nLab
geometric Langlands program

Idea

The geometric Langlands program is the analogue of the Langlands program with number fields replaced by function fields. See also geometric Langlands correspondence.

Related concepts

• Hitchin fibration

duality in physics, duality in string theory

• S-duality

  • electro-magnetic duality

  • geometric Langlands correspondence

  • quantum geometric Langlands correspondence

References

• geometric Laglands page
• Alexander Beilinson, Vladimir Drinfeld, Quantization of the Hitchin system and Hecke eigensheaves, draft, pdf
• Gerard Laumon, Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondance de Drinfeld-Langlands, math.AG/0207078
• Ngô Bảo Châu, Le lemme fondamental pour les algebres de Lie, arxiv/0806.4566
• James Arthur, The Work of Ngô Bảo Châu, Proc. ICM Hyderabad 2010, pdf
• lecture notes on an introductory talk by Tony Pantev: Pantev on Langlands I, Pantev on Langlands II
• Edward Frenkel, Langlands correspondence for loop groups, description, pdf
• E. Frenkel, Overview of the links between the Langlands program and 4D super Yang–Mills theory, KITP talk 2010, video page, notes pdf
• E. Frenkel, a Bourbaki exposition, pdf
• E. Frenkel, Langlands duality for representations of quantum groups, arxiv/0809.4453

An exposition of the relation to S-duality and electro-magnetic duality is in

• Edward Frenkel, What Do Fermat’s Last Theorem and Electro-magnetic Duality Have in Common? KITP talk 2011 (web)