西湖数论研讨班第二期

来源:赵永强 发布时间:2017-12-05 作者: 阅读数:431次

地点:理学研究所大楼509

1.演讲人:复旦大学上海数学中心石荣刚研究员

时间:12月16号上午9:00-12:00

题目:Mixing, equidistribution and lattice points counting on   homogeneous spaces

摘要:We review basic concepts for subgroup actions on homogeneous spaces from the spectral point of view. Among them we emphasize mixing and effective mixing properties on the quotient of semi-simple Lie groups. As an application, we present the work of Eskin-Mcmullen on equidistribution of measures and lattice points counting. If time permits we will introduce some recent progress on effective k-step mixing and effective k-step equidistributions.

2.演讲人:山东大学赵立璐教授

时间:12月16号下午13:30-16:30.

题目:Vinogradov均值定理

摘要:我们将介绍Vinogradov均值定理的基本内容,经典的处理方法以及最新的发展。另外,我们还将介绍该均值定理在数论中的一些应用。

3.演讲人:复旦大学上海数学中心吴晨彦研究员

时间: 12月17号上午8:30-11:30.

题目:Theta correspondence, period integrals and Arthur parameters

摘要:In this talk, we will introduce the (global) theta correspondence and derive some key results. We will define an invariant called the first occurrence associated to theta correspondence and show how it relates to period integrals of  residues of certain Eisenstein series. After giving an overview of Arthur's classification of automorphic representations, we show  that our result can be used to detect the existence of certain simple  factors in the Arthur parameter of cuspidal automorphic  representations.

4. 演讲人:上海大学王玉超博士

时间:12月17号下午13:00-16:00.

题目:Birch's theorem on forms in many variables

摘要:A topic of central importance in number theory regards solutions of Diophantine equations. The Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in every completion of the rational number fields. In this talk, we will introduce a renowned result due to Birch, which establishes the Hasse principle for certain systems of homogeneous equations with a large number of variables compared to the degrees. We will also talk about related problems and improvements. In particular, we will focus our attention on the case that the system only has a single equation.


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