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Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
2007/05/10
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
戸松玲治 (東大数理)
自己準同型の収束と近似的内部性
戸松玲治 (東大数理)
自己準同型の収束と近似的内部性
2007/05/09
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
宮崎 直 (東京大学大学院数理科学研究科)
$(g,K)$-module structures of principal series representations
of $Sp(3,R)$
宮崎 直 (東京大学大学院数理科学研究科)
$(g,K)$-module structures of principal series representations
of $Sp(3,R)$
2007/05/08
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
森山 哲裕 (東京大学大学院数理科学研究科)
On the vanishing of the Rohlin invariant
森山 哲裕 (東京大学大学院数理科学研究科)
On the vanishing of the Rohlin invariant
[ Abstract ]
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.
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 Groups and Representation Theory
17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
荒川知幸 (奈良女子大学)
Affine W-algebras and their representations
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
荒川知幸 (奈良女子大学)
Affine W-algebras and their representations
[ Abstract ]
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.
[ Reference URL ]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.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/05/07
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
辻 元 (上智大学)
Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems
辻 元 (上智大学)
Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems
Algebraic Geometry Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
謝啓鴻(Xie Qihong) (東大・数理)
Pathologies on ruled surfaces in positive characteristic
謝啓鴻(Xie Qihong) (東大・数理)
Pathologies on ruled surfaces in positive characteristic
[ Abstract ]
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.
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.
2007/05/02
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
長谷川 泰子 (東京大学大学院数理科学研究科)
Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields
長谷川 泰子 (東京大学大学院数理科学研究科)
Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields
2007/05/01
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
下村 明洋 (学習院大理学部)
非線型シュレディンガー方程式の解の長時間挙動について
下村 明洋 (学習院大理学部)
非線型シュレディンガー方程式の解の長時間挙動について
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
飯田正敏 (城西大学)
Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
飯田正敏 (城西大学)
Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$
[ Abstract ]
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.
[ Reference URL ]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.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/04/26
Seminar for Mathematical Past of Asia
17:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)
公田 藏 (立教大学名誉教授)
明治前期の日本において学ばれたユークリッド幾何学
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
公田 藏 (立教大学名誉教授)
明治前期の日本において学ばれたユークリッド幾何学
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
緒方芳子 (東大数理)
Nonequilibrium steady states in quantum systems
緒方芳子 (東大数理)
Nonequilibrium steady states in quantum systems
2007/04/25
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
津嶋 貴弘 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class
津嶋 貴弘 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class
2007/04/24
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
五味 清紀 (東京大学大学院数理科学研究科)
Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators
五味 清紀 (東京大学大学院数理科学研究科)
Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators
[ Abstract ]
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.
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 Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Taro Yoshino (吉野太郎) (University of Tokyo)
Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino
Taro Yoshino (吉野太郎) (University of Tokyo)
Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds
[ Abstract ]
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.
[ Reference URL ]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.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino
2007/04/23
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
平地健吾 (東京大学)
Generalization of Q-curvature in CR geometry
平地健吾 (東京大学)
Generalization of Q-curvature in CR geometry
2007/04/19
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
勝良健史 (東大数理)
Graph algebras, Exel-Laca algebras and ultragraph algebras
勝良健史 (東大数理)
Graph algebras, Exel-Laca algebras and ultragraph algebras
2007/04/17
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
小薗 英雄 (東北大学・大学院理学研究科)
Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains.
小薗 英雄 (東北大学・大学院理学研究科)
Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains.
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
小林 俊行 (東京大学大学院数理科学研究科)
Existence Problem of Compact Locally Symmetric Spaces
小林 俊行 (東京大学大学院数理科学研究科)
Existence Problem of Compact Locally Symmetric Spaces
[ Abstract ]
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.
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.
2007/04/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
本多 宣博 (東京工業大学)
Joyce計量のツイスター空間の具体的な構成方法
本多 宣博 (東京工業大学)
Joyce計量のツイスター空間の具体的な構成方法
Lectures
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Francois Hamel (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
Francois Hamel (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
[ Abstract ]
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.
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.
2007/04/14
Infinite Analysis Seminar Tokyo
13:00-16:30 Room #117 (Graduate School of Math. Sci. Bldg.)
長尾健太郎 (京大理) 13:00-14:30
q-Fock空間と非対称Macdonald多項式
The Quantum Knizhnik-Zamolodchikov Equation
and Non-symmetric Macdonald Polynomials
長尾健太郎 (京大理) 13:00-14:30
q-Fock空間と非対称Macdonald多項式
[ Abstract ]
斎藤-竹村-Uglov,Varagnolo-Vasserotによって,q-Fock空間に
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,
非対称Macdonald多項式を用いて構成することができます.
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,
量子トロイダル代数の作用を組合せ論的に記述することができます.
今回のセミナーでは,斎藤-竹村-Uglov,Varagnolo-Vasserotの構成を
振り返ったあとで,同時固有ベクトルの構成法を紹介します.
最後に箙多様体の同変K群との関連について少しだけ言及します.
笠谷昌弘 (京大理) 15:00-16:30斎藤-竹村-Uglov,Varagnolo-Vasserotによって,q-Fock空間に
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,
非対称Macdonald多項式を用いて構成することができます.
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,
量子トロイダル代数の作用を組合せ論的に記述することができます.
今回のセミナーでは,斎藤-竹村-Uglov,Varagnolo-Vasserotの構成を
振り返ったあとで,同時固有ベクトルの構成法を紹介します.
最後に箙多様体の同変K群との関連について少しだけ言及します.
The Quantum Knizhnik-Zamolodchikov Equation
and Non-symmetric Macdonald Polynomials
[ Abstract ]
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.
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.
2007/04/12
Seminar on Mathematics for various disciplines
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Boris Khesin (University of Toronto)
Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
http://coe.math.sci.hokudai.ac.jp/
Boris Khesin (University of Toronto)
Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
[ Abstract ]
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.
[ Reference URL ]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.
http://coe.math.sci.hokudai.ac.jp/
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
小西由紀子 (東大数理)
ミラー対称性
小西由紀子 (東大数理)
ミラー対称性
2007/04/11
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
C. W. Oosterlee (Delft University of Technology)
The numerical treatment of pricing early exercise options under L'evy processes
http://coe.math.sci.hokudai.ac.jp/
C. W. Oosterlee (Delft University of Technology)
The numerical treatment of pricing early exercise options under L'evy processes
[ Abstract ]
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.
[ Reference URL ]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.
http://coe.math.sci.hokudai.ac.jp/
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
斎藤 毅 (東京大学大学院数理科学研究科)
l進層の暴分岐と特性サイクル
斎藤 毅 (東京大学大学院数理科学研究科)
l進層の暴分岐と特性サイクル
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