Mod p Langlands for GL2
Abstract
The mod p Langlands program is an attempt to relate mod p Galois representations of a local field to mod p representations of the p-adic points of a reductive group. This is inspired by the classical local Langlands (l-adic coefficients) and it is partially a stepping stone towards the p-adic Langlands (p-adic coefficients). I will explain this for GL2/Qp, where one can explicitly describe both sides, and I will relate it to congruences between modular forms.