Event

Brandon Levin, University of Chicago

Wednesday, January 18, 2017 16:00to17:00
Burnside Hall BURN 1205, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA

Title:

 Serre's conjecture on modular forms 

 

Abstract:

The Langlands program is a far-reaching set of conjectural connections between analytic objects (e.g., modular forms) and arithmetic objects (e.g., elliptic curves). In 1987, Serre made a bold conjecture about modular forms in the spirit of a characteristic p Langlands program. Serre's conjecture (now a Theorem due to Khare-Wintenberger and Kisin) has a number of interesting consequences including Fermat's Last Theorem.  This talk will begin with overview of Serre's original conjecture (the two dimensional case). There are now a number of generalizations of this conjecture to higher dimensions. After introducing these higher dimensional analogues, I will describe recent progress towards the weight part of these conjectures. This is joint work with Daniel Le and Bao V. Le Hung.

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