EVENT DETAILS AND ABSTRACT

Title: Adequate subgroups
Speaker: Pham Huu Tiep
Speaker Info: University of Arizona
Brief Description:
Special Note:
Abstract:

The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result, as well as related results on bounding the dimension of first cohomology groups for finite simple groups, and on indecomposable modules of small dimension. This is joint work with R. M. Guralnick and F. Herzig.