Group, Lie and Number Theory Seminar

A basic question in the spirit of Serre's modularity conjecture is when (or whether) a mod p Galois representation can be lifted to a geometric p-adic representation. Two basic techniques are available: the first comes from applying potential automorphy and automorphy lifting theorems, and gives the most robust results for Galois representations valued in certain classical groups; the second is a purely Galois-theoretic method, originally developed by Ravi Ramakrishna, that applies more readily to general groups. In this talk I will discuss some new techniques in the spirit of Ramakrishna's work. This is joint work with Najmuddin Fakhruddin and Chandrashekhar Khare. Speaker(s): Stefan Patrikis (University of Utah)