Speaker: Michael Schein
Title: Weights in Generalizations of Serre's Conjecture
Affiliation: Hebrew University, Jerusalem
Date: Monday, January 28, 2008
Place and Time: Room 101, Love Building, 3:35-4:30 pm

Abstract. Given a prime p and a modular form, one can associate to it a two-dimensional mod p representation of the absolute Galois group of Q. Given such a mod p representation, J.-P. Serre conjectured in the 1970's when it should arise from a modular form in this way, and, if so, what the weights and levels of the associated modular forms are. We will explain these notions and discuss generalizations of the conjecture to totally real fields and to Galois representations of arbitrary dimension, as well as theorems toward these new conjectures.
If time permits, we will discuss the connections between these generalizations of Serre's conjecture and the emerging mod p local Langlands correspondence.