Back to Departmental Colloquium: Spring 2017
Departmental Colloquium
Date: Thursday, Jan 26, 2017
Time: 4:00PM
Location: JWB 335
Brandon Levin
University of Chicago
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. |
Number Theory