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Seminar information archive
Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～
2010/02/16
Tuesday Seminar on Topology
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Dieter Kotschick (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
Dieter Kotschick (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
[ Abstract ]
The Chern numbers of n-dimensional smooth projective varieties span a vector space whose dimension is the number of partitions of n. This vector space has many natural subspaces, some of which are quite small, for example the subspace spanned by Hirzebruch--Todd numbers, the subspace of topologically invariant combinations of Chern numbers, the subspace determined by the Hodge numbers, and the subspace of Chern numbers that can be bounded in terms of Betti numbers. I shall explain the relation between these subspaces, and characterize them in several ways. This leads in particular to the solution of a long-standing open problem originally formulated by Hirzebruch in the 1950s.
The Chern numbers of n-dimensional smooth projective varieties span a vector space whose dimension is the number of partitions of n. This vector space has many natural subspaces, some of which are quite small, for example the subspace spanned by Hirzebruch--Todd numbers, the subspace of topologically invariant combinations of Chern numbers, the subspace determined by the Hodge numbers, and the subspace of Chern numbers that can be bounded in terms of Betti numbers. I shall explain the relation between these subspaces, and characterize them in several ways. This leads in particular to the solution of a long-standing open problem originally formulated by Hirzebruch in the 1950s.
2010/02/05
thesis presentations
09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Takahiro Tsushima (University of Tokyo)
Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)
Takahiro Tsushima (University of Tokyo)
Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Abe (University of Tokyo)
Comparison between Swan conductors and characteristic cycles (JAPANESE)
Tomoyuki Abe (University of Tokyo)
Comparison between Swan conductors and characteristic cycles (JAPANESE)
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
宮﨑 直 (東京大学大学院数理科学研究科)
The structures of generalized principal series representations of SL(3,R) and related Whittaker functions (SL(3,R)の一般主系列表現の構造と関連するWhittaker関数)
宮﨑 直 (東京大学大学院数理科学研究科)
The structures of generalized principal series representations of SL(3,R) and related Whittaker functions (SL(3,R)の一般主系列表現の構造と関連するWhittaker関数)
thesis presentations
14:15-15:30 Room #118 (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)
PRINCIPAL SERIES AND GENERALIZED PRINCIPAL SERIES WHITTAKER FUNCTIONS WITH PERIPHERAL K-TYPES ON THE REAL SYMPLECTIC GROUP OF RANK 2 (実二次シンプレクティック群上の主系列表現及び一般主系列表現の周辺的K-TYPEを持つWHITTAKER 関数)
長谷川 泰子 (東京大学大学院数理科学研究科)
PRINCIPAL SERIES AND GENERALIZED PRINCIPAL SERIES WHITTAKER FUNCTIONS WITH PERIPHERAL K-TYPES ON THE REAL SYMPLECTIC GROUP OF RANK 2 (実二次シンプレクティック群上の主系列表現及び一般主系列表現の周辺的K-TYPEを持つWHITTAKER 関数)
thesis presentations
09:45-11:00 Room #122 (Graduate School of Math. Sci. Bldg.)
