Harmonic analysis on reductive p-adic groups

Over the last decade many old and seemingly unapproachable problems in p-adic representation theory have fallen. In this talk, I will (eventually) discuss some problems in the area that have been recently solved via Bruhat-Tits theory. This gorgeous theory was (re)introduced to the subject through the fundamental work of Allen Moy and Gopal Prasad in the mid 1990s. We shall attempt to dispel the notion that this is not good colloquium material by using Michigan's "time-tested algorithm" for giving a colloquium talk. (seehttp://www.math.lsa.umich.edu/seminars/colloq/visitor.html)