Brandon Levin
Rice University
Title
Modularity lifting in dimension three
Abstract
I will discuss joint with Robin Bartlett and Bao V. Le Hung on modularity lifting for three-dimensional Galois representations that are potentially crystalline of minimal regular weight at all places above p. I will begin by reviewing the Taylor-Wiles method and the analogous results in dimension two due to Kisin. I will then outline our approach to generalizing Kisin’s resolution of the local crystalline deformation ring in the very ramified setting when dimension is greater than 2.
