Representations of p-adic groups

Abstract:

The Langlands program is a far-reaching collection of conjectures that relate different areas of mathematics including number theory and representation theory. A fundamental problem on the representation theory side of the Langlands program is the construction of all (irreducible, smooth, complex) representations of p-adic groups. In my talk I will introduce p-adic groups and provide an overview of our understanding of their representations, with a focus on recent developments. I will also briefly discuss applications to other areas.