Tony Feng, UC Berkeley

Abstract: I will give introduce the Breuil-Mezard Conjecture, which predicts the existence of hypothetical “Breuil-Mezard cycles” in the moduli space of representations of Galois groups of p-adic numbers. I will talk about a new approach to the Breuil-Mezard Conjecture, joint with Bao Le Hung, which is based on the intuition that it is analogous to homological mirror symmetry. In particular, we construct Breuil-Mezard cycles by combining certain instances of homological mirror symmetry with Bezrukavnikov-Mirkovic-Vilonen localization and a bit of the theory of quantum groups. This talk will be aimed at a general audience of algebraists.