285P Introduction to the Geometric Langlands Program

Spring 2020

This course will discuss the categorical version of the Langlands correspondence for a complex curve.

The lectures will be on zoom at 9am-10:50am on Mondays and Wednesdays.

More details to come. Any question, send me an email.

Prerequisites: Lie Theory, Algebraic Geometry, Homological Algebra.


Geometric Langlands

Notes on Geometric Langlands (Dennis Gaitsgory's webpage with many articles)
Notes from the Chicago Geometric Langlands Seminar
David Ben Zvi's Geometric Langlands webpage
E.Frenkel, Langlands Correspondence for Loop Groups, Cambridge University Press, 2007
E.Frenkel, Lectures on the Langlands Program and Conformal Field Theory, arXiv:hep-th/0512172
E. Frenkel, D. Gaitsgory and K. Vilonen, On the geometric Langlands conjecture, J. Amer. Math. Soc. 15 (2002), 367–417.
G. Laumon, Correspondence de Langlands géométrique pour les corps de fonctions, Duke Math. Jour. 54 (1987), 309–359.
G. Laumon, Transformation de Fourier généralisée, arXiv:alg-geom/9603004
I. Mirkovic and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Ann. of Math. 166 (2007), 95–143.
M. Rothstein. Sheaves with connection on abelian varieties, Duke Math. J., 84(3):565–598, 1996

Langlands over function fields

G.Laumon, La correspondance de Langlands sur les corps de fonctions, Astérisque, tome 276 (2002), Séminaire Bourbaki, exp. no 873, p. 207-265.
B. Stroh, La paramétrisation de Langlands globale sur les corps des fonctions (d'après Vincent Lafforgue), Séminaire Bourbaki, 2015-2016, exp no. 1110.

J.Bernstein and S.Gelbart editors, An Introduction to the Langlands Program, Birkhäuser, 2003.