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過去の記録
過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
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
宮尾 忠宏 氏 (岡山大自然科学研究科 学振特別研究員 )
量子電磁場中を運動する原子の安定性について
宮尾 忠宏 氏 (岡山大自然科学研究科 学振特別研究員 )
量子電磁場中を運動する原子の安定性について
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
渡邉 忠之 氏 (京都大学数理解析研究所)
Kontsevich's characteristic classes for higher dimensional homology sphere bundles
Tea: 16:00 - 16:30 コモンルーム
渡邉 忠之 氏 (京都大学数理解析研究所)
Kontsevich's characteristic classes for higher dimensional homology sphere bundles
[ 講演概要 ]
As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich
constructed universal characteristic classes of smooth fiber bundles with fiber
diffeomorphic to a singularly framed odd dimensional homology sphere.
In this talk, I will give a sketch proof of our result on non-triviality of the
Kontsevich classes for 7-dimensional homology sphere bundles.
As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich
constructed universal characteristic classes of smooth fiber bundles with fiber
diffeomorphic to a singularly framed odd dimensional homology sphere.
In this talk, I will give a sketch proof of our result on non-triviality of the
Kontsevich classes for 7-dimensional homology sphere bundles.
2007年05月14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
Si, Quang Duc 氏 (東大数理)
Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables
Si, Quang Duc 氏 (東大数理)
Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables
2007年05月10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
戸松玲治 氏 (東大数理)
自己準同型の収束と近似的内部性
戸松玲治 氏 (東大数理)
自己準同型の収束と近似的内部性
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
宮崎 直 氏 (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 氏 (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
森山 哲裕 氏 (東京大学大学院数理科学研究科)
On the vanishing of the Rohlin invariant
Tea: 16:00 - 16:30 コモンルーム
森山 哲裕 氏 (東京大学大学院数理科学研究科)
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.
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。
荒川知幸 氏 (奈良女子大学)
Affine W-algebras and their representations
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
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。
荒川知幸 氏 (奈良女子大学)
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 ]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
辻 元 氏 (上智大学)
Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems
辻 元 氏 (上智大学)
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
謝啓鴻(Xie Qihong) 氏 (東大・数理)
Pathologies on ruled surfaces in positive characteristic
謝啓鴻(Xie Qihong) 氏 (東大・数理)
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.
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
長谷川 泰子 氏 (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 氏 (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
下村 明洋 氏 (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 氏 (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
飯田正敏 氏 (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 氏 (城西大学)
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 ]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
公田 藏 氏 (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
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
公田 藏 氏 (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
[ 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
緒方芳子 氏 (東大数理)
Nonequilibrium steady states in quantum systems
緒方芳子 氏 (東大数理)
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
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
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
五味 清紀 氏 (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
Tea: 16:00 - 16:30 コモンルーム
五味 清紀 氏 (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
[ 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.
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
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino
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 ]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
平地健吾 氏 (東京大学)
Generalization of Q-curvature in CR geometry
平地健吾 氏 (東京大学)
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
勝良健史 氏 (東大数理)
Graph algebras, Exel-Laca algebras and ultragraph algebras
勝良健史 氏 (東大数理)
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
小薗 英雄 氏 (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 氏 (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.
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
小林 俊行 氏 (東京大学大学院数理科学研究科)
Existence Problem of Compact Locally Symmetric Spaces
Tea: 16:00 - 16:30 コモンルーム
小林 俊行 氏 (東京大学大学院数理科学研究科)
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.
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
本多 宣博 氏 (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 氏 (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
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
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.
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
長尾健太郎 氏 (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 氏 (京大理) 13:00-14:30
q-Fock空間と非対称Macdonald多項式
[ 講演概要 ]
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 氏 (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
[ 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.
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
http://coe.math.sci.hokudai.ac.jp/
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 ]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/
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