Number Theory

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

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.
Date: Monday, November 19, 2012
Time: 5:00PM
Where: Lunt 107
Contact Person: Simon Marshall
Contact email: slm@math.northwestern.edu
Contact Phone: 847-467-0715
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