Speaker: Daxin Xu, California Institute of Technology

Title: Exponential sums, differential equations and geometric Langlands correspondence

Date: 01/09/2020

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

The understanding of various exponential sums plays a central role in the study of number theory. I will first review the relationship between the Kloosterman sums and the classical Bessel differential equation. Recently, there are two generalizations of this story (corresponding to GL_2-case) for arbitrary reductive groups using ideas from the geometric Langlands program, due to Frenkel-Gross, Heinloth-Ngô-Yun. In the end, I will discuss my joint work with Xinwen Zhu where we unify previous two constructions from the p-adic aspect and identify the exponential sums associated to different groups as conjectured by Heinloth-Ngô-Yun.