Recent advances in the Langlands Program

By E. Frenkel. 2003

69 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f8562c696b66288a52532fd2f7cced991ec2d4c

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Citations in the corpus

Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case (2006, background): “Indeed, a group one-morphism BGm → BGm by definition corresponds to a tensor functor αS : Pic(S) → Pic(S) defined for every scheme S over W and satisfying some obvisous compatibility conditions (with respect to inverse images).”
Riemann's zeta function and beyond (2003, background): “Using very clever and intricate arguments, Hecke was able to express his L-series in terms of generalized “θ-functions”, and to then derive their analytic continuation, functional equation, and boundedness in vertical strips, a la Riemann.”
Lectures on the Langlands program and conformal field theory (2005, background): “My earlier review articles [28, 29] contain some of the material of the present notes in a more concise form as well as additional topics not covered here.”