, I will present some of the applications of these results. This review is partly based on lectures on random matrices given by P. Bickel, N. El-Karoui and A. Guionnet, and also some seminars at UC Berkeley.

(# This talk is almost the same as the talk I gave at ISM on June 1.)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/05.html

### 2007/07/20

#### Colloquium

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

ソリトン物理はおもしろい---スピノル型ボーズ・アインシュタイン凝縮体におけるソリトン

### 2007/07/19

#### Seminar for Mathematical Past of Asia

17:00-18:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

On a class of II$_1$ factors with at most one Cartan subalgebra

### 2007/07/18

#### Number Theory Seminar

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

Tropical toric varieties

#### Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)

Easy full-joint estimators of stable processes
[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/04.html

### 2007/07/17

#### Tuesday Seminar on Topology

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

Orbifold Cohomology of Wreath Product Orbifolds and
Cohomological HyperKahler Resolution Conjecture
[ Abstract ]
Chen-Ruan orbifold cohomology ring was introduced in 2000 as
the degree zero genus zero orbifold Gromov-Witten invariants with
three marked points. We will review its construction in the case of
global quotient orbifolds, following Fantechi-Gottsche and
Jarvis-Kaufmann-Kimura. We will describe the orbifold cohomology of
wreath product orbifolds and explain its application to Ruan's
cohomological hyperKahler resolution conjecture.

### 2007/07/12

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Normalizers of MASAs and irreducible subfactors

### 2007/07/11

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Andreas Rosenschon (University of Alberta)
Algebraic cycles on products of elliptic curves over p-adic fields

### 2007/07/10

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Danny C. Calegari (California Institute of Technology)
Combable functions, quasimorphisms, and the central limit theorem
(joint with Koji Fujiwara)

[ Abstract ]
Quasimorphisms on groups are dual to stable commutator length,
and detect extremal phenomena in topology and dynamics. In typical groups
(even in a free group) stable commutator length is very difficult to
calculate, because the space of quasimorphisms is too large to study
In this talk, we show that a large class of quasimorphisms - the so-called
"counting quasimorphisms" on word-hyperbolic groups - can be effectively
described using simple machines called finite state automata. From this,
and from the ergodic theory of finite directed graphs, one can deduce a
number of properties about the statistical distribution of the values of a
counting quasimorphism on elements of the group.

### 2007/07/09

#### Seminar on Geometric Complex Analysis

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

Geometry of hyperkahler quotients