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Recent advances in the Langlands Program

Author: Edward Frenkel
Translated by:
Journal: Bull. Amer. Math. Soc. 41 (2004), 151-184
MSC (2000): Primary 11R39, 14D20
Published electronically: January 8, 2004
MathSciNet review: 2043750
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Abstract: These are the notes for the lecture given by the author at the ``Mathematical Current Events" Special Session of the AMS meeting in Baltimore on January 17, 2003. Topics reviewed include the Langlands correspondence for $GL(n)$ in the function field case and its proof by V. Drinfeld and L. Lafforgue; the geometric Langlands correspondence for $GL(n)$ and its proof by D. Gaitsgory, K. Vilonen and the author; and the work of A. Beilinson and V. Drinfeld on the quantization of the Hitchin system and the Langlands correspondence for an arbitrary semisimple algebraic group.

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Additional Information

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

Received by editor(s): May 1, 2003
Received by editor(s) in revised form: September 22, 2003
Published electronically: January 8, 2004
Additional Notes: Partially supported by grants from the Packard Foundation and the NSF
Notes for the lecture at the “Mathematical Current Events” Special Session at the AMS meeting in Baltimore, January 17, 2003
Article copyright: © Copyright 2004 By the author