Pure Mathematics colloquium

Florian Herzig, University of Toronto

"Mod p representations of p-adic groups"

Over the complex field, the local Langlands correspondence
provides a precise relationship between irreducible representations of $GL_n(\mathbb{Q}_p)$ and n-dimensional Galois representations. It is expected that there is an analogous such correspondence over the algebraic closure of $\mathbb{F}_p$. However, so far this is only known when n equals 1 or 2. Motivated by this problem, we describe a classification for irreducible representations of $GL_n(\mathbb{Q}_p)$ over the algebraic closure of $\mathbb{F}_p$. If time permits we will comment on how this result extends to other p-adic groups.