首师大数论研究组讲座（8月4-5日周四周五暑假报告会）
Zhibin Liang
首都师范大学暑假报告会
时间: 8月4日-5日
地点: 首都师范大学数学科学学院311教室
8月4日上午
主持人: 邱德荣
报告人: Hongyu He(路易斯安娜大学)
题目: 待定
时间: 2011年 8月4日9:30-10:30
报告人: 欧阳毅(中国科技大学)
题目: 待定
时间: 2011年 8月4日10:45-11:45
8月5日上午
主持人: 李克正
报告人: 张磊(Universität Duisburg-Essen Fakultät für Mathematik)
题目: the algebraic fundamental group
摘要： The algebraic fundamental group was first defined in Deligne's beautiful artical "le groupe fondamental de la droite projective moins trois points". It is the tannakian group of the category of vector bundles with integralable connections over a field k of char 0. This category, as a k-linear rigid tensor category, is equivalent (actually equal) to the category of O-coherent D-modules. Thus this defination is natually extend to char p>0. In the lecture I will sketch how I have proved the exactness of the homotopy sequence with respect to a fibration. This is an analogue of the homotopy exact sequence of the topological fundamental group with respect to serre fibration and the homotopy exact sequence of the etale fundamental group which was developped in SGA1 expose X.
时间: 2011年 8月5日9:00-9:45
报告人: Jerome W. Hoffman(路易斯安娜大学)
题目: Algebraic curves of GL(2)-type
摘要: Let F be a number field and G_F is
its absolute Galois group. If V is a two dimensional representation of G_F, it
is a big open problem determine whether V is modular. Huge progress on this has
been made in the case F = Q, with the solution to Serre's conjecture. This talk
is concerned with the explicit construction of such two dimensional representations
coming from motives. Especially we will explain how to construct families of
genus 2 curves whose Jacobian varieties have extra endomorphisms. This is
tied into the classical theory of Humbert
surfaces.
时间: 2011年 8月5日10:00-10:45
报告人: 陈华一(巴黎第七大学)
题目: 赋范向量丛的半稳定性
摘要: 本报告将介绍数域上赋范向量丛的半稳定性以及其与几何不变量理论
的关系
时间: 2011年 8月5日11:00-11:45
8月5日下午
主持人: 梁志斌
报告人: 刘若川(University of Michigan)
题目: 待定
时间: 2011年 8月5日2:00-2:45
报告人: 恽之玮(普林斯顿大学)
题目: Serre's question on exceptional motivic Galois groups
摘要: More than two decades ago, J.P.Serre asked the following question: can exceptional Lie group be realized as the motivic Galois group of some motive over a number field? Concretely, this means whether there are Galois representations of number fields, with Zariski dense image in a given simple Lie group, which "come from geometry". The question has been open for all exceptional groups other than G_2. In this talk, I will give a uniform construction of motives over a number field, which give an affirmative answer to Serre's question for most simple Lie groups, including E_7, E_8, F_4 and G_2.
时间: 2011年 8月5日3:00-3:45
报告人: 许晨阳(University of Utah and Beijing University)
题目: Moduli of higher dimensional varieties
摘要: I will survey the recent progress in the construction of compact moduli spaces, which is an analogue of Deligne-Mumford's construction for curves.
时间: 2011年 8月5日4:00-4:45
报告人: 张超(Universiteit Leiden and Università degli studi di Milano)
题目: 正交型志村簇介绍
摘要: 见附件
时间: 2011年 8月5日5:00-5:45
--
Very best wishes
Zhibin Liang
Building 104 Room 103
Nanhudongyuanyiqu
Wangjing, Chaoyang District
Beijing China,
100102
Zhibin Liang
Zhibin Liang
首都师范大学暑假报告会
时间: 8月4日-5日
地点: 首都师范大学数学科学学院311教室
8月4日 上午
主持人: 杨紫峰
报告人: 张磊(Universität Duisburg-Essen Fakultät für Mathematik)
题目: the algebraic fundamental group
摘要： The algebraic fundamental group was first defined in Deligne's beautiful artical "le groupe fondamental de la droite projective moins trois points". It is the tannakian group of the category of vector bundles with integralable connections over a field k of char 0. This category, as a k-linear rigid tensor category, is equivalent (actually equal) to the category of O-coherent D-modules. Thus this defination is natually extend to char p>0. In the lecture I will sketch how I have proved the exactness of the homotopy sequence with respect to a fibration. This is an analogue of the homotopy exact sequence of the topological fundamental group with respect to serre fibration and the homotopy exact sequence of the etale fundamental group which was developped in SGA1 expose X.
时间: 2011年 8月5日9:45-10:30
报告人: Hongyu He(路易斯安娜大学)
题目: Generalization of Godement's Theorem on Positive Definite Functions
摘要: In his thesis, Godement proved that every continuous square integrable positive definite function on a LCT group has a (convolutional) positive definite square root that is square integrable. He also proved that the inner product between two p.d. square integrable functions is nonnegative. I shall discuss a generalization of Godement's results to matrix-valued positive definite functions. If time allows, I will discuss some applications to theta correspondence.
时间: 2011年 8月4日10:40-11:40
8月5日 上午
主持人: 李克正
报告人: 欧阳毅(中国科技大学)
题目: 待定
时间: 2011年 8月4日8:45-9:45
报告人: Jerome W. Hoffman(路易斯安娜大学)
题目: Algebraic curves of GL(2)-type
摘要: Let F be a number field and G_F is
its absolute Galois group. If V is a two dimensional representation of G_F, it
is a big open problem determine whether V is modular. Huge progress on this has
been made in the case F = Q, with the solution to Serre's conjecture. This talk
is concerned with the explicit construction of such two dimensional representations
coming from motives. Especially we will explain how to construct families of
genus 2 curves whose Jacobian varieties have extra endomorphisms. This is
tied into the classical theory of Humbert
surfaces.
时间: 2011年 8月5日10:00-10:45
报告人: 陈华一(巴黎第七大学)
题目: 赋范向量丛的半稳定性
摘要: 本报告将介绍数域上赋范向量丛的半稳定性以及其与几何不变量理论
的关系
时间: 2011年 8月5日11:00-11:45
8月5日下午
主持人: 梁志斌
报告人: 刘若川(University of Michigan)
题目: Global triangulations of refined families of p-adic Galois representations
摘要: I'll explain the basic theory of trianguline representations and sketch some recent advances on families of trianguline representations.
时间: 2011年 8月5日2:00-2:45
报告人: 恽之玮(麻省理工学院)