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Marie-France Vigneras is a mathematician interested in the Langlands program. Initially proposed by Robert Langlands in 1967, the Langlands program unifies number theory and automorphic representations of groups. The Langlands program has invaded a large part of mathematics and is popping up in physics. The geometric Langlands program is related to electric-magnetic duality in physics. Fermat’s last theorem (proven by Wiles and Taylor) was a part of this program; as a result, many algebraic geometers, number theorists, and group specialists are now working closely together.
In the past four years, following the insights of Breuil relating the Langlands and Fontaine’s theories, research has exploded around the p-adic representations of p-adic groups. At the Radcliffe Institute, Vigneras will work on the yet undeveloped p-adic.