##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Tony Feng

#### UC Berkeley

## Mirror symmetry and the Breuil-Mezard Conjecture

##### Abstract:

Mirror symmetry and the Breuil-Mezard Conjecture Abstract: 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.

### November 16, 2023

### 2:00 PM

APM 6402 and Zoom; see https://www.math.ucsd.edu/~nts

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