污污草莓视频

Title:

听Serre's conjecture on modular forms听

听

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.听Serre's conjecture (now a Theorem due to Khare-Wintenberger and Kisin) has a number of interesting consequences including Fermat's Last Theorem.听 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.听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.