Cheng-Chiang Chai (IAS)
Old and new methods on orbital integralss

Abstract: Despite their necessary appearance in trace formulas and characters, p-adic orbital integrals are notoriously difficult to compute. In this talk, we sketch methods (of Goresky-Kottwitz-MacPherson, and of myself) feasible for small groups and special cases, while demonstrating general combinatorial and geometrical phenomenon. We will restrict ourselves to the classical conjugacy orbital integral, but briefly comment on the Jacquet-Rallis representation GL(n-1) acting on gl(n) when time permits.