Local compactified Jacobians, orbital integrals and uniform bounds


Cheng-Chiang Tsai ( Stanford University, USA )
2016-12-30  13:30 - 14:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

Orbital integrals integrate test functions over conjugacy orbits of p-adic reductive groups. They appear in the Arthur-Selberg trace formula, which is fundamental to the study of automorphic representations. In this talk, we explain some modern aspects of orbital integrals by demonstrating the $GL_n$ case for which we deal with lattice countings and local compactified Jacobians. After that we discuss their asymptotic properties and present a result about uniform bounds on orbital integrals as an application.