## 過去の記録

### 2007年05月09日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

$(g,K)$-module structures of principal series representations
of $Sp(3,R)$

### 2007年05月08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

On the vanishing of the Rohlin invariant
[ 講演概要 ]
The vanishing of the Rohlin invariant of an amphichiral integral
homology $3$-sphere $M$ (i.e. $M \\cong -M$) is a natural consequence
of some elementary properties of the Casson invariant. In this talk, we
give a new direct (and more elementary) proof of this vanishing
property. The main idea comes from the definition of the degree 1
part of the Kontsevich-Kuperberg-Thurston invariant, and we progress
by constructing some $7$-dimensional manifolds in which $M$ is embedded.

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
この週には同氏による集中講義 14:40-16:40 が行われます。セミナーの時刻はいつもと違いますのでご注意ください。

Affine W-algebras and their representations
[ 講演概要 ]
The W-algebras are an interesting class of vertex algebras, which can be understood as a generalization of Virasoro algebra. It was originally introduced by Zamolodchikov in his study of conformal field theory. Later Feigin-Frenkel discovered that the W-algebras can be defined via the method of quantum BRST reduction. A few years ago this method was generalized by Kac-Roan-Wakimoto in full generality, producing many interesting vertex algebras. Almost at the same time Premet re-discovered the finite-dimensional version of W-algebras (finite W-algebras), in connection with the modular representation theory.

In the talk we quickly recall the Feigin-Frenkel theory which connects the Whittaker models of the center of $U({\\mathfrak g})$ and affine (principal) W-algebras, and discuss their representation theory. Next we recall the construction of Kac-Roan-Wakimoto and discuss the representation theory of affine W-algebras associated with general nilpotent orbits. In particular, I explain how the representation theory of finite W-algebras (=the endmorphism ring of the generalized Gelfand-Graev representation) applies to the representation of affine W-algebras.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年05月07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) 128号室

Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Pathologies on ruled surfaces in positive characteristic
[ 講演概要 ]
We discuss some pathologies of log varieties in positive characteristic. Mainly, we show that on ruled surfaces there are counterexamples of several logarithmic type theorems. On the other hand, we also give a characterization of the counterexamples of the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface by means of the Tango invariant of the base curve.

### 2007年05月02日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields

### 2007年05月01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

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$
[ 講演概要 ]
Asymptotic expansion of the matrix coefficents of class-1 principal series representation was considered by Harish-Chandra. The coefficient of the leading exponent of the expansion is called the c-function which plays an important role in the harmonic analysis on the Lie group.

In this talk, we consider the Harish-Chandra expansion of the matrix coefficients of the standard representation which is the parabolic induction with respect to a non-minimal parabolic subgroup of $Sp(2,R)$.

This is the joint study with Professor T. Oda.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年04月26日(木)

#### アジア数学史セミナー

17:00-18:30   数理科学研究科棟(駒場) 123号室

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

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Nonequilibrium steady states in quantum systems

### 2007年04月25日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

Localized Characteristic Class and Swan Class

### 2007年04月24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

Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators
[ 講演概要 ]
A problem in twisted $K$-theory is to realize twisted $K$-groups generally by means of finite-dimensional geometric objects, like vector bundles. I would like to talk about an approach toward the problem by means of Mikio Furuta's generalized vector bundles. By using a twisted version of the generalized vector bundle and a finite-dimensional approximation of Fredholm operators, I construct a group into which there exists a natural injection from the twisted $K$-group twisted by any third integral cohomology class.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Taro Yoshino (吉野太郎) 氏 (University of Tokyo)
Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds

[ 講演概要 ]
The existence problem of compact Clifford-Klein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its `infinitesimal' homogeneous space.
This homogeneous space is easier to consider the existence problem of compact Clifford-Klein forms.
In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact Clifford-Klein forms to certain algebraic problem, which was already studied from other motivation.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino

### 2007年04月23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) 128号室

Generalization of Q-curvature in CR geometry

### 2007年04月19日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Graph algebras, Exel-Laca algebras and ultragraph algebras

### 2007年04月17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

Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains.

#### 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

Existence Problem of Compact Locally Symmetric Spaces
[ 講演概要 ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I will give a survey on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds with emphasis on the existence problem of compact models of locally symmetric spaces.

### 2007年04月16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) 128号室

Joyce計量のツイスター空間の具体的な構成方法

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 056号室
Francois Hamel 氏 (エクス・マルセーユ第3大学 (Universite Aix-Marseille III))
Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators
[ 講演概要 ]
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.

The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.

### 2007年04月14日(土)

#### 東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 117号室

q-Fock空間と非対称Macdonald多項式
[ 講演概要 ]

A型量子トロイダル代数のレベル(0,1)表現の構造が入ることが知られています.
この表現をある可換部分代数に制限して得られる作用の同時固有ベクトルを,

さらにこの同時固有ベクトルをq-Fock空間の基底とすることで,

The Quantum Knizhnik-Zamolodchikov Equation
and Non-symmetric Macdonald Polynomials
[ 講演概要 ]
We construct special solutions of the quantum Knizhnik-Zamolodchikov equation
on the tensor product of the vector representation of
the quantum algebra of type $A_{N-1}$.
They are constructed from non-symmetric Macdonald polynomials
through the action of the affine Hecke algebra.
As special cases,
(i) the matrix element of the vertex operators
of level one is reproduced, and
(ii) we give solutions of level $\\frac{N+1}{N}-N$.
(ii) is a generalization of the solution of
level $-\\frac{1}{2}$ by V.Pasquier and me.

This is a jount work with Y.Takeyama.

### 2007年04月12日(木)

#### 諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 056号室
Boris Khesin 氏 (University of Toronto)
Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
[ 講演概要 ]
We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid
Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.

Further, we consider the non-holonomic optimal transport problem,
related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

ミラー対称性

### 2007年04月11日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
C. W. Oosterlee 氏 (Delft University of Technology)
The numerical treatment of pricing early exercise options under L'evy processes
[ 講演概要 ]
In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics.

Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining European option prices. For American prices a linear complementarity problem with the partial integro-differential operator needs to be solved. We outline the difficulties and possible solutions in this context.

At the same time we would also like to present a different pricing approach based on numerical integration and the fast Fourier Transform. Both approaches are compared in terms of accuracy and efficiency.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

l進層の暴分岐と特性サイクル

### 2007年04月10日(火)

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 370号室
Thomas DURT 氏 (ブリユッセル自由大学・VUB)
Applications of the Generalised Pauli Group in Quantum Information
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf