Brandon Levin ( U. of Chicago)
Weight elimination in Serre-type conjectures

Abstract: I will discuss recent results towards the weight part of Serre's conjecture for GL_n as formulated by Herzig. The conjecture predicts the set of weights where an odd n-dimensional mod p Galois representation will appear in cohomology (modular weights) in terms of the restriction of the representation to the decomposition group at p. We show that the set of modular weights is always contained in the predicted set in generic situations. This is joint work with Daniel Le and Bao V. Le Hung.