Speaker: Kalyani Kansal
Date: December 18, 2025
Affiliation: Imperial College

Abstract: In this talk I will give an introduction to the p-adic Langlands program and its connection with modularity lifting. I will then introduce the Emerton–Gee stack, which parameterizes p-adic Galois representations, and briefly explain the conjectural categorical p-adic Langlands correspondence formulated by Emerton, Gee, and Hellmann. After this general overview, I will focus on two-dimensional representations of a p-adic Galois group with mod p coefficients and describe aspects of the geometry of the corresponding mod p Emerton–Gee stack, with an emphasis on certain scheme-theoretic loci of p-adic Hodge-theoretic interest. Finally, I will sketch how this description of the mod p stack leads to local–global compatibility results that feed into modularity lifting and the p-adic Langlands program.