来源：超级管理员 发布时间：2018-03-07 作者： 阅读数：527次
Title: The Hasse Principle for quartic hypersurface (I)
Abstract：Let 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.
Title：Homogeneous dynamics and their applications to number theory (I)
Abstract：In 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.
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.
Title：Homogeneous dynamics and their applications to number theory (II)
Title：Homogeneous dynamics and their applications to number theory (III)