EVENT DETAILS AND ABSTRACT

Title: Adequate subgroups
Speaker: Florian Herzig
Speaker Info: Toronto
Brief Description:
Special Note:
Abstract:

One of the crucial hypotheses in modularity/automorphy lifting theorems is that the residual image of the given n-dimensional p-adic Galois representation be a "sufficiently big" subgroup of GL_n. The largest class of subgroups that is known to work for this purpose is that of "adequate" subgroups (introduced by Jack Thorne). In this talk we first motivate why a bigness assumptions matters for automorphy theorems and then discuss work in progress showing that most subgroups of GL_n that act irreducibly are adequate, provided that n < p. This is joint work with Robert Guralnick and Pham Huu Tiep.