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Langlands Program, trace formulas, and their geometrization

Author: Edward Frenkel
Journal: Bull. Amer. Math. Soc. 50 (2013), 1-55
MSC (2010): Primary 11R39, 14D24, 22E57
Published electronically: October 12, 2012
MathSciNet review: 2994994
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Abstract: The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey of my recent joint work with Robert Langlands and Ngô Bao Châu on a new approach to proving the Functoriality Conjecture using the trace formulas, and on the geometrization of the trace formulas. In particular, I discuss the connection of the latter to the categorification of the Langlands correspondence.

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Additional Information

Edward Frenkel
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720

Received by editor(s): February 10, 2012
Received by editor(s) in revised form: June 17, 2012
Published electronically: October 12, 2012
Additional Notes: Supported by DARPA under the grant HR0011-09-1-0015
Dedicated: Notes for the AMS Colloquium Lectures at the Joint Mathematics Meetings in Boston, January 4–6, 2012
Article copyright: © Copyright 2012 American Mathematical Society