## Seminar information archive

#### Infinite Analysis Seminar Tokyo

11:00-12:00   Room #117 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

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

### 2009/06/18

#### Operator Algebra Seminars

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

The super Virasoro algebra and noncommutative geometry

### 2009/06/17

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Variational problems for anisotropic surface energies
[ Abstract ]
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.

### 2009/06/16

#### Tuesday Seminar on Topology

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

The abelianization of the level 2 mapping class group
[ Abstract ]
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.

### 2009/06/15

#### Seminar on Geometric Complex Analysis

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

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

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
On the Schur-Szeg\\"o composition of polynomials
[ Abstract ]
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

$$(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma_1,\\ldots ,\\sigma_{n-1})$$

#### Algebraic Geometry Seminar

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

アーベル曲面の分解と2次形式

[ Abstract ]

ありうる。いくつかの場合に分解の個数公式が求められてきた(林田、塩田-三谷
)。本講演では、すべての分解可能な複素Abel曲面に対して、2次形式論の技法
を用いて分解数の公式を与える。関連して次のことも話す:合同モジュラー曲線

の等長群の関係。

### 2009/06/11

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
A topos for algebraic quantum theory

### 2009/06/10

#### Number Theory Seminar

16:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Kahn (Paris第7大学)
On the classifying space of a linear algebraic group

#### Lectures

15:30-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)

### 2009/06/09

#### Tuesday Seminar on Topology

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

A finite-dimensional construction of the Chern character for
twisted K-theory
[ Abstract ]
Twisted K-theory is a variant of topological K-theory, and
is attracting much interest due to applications to physics recently.
Usually, twisted K-theory is formulated infinite-dimensionally, and
hence known constructions of its Chern character are more or less
abstract. The aim of my talk is to explain a purely finite-dimensional
construction of the Chern character for twisted K-theory, which allows
us to compute examples concretely. The construction is based on
twisted version of Furuta's generalized vector bundle, and Quillen's
superconnection.
This is a joint work with Yuji Terashima.

### 2009/06/08

#### Seminar on Geometric Complex Analysis

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

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Kiyonori Gomi (Kyoto University)
Multiplication in differential cohomology and cohomology operation
[ Abstract ]
The notion of differential cohomology refines generalized
cohomology theory so as to incorporate information of differential
forms. The differential version of the ordinary cohomology has been
known as the Cheeger-Simons cohomology or the smooth Deligne
cohomology, while the general case was introduced by Hopkins and
Singer around 2002.

The theme of my talk is the cohomology operation induced from the
squaring map in the differential ordinary cohomology and the
differential K-cohomology: I will relate these operations to the
Steenrod operation and the Adams operation. I will also explain the
roles that the squaring maps play in 5-dimensional Chern-Simons theory
for pairs of B-fields and Hamiltonian quantization of generalized
abelian gauge fields.

### 2009/06/04

#### Operator Algebra Seminars

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

Determinant for rectangular martices

### 2009/06/03

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Evolution of microstructures on crystal surfaces by surface diffusion
[ Abstract ]
We have studied the shape evolution of microstructures fabricated on silicon surfaces by surface diffusion during annealing. Various interesting phenomena, such as corner rounding, facet growth, and void formation, have been experimentally observed. We discuss these observations both from macroscopic and mesoscopic viewpoints. The evolution of macroscopic surface profiles is discussed using evolution equations based on the continuum surface picture. We analyze the mesoscopic scale aspects of the shape evolution using a step-flow model.

#### Seminar on Probability and Statistics

15:00-16:10   Room #128 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

DNA配列多様性と形質多様性との関係を検出するにあたり、このDNA配列集団の多様性と不均一性は、遺伝因子間の非独立性として、関係検出過程に大きな影響を与えることから、DNA配列集団の多様性の把握そのものが、遺伝統計学の課題となっている。
ヒトDNA配列は4種類の塩基が長さ30億であるため、『生命体として成立しうる』という制約の下、非常に多様な配列を取り得る。このDNA配列が取り得る範囲をDNA配列の空間とみなしたとき、DNA配列集団の多様性は、その空間におけるDNA配列集団の分布状態となる。

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/04.html

#### Number Theory Seminar

16:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Kahn (Paris第7大学)

### 2009/06/02

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander Voronov (University of Minnesota)
Graph homology: Koszul duality = Verdier duality
[ Abstract ]
Graph cohomology appears in computation of the cohomology of the moduli space of Riemann surfaces and the outer automorphism group of a free group. In the former case, it is graph cohomology of the commutative and Lie types, in the latter it is ribbon graph cohomology, that is to say, graph cohomology of the associative type. The presence of these three basic types of algebraic structures hints at a relation between Koszul duality for operads and Poincare-Lefschetz duality for manifolds. I will show how the more general Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This is a joint work with Andrey Lazarev.

#### Tuesday Seminar of Analysis

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

### 2009/05/28

#### Operator Algebra Seminars

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

The Rohlin property for automorphisms of the Jiang-Su algebra

### 2009/05/27

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Gombodorj Bayarmagnai (東京大学大学院数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)

### 2009/05/26

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Myriam Ounaies (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
[ Abstract ]
We call Hörmander algebras the spaces $A_p(\\mathbb C)$ of entire functions $f$ such that, for all $z$ in $\\mathbb C$, \$|f(z)|\\le Ae^{Bp(z)},\$ where $A$ and $B$ are some positive constants (depending on $f$) and $p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence $\\{a_j\\}$ of complex numbers and a sequence of complex values $\\{b_j\\}$, under what conditions does there exist a function $f\\in A_p(\\mathbb C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what is the trace of $A_p(\\mathbb C)$ on $\\{a_j\\}$ ?
We say that $\\{a_j\\}$ is an interpolating sequence if the trace is defined by the space of all $\\{b_j\\}$ satisfying $|b_j|\\le A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use Hörmander's $L^2$-estimates for the $\\bar\\partial$-equation to describe the trace when the weight $p$ is radial and doubling and to characterize the interpolating sequences for more general weights.

#### Tuesday Seminar on Topology

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

Configuration space integrals and the cohomology of the space of long embeddings

[ Abstract ]
It is known that some non-trivial cohomology classes, such as finite type invariants for (long) 1-knots (Bott-Taubes, Kohno, ...) and invariants for codimension two, odd dimensional long embeddings (Bott, Cattaneo-Rossi, Watanabe) are given as configuration space integrals associated with trivalent graphs.
In this talk, I will describe more cohomology classes by means of configuration space integral, in particular those arising from non-trivalent graphs and a new formulation of the Haefliger invariant for long 3-embeddings in 6-space, in relation to Budney's little balls operad action and Roseman-Takase's deform-spinning.
This is in part a joint work with Tadayuki Watanabe.

### 2009/05/25

#### Seminar on Geometric Complex Analysis

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

Brody曲線の空間の幾何と平均次元

### 2009/05/22

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]