Serre Conjectures and p-adic Local Langlands
12-30 June 2017
Our research project is framed in the p-adic local Langlands program, which has the ambition to describe Fontaine’s theory of p-adic local Galois representations in terms of p-adic representations of p-adic groups. The p-adic local correspondence is expected to be realized in suitable spaces of p-adic automorphic forms and we aim at using techniques involving local/global compatibility to prove strong evidence towards the local correspondence. At present very little is known outside the particular case of GL2(Qp) ([Col10]). One of the main leitfaden toward its generalization is the Breuil-Mézard conjecture, a statement which relies the special ber of potentially crystalline deformation rings to weights in Hecke isotypical spaces of algebraic automorphic forms.

Daniel Le (University of Toronto)
Viet Bao Le Hung (University of Chicago)
Brandon Levin (University of Chicago)
Stefano Morra (Université de Montpellier)