题 目 二:Exponential sums, differential equations and geometric Langlands Correspondence
摘 要 二: In 1970's, Dwork established a relationship between the Bessel differential equation and the Kloosterman sums. Such a relationship can be regarded as an instance of the geometric Langlands correspondence for GL_2. In this talk, I will first review some classical results on exponential sums and differential equations, and then discuss some recent progress on generalizations of Dwork's result from the perspective of geometric Langlands correspondence.