二木 昌宏 (東京大学大学院数理科学研究科)
On the generalized suspension theorem for directed Fukaya categories (有向深谷圏の懸垂定理の一般化について)
二木 昌宏 (東京大学大学院数理科学研究科)
On the generalized suspension theorem for directed Fukaya categories (有向深谷圏の懸垂定理の一般化について)
thesis presentations
11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)
松尾 信一郎 (東京大学大学院数理科学研究科)
On the Runge theorem for instantons (インスタントンに対するRungeの近似定理について)
松尾 信一郎 (東京大学大学院数理科学研究科)
On the Runge theorem for instantons (インスタントンに対するRungeの近似定理について)
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
西岡 斉治 (東京大学大学院数理科学研究科)
Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)
西岡 斉治 (東京大学大学院数理科学研究科)
Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
水田 有一 (東京大学大学院数理科学研究科)
Weak Amenability for a Group Acting on a Finite Dimensional CAT(0) Cube Complex (有限次元CAT(0)方体複体に作用する群の弱従順性)
水田 有一 (東京大学大学院数理科学研究科)
Weak Amenability for a Group Acting on a Finite Dimensional CAT(0) Cube Complex (有限次元CAT(0)方体複体に作用する群の弱従順性)
thesis presentations
14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)
酒匂 宏樹 (東京大学大学院数理科学研究科)
Stone-Čech boundaries of discrete groups and measure equivalence theory (離散群のストーン-チェック境界と測度同値理論)
酒匂 宏樹 (東京大学大学院数理科学研究科)
Stone-Čech boundaries of discrete groups and measure equivalence theory (離散群のストーン-チェック境界と測度同値理論)
thesis presentations
09:45-11:00 Room #128 (Graduate School of Math. Sci. Bldg.)
西山 了允 (東京大学大学院数理科学研究科)
CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)
西山 了允 (東京大学大学院数理科学研究科)
CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)
2010/02/04
thesis presentations
09:45-11:00 Room #122 (Graduate School of Math. Sci. Bldg.)
久野 雄介 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications to local signatures for fibered 4-manifolds (射影多様体に対するMeyer函数と,その局所符号数への応用)
久野 雄介 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications to local signatures for fibered 4-manifolds (射影多様体に対するMeyer函数と,その局所符号数への応用)
thesis presentations
11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)
服部 広大 (東京大学大学院数理科学研究科)
On hyperkähler manifolds of type A∞ (A∞型超ケーラー多様体について)
服部 広大 (東京大学大学院数理科学研究科)
On hyperkähler manifolds of type A∞ (A∞型超ケーラー多様体について)
thesis presentations
13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)
篠原 克寿 (東京大学大学院数理科学研究科)
On the index problem for C1-generic wild homoclinic classes (C1通有的に野性的なホモクリニック類の指数問題について)
篠原 克寿 (東京大学大学院数理科学研究科)
On the index problem for C1-generic wild homoclinic classes (C1通有的に野性的なホモクリニック類の指数問題について)
thesis presentations
14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)
佐藤 正寿 (東京大学大学院数理科学研究科)
The abelianization of the level d mapping class group (レベルd写像類群のアーベル化)
佐藤 正寿 (東京大学大学院数理科学研究科)
The abelianization of the level d mapping class group (レベルd写像類群のアーベル化)
thesis presentations
14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)
毛 仕寛 (東京大学大学院数理科学研究科)
Singularities for Solutions to Schrödinger Equations (シュレーディンガー方程式の解の特異性)
毛 仕寛 (東京大学大学院数理科学研究科)
Singularities for Solutions to Schrödinger Equations (シュレーディンガー方程式の解の特異性)
thesis presentations
15:45-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Si, Duc Quang (東京大学大学院数理科学研究科)
Nevanlinna theory for holomorphic mappings and related problems (正則写像のネヴァンリンナ理論と関連する問題)
Si, Duc Quang (東京大学大学院数理科学研究科)
Nevanlinna theory for holomorphic mappings and related problems (正則写像のネヴァンリンナ理論と関連する問題)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
高岡 洋介 (東京大学大学院数理科学研究科)
On existence of models for the logical system MPCL (単相格論理系におけるモデルの存在について)
高岡 洋介 (東京大学大学院数理科学研究科)
On existence of models for the logical system MPCL (単相格論理系におけるモデルの存在について)
thesis presentations
13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)
岩尾 慎介 (東京大学大学院数理科学研究科)
Exact Solutions of Ultradiscrete Integrable Systems (超離散可積分系の厳密解)
岩尾 慎介 (東京大学大学院数理科学研究科)
Exact Solutions of Ultradiscrete Integrable Systems (超離散可積分系の厳密解)
thesis presentations
14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
中田 庸一 (東京大学大学院数理科学研究科)
Vertex operators and background solutions for ultradiscrete soliton equations (超離散ソリトン方程式における頂点作用素と背景解)
中田 庸一 (東京大学大学院数理科学研究科)
Vertex operators and background solutions for ultradiscrete soliton equations (超離散ソリトン方程式における頂点作用素と背景解)
2010/02/02
Lie Groups and Representation Theory
