中科院数学与系统科学研究院

数学研究所

数论研讨班

报告人：迟敬人 博士  (University of Maryland)

题  目：Global approach to p-adic orbital integrals

时  间：2020.12.18（星期五）, 08:30-09:30

地  点：数学院南楼N204

Zoom会议：671 5040 2177  密码：918174

摘 要：We discuss some problems in local p-adic harmonic analysis arising in trace formulas and arithmetic geometry of Shimura varieties. These include estimates of p-adic orbital integrals of spherical Hecke functions and character identities of test functions arising in bad reduction of Shimura varieties. Although the problems are purely local, we approach them by geometric and global methods. For spherical Hecke functions, we survey the method using the geometry of certain generalized affine Springer fibers, whose dimension and number of irreducible components control the asymptotic estimates of the corresponding orbital integrals. In the function field setting these varieties have natural global deformations which provides a powerful tool to obtain local geometric information. For test functions of Shimura varieties, we will mention ongoing joint work with Thomas Haines where we apply recent advances in classification of automorphic representations to prove local orbital integral and character identities.