Representations of p-adic groups

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 local Langlands program is the construction of all (irreducible, smooth) representations of p-adic groups.

I intend to provide an overview of our understanding of the complex and mod-ℓ representations of p-adic groups and outline recent developments.