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Fanny Kassel (Orsay)
Deformation of compact quotients of homogeneous spaces
Fanny Kassel (Orsay)
Deformation of compact quotients of homogeneous spaces
[ Abstract ]
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Fanny Kassel (Univ. Paris-Sud, Orsay)
Deformation of compact quotients of homogeneous spaces
Fanny Kassel (Univ. Paris-Sud, Orsay)
Deformation of compact quotients of homogeneous spaces
[ Abstract ]
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of
SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting
properly discontinuously.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of
SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting
properly discontinuously.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel
2010/02/01
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
大沢健夫 (名古屋大学多元数理科学研究科)
Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds
大沢健夫 (名古屋大学多元数理科学研究科)
Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
大川 新之介 (東大数理)
Extensions of two Chow stability criteria to positive characteristics
大川 新之介 (東大数理)
Extensions of two Chow stability criteria to positive characteristics
[ Abstract ]
I will talk about two results on Chow (semi-)stability of cycles in positive characteristics, which were originally known in characteristic 0. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of the log canonical threshold of Chow divisor. A couple of examples will be discussed in detail.
I will talk about two results on Chow (semi-)stability of cycles in positive characteristics, which were originally known in characteristic 0. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of the log canonical threshold of Chow divisor. A couple of examples will be discussed in detail.
Kavli IPMU Komaba Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Timur Sadykov (Siberian Federal University)
Bases in the solution space of the Mellin system
Timur Sadykov (Siberian Federal University)
Bases in the solution space of the Mellin system
[ Abstract ]
I will present a joint work with Alicia Dickenstein.
We consider algebraic functions $z$ satisfying equations of the
form
\\begin{equation}
a_0 z^m + a_1z^{m_1} + a_2 z^{m_2} + \\ldots + a_n z^{m_n} +
a_{n+1} =0.
\\end{equation}
Here $m > m_1 > \\ldots > m_n>0,$ $m,m_i \\in \\N,$ and
$z=z(a_0,\\ldots,a_{n+1})$ is a function of the complex variables
$a_0, \\ldots, a_{n+1}.$ Solutions to such equations are
classically known to satisfy holonomic systems of linear partial
differential equations with polynomial coefficients. In the talk
I will investigate one of such systems of differential equations which
was introduced by Mellin. We compute the holonomic rank of the
Mellin system as well as the dimension of the space of its
algebraic solutions. Moreover, we construct explicit bases of
solutions in terms of the roots of initial algebraic equation and their
logarithms. We show that the monodromy of the Mellin system is
always reducible and give some factorization results in the
univariate case.
I will present a joint work with Alicia Dickenstein.
We consider algebraic functions $z$ satisfying equations of the
form
\\begin{equation}
a_0 z^m + a_1z^{m_1} + a_2 z^{m_2} + \\ldots + a_n z^{m_n} +
a_{n+1} =0.
\\end{equation}
Here $m > m_1 > \\ldots > m_n>0,$ $m,m_i \\in \\N,$ and
$z=z(a_0,\\ldots,a_{n+1})$ is a function of the complex variables
$a_0, \\ldots, a_{n+1}.$ Solutions to such equations are
classically known to satisfy holonomic systems of linear partial
differential equations with polynomial coefficients. In the talk
I will investigate one of such systems of differential equations which
was introduced by Mellin. We compute the holonomic rank of the
Mellin system as well as the dimension of the space of its
algebraic solutions. Moreover, we construct explicit bases of
solutions in terms of the roots of initial algebraic equation and their
logarithms. We show that the monodromy of the Mellin system is
always reducible and give some factorization results in the
univariate case.
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