My research focuses on various aspects of Symmetry in Mathematics and Physics. Recently, I have been exploring fascinating links between the Langlands Program and dualities in Physics.
Math 53. Multivariable Calculus
As part of this project, I have co-organized a Mini-Program "Gauge Theory and Langlands Duality" and a Conference "Dualities in Physics and Mathematics" at the Kavli Institute for Theoretical Physics in Santa Barbara. The talks are available online here and here.
Next conference in this series "Langlands-Type Dualities in Quantum Field Theory" will be held at KITP in August, 2010.
Other conferences that I have co-organized recently:
"Langlands Duality and Physics" at the Erwin Schroedinger International Institute for Mathematical Physics, Vienna, January 9-20, 2007.
"The Geometric Langlands Program" at the Lorentz Center, Leiden, July 7-11, 2008.
Article in the Berkeley Science Matters on the Grand Unified Theory of Mathematics.
My Seminaire Bourbaki talk on Gauge Theory and Langlands duality.
Langlands Program and Physics - Lecture Notes on the Langlands duality and Conformal Quantum Field Theory.
Review of the Langlands Program that I wrote for the Bulletin of the American Mathematical Society .
Text of my lecture on the occasion of receiving the 2002 Hermann Weyl Prize at the XXIV Colloquium on Group Theoretical Methods in Physics .
My Seminaire Bourbaki talk on vertex algebras.
Gerard Laumon's talk at Seminