Seminar in Algebraic Geometry and Number Theory

Abstract: The local Langlands correspondence (LLC) is a kaleidoscope of conjectures relating local Galois theory, complex Lie theory, and representations of p-adic groups. The LLC is divided into two parts: first, there is the tame or depth-zero part, where much is known and proofs tend to be uniform for all residue characteristics p. Then there is the positive-depth (or wild) part of the correspondence, where there is much that still needs to be explored. I will talk about recent results that build our understanding of this wild part of the LLC via epipelagic representations and their Langlands parameters.