Student Number Theory:Shalika germs

A basic object of study in the invariant harmonic analysis on a reductive p-adic group are the orbital integrals associated to the regular semisimple elements in its Lie algebra. There are many such orbital integrals, however the study of these infinitely many integrals can be in a sense reduced to studying a finite amount of data: the finite collection of nilpotent orbital integrals and their associated Shalika germs. We explain how this works and if time permits we give some applications of the theory.