# Joint IAS/Princeton Arithmetic Geometry Seminar

## Mirror Symmetry and the Breuil-Mezard Conjecture

The Breuil-Mezard Conjecture predicts the existence of hypothetical "Breuil-Mezard cycles" that should govern congruences between mod p automorphic forms on a reductive group G. Most of the progress thus far has been concentrated on the case G = GL_2, which has several special features. I will talk about joint work with Bao Le Hung on a new approach to the Breuil-Mezard Conjecture, which applies for arbitrary groups (and in particular, in arbitrary rank). It is based on the intuition that the Breuil-Mezard conjecture is analogous to homological mirror symmetry.

### Date & Time

December 04, 2023 | 4:30pm – 5:30pm

### Location

Simonyi Hall 101 and Remote Access### Speakers

Tony Feng, UC Berkeley