Number Theory Seminar

Orbital integrals are a kind of p-adic integrals with a simple definition: integrating over some conjugacy orbit. It is similar to evaluating characters at conjugacy classes as in basic representation theory of finite groups, and is thus a fundamental object in the representation theory of p-adic groups. It becomes important to number theory due to its substantial use in trace formula for the study of automorphic representations and Langlands program. In this talk, we discuss how ideas in (geometric) representation theory lead to heuristics and results regarding upper bounds of orbital integrals.