Title: Bessel equations, hypergeometric sums and geometric Langlands correspondence
Speaker: Daxin Xu ( Academy of Mathematics and System Science Chinese Academy of Sciences )
Time: Monday,August 8, 2022, 14:00-15:30
Location: 901, Lixue Building
Abstract：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 and Heinloth-Ngô-Yun. 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. I will also talk about my recent joint work with Masoud Kamgarpour and Lingfei Yi on the generalization of the above story to hypergeometric sheaves.
