## Seminar information archive

### 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
directly without adding more structure.
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

### 2007/07/06

#### Seminar on Probability and Statistics

15:00-16:10   Room #122 (Graduate School of Math. Sci. Bldg.)
Arturo KOHATSU-HIGA (大阪大学大学院基礎工学研究科)
Estimating multidimensional densities through the Malliavin-Thalmaier formula
[ Abstract ]
TBA
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/03.html

### 2007/07/05

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Rolf Dyre Svegstrup (東大数理)
Factorization in $C^*$-Algebras

### 2007/07/04

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Lars Diening (Universitat Freiburg)
The Lipschitz truncation method
[ Abstract ]
We study the existence of weak solutions to the incompressible $p$-Navier Stokes equations. This system can be used to describe the flow of honey, ketchup, blood, suspensions, polymers, and glaciers. We are interested in small values of $p$, where the method of monotone operators fails. We establish weak solutions by means of the Lipschitz truncation technique, where Sobolev Functions are approximated by Lipschitz functions in a special way. We apply the technique also to electrorheological fluids, where the exponent $p$ depends on the electric field.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

#### Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

A Special Lagrangian Fibration in the TAUB-NUT Space
[ Abstract ]
この講演では, Taub-NUT space における special Lagrangian fibration の具体的構成について述べるつもりである.Taub-NUT space は複素多様体としては二次元複素空間であるが,計量が通常と異なり完備で非平坦なリッチ平坦計量をもつ Hyper-Kahler 多様体として特徴づけられる.この空間の special Lagrangian fibration が,Ionel-Min Oo の手法を用いることで具体的に構成できることを見る.

Symmetries in generalized complex geometry
[ Abstract ]

### 2007/07/03

#### Tuesday Seminar on Topology

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

Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation
(joint work with Mitsuhiko Takasawa)
[ Abstract ]
We concern two invariants of pseudo-Anosov mapping classes.
One is the dilatation of pseudo--Anosov maps and the other is the volume
of mapping tori. To study how two invariants are related, fixing a surface
we represent a mapping class by using the standard generator set and compute
these two for all pseudo--Anosov mapping classes with up to some word length.
In the talk, we observe two properties:

(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to
the volume is bounded from below by some positive constant which only
depends on the surface.

(2) The conjugacy class having the minimal dilatation reaches the minimal volume.

On the observation (1), in case of the mapping class group of a once--punctured
torus, we give a concrete lower bound of the ratio.

### 2007/07/02

#### Seminar on Geometric Complex Analysis

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

On the Meyer function for theta divisors

### 2007/06/29

#### Lie Groups and Representation Theory

15:30-17:45   Room #122 (Graduate School of Math. Sci. Bldg.)
Salem Ben Said (Nancy大)
On the theory of Bessel functions associated with root systems
[ Abstract ]
The theory of spherical functions on Riemannian symmetric spaces G/K and on non-compactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of Heckman-Opdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to non-compactly causal symmetric spaces.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2007/06/28

#### Operator Algebra Seminars

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

A new construction of causal nets of operator algebras

### 2007/06/27

#### Seminar on Probability and Statistics

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

Empirical likelihood method for time series analysis
[ Abstract ]
For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Stephen Lichtenbaum (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
[ Abstract ]
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.

#### Mathematical Finance

17:30-19:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Selection and Performance Analysis of Asia-Pacific Hedge Funds

### 2007/06/25

#### Seminar on Geometric Complex Analysis

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

### 2007/06/22

#### Algebraic Geometry Seminar

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Qi Zhang (Missouri大学)
Projective varieties with nef anti-canonical divisors
[ Abstract ]
Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.

### 2007/06/21

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Richard D. Burstein (UC Berkeley)
Subfactors Arising from Symmetric Commuting Squares (following Jones/Sunder)

### 2007/06/20

#### Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

LeBrun-Mason 対応とその簡約について
[ Abstract ]
LeBrun と Mason は近年,正則円板の族に関するツイスター型の対応を発見した.彼らは次元の異なる二つのタイプの対応を示しているが,どちらも Penrose や Hitchin による解析的・局所的な理論の,非解析的・大域的な version とみなすことができる.一方 Penrose らの枠組みにおいては,次元の異なるツイスター型対応を関連づける次元簡約という現象が生じることが,Dunajski などによって最近研究されている.この講演では,LeBrun らの大域的な状況で簡約理論を展開しようとするときに生じる問題点を示し,ある種の特異性を導入することでこれを解決できることを説明したい.論文:math.DG/0701116

Deformations of generalized Kahler and Calabi-Yau structures
[ Abstract ]

#### Lectures

15:00-16:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Y.S. Chow (台湾中央研究院数学研究所)
On evolution games with local interaction and mutation

### 2007/06/19

#### Tuesday Seminar of Analysis

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

Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\\"odinger equation

#### Lie Groups and Representation Theory

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

Rigid local systemとその切断の積分表示,および接続係数
[ Abstract ]
A local system on $CP^1-\\{finite points\\}$ is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory.

### 2007/06/18

#### Seminar on Geometric Complex Analysis

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

An intrinsic characterization of the unit polydisc

### 2007/06/16

#### Infinite Analysis Seminar Tokyo

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

Lie theoretic structures for the generalized symmetric groups
[ Abstract ]

modular表現論とKac-Moody Lie環/量子群といったLie theoreticな対象との関係が研究
されて来た。このうち対称群のmodular表現論については、

(1) 標数p>0において、対称群\\mathfrak{S}_nの(有限次元)表現のGrothendieck群の
(nを走らせた)直和には、Kac-Moody Lie環g(A^{1}_{p-1})のレベル1基本既約最高
weight表現の構造を入れることが出来る。

(2) 対称群の既約表現の同型類の直和には、量子群U_q(g(A^{1}_{p-1}))の
レベル1基本既約最高weight表現に付随する(Kashiwaraの意味での)結晶構造を

と、その関係をまとめることが出来る。

に付随する量子群との関係を示唆する結果を得たので、まずはそれを解説したい。

なお、G(m,1,n)の群環のq-変形と考えられているcyclotomic Hecke algebraにおいて、
qが1でない1の羃根の場合は既に(1),(2)の対応物が知られているので、時間が許せば
それとの比較についても解説したい。

Wirtinger 積分の構造について
[ Abstract ]
Wirtinger はガウスの超幾何函数 $_2F_1$ を一意化する目的でこれを
テータ函数の冪積の積分で表わす表示を1902年に得た.Wirtinger の発見以降,
この積分に関する組織的な研究は講演者の調べた限りではほとんど無いのであるが,
この積分を講演者は前述に因んで Wirtinger 積分と呼んでいる.
この積分は実質的には超幾何函数なのであるが,あえてこの事実を忘れテータ函数の

できれば,それはテータ函数論の観点からのガウスの超幾何函数論の再構成と

ことである.