Langlands Program, Trace Formulas, and their Geometrization

Details Langlands Program, Trace Formulas, and their Geometrization Langlands Program, Trace Formulas, and their Geometrization

2012-02-09

arxiv.org/abs/1202.2110v1

Mathematics

Representation Theory

Notes for the AMS Colloquium Lectures given by the author at the 2012 Joint Mathematics Meetings in Boston, January 4-6, 2012

Scientific paper

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 Ngo Bao Chau (arXiv:1003.4578 and arXiv:1004.5323) 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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