西湖数论研讨班第四期

来源:超级管理员 发布时间:2018-03-07 作者: 阅读数:1451次

地点:理学研究所大楼509.

1.演讲人:上海交通大学李红泽教授

时间:3月24号上午9:00-12:00

Title: The Hasse Principle for quartic hypersurface (I)

AbstractLet X be a quartic hypersurface corresponding to the zero locus of a homogeneous quartic polynomial F in n variables with integral coefficients. The variety X is said to satisfy the Hasse Principle if X contains a rational point provided that it contains an adelic point.

In this talk, we will introduce Marmon and Vishe's recent result for quartic hypersurface, especially the Hasse Principle for smooth projective quartic hypersurface of dimension greater than or equal to 28 defined over Q. In part I, we will focus on the analytic part of that result.

 

2.演讲人:四川大学杨磊研究员

时间:3月24号下午13:30-15:30.

TitleHomogeneous dynamics and their applications to number theory (I)

AbstractIn this short course, we will begin with some basic facts on dynamical systems of Lie group actions on homogeneous spaces. We then will talk about their applications to number theory. We will focus on the proof of Oppenheim's conjecture by Margulis and a result by Eskin, Mozes and Shah on counting integer points on homogeneous varieties. If time permits, we will talk about some problems in Diophantine approximation and how to solve them using homogeneous dynamics. I will make the lectures self contained and accessible to general audience without background in dynamical systems.

 

3.演讲人:上海交通大学李红泽教授

时间: 3月25号上午8:30-11:30.

Title:The Hasse Principle for quartic hypersurface (II)

Abstract:Let F(X) be a form in n variables with integral coefficients. Determining whether F(X)=0 has a non-trivial rational solution is a fundamental question in number theory.

In part I, we give an introduction to Marmon and Vishe's result for quartic forms, especially, the analytic part of that result. In this talk, we will give the complete proof of that result.

 

4. 演讲人:四川大学杨磊研究员

时间:3月25号下午13:00-15:00.

Title:Homogeneous dynamics and their applications to number theory (II) 

摘要同上。

5. 演讲人:四川大学杨磊研究员

时间:3月26号上午9:00-11:00.

Title:Homogeneous dynamics and their applications to number theory (III) 

摘要同上。

 

报名链接:http://www.wias.org.cn/index.php?a=details&type=4