I was asked to give a series of talks in an `automorphic representations’ learning seminar at Berkeley. Specifically, I was asked to talk about the local representation theory of and aspects of the global representation theory of .

These are ongoing but I thought I’d post my notes for the first two talks. The first is on the representation theory of and the second is on the representation theory of with a focus on the relationship to modular forms.

These notes are a bit on the ‘basic’ side, leaving most technical details/proofs to the more comprehensive texts. This could be useful for some people who just want to get an overview of the ideas involved.

Anyways, feedback welcome as always!

Representations of GL_2(A_Q^\infty)