Complex Representations of GL(2,F_q)

In these talks I will give a classification of the irreducible representations of GL(2, F_q) using techniques that generalize to both higher n and to p-adic fields (in particular, this means I will not be using any character theory). Such techniques are of particular interest to number theorists as some of these representations have applications to automorphic forms and Eisenstein series. Additionally, I will mention where Hecke algebras (both finite and affine) come into the picture in the p-adic case, and where various special functions come in as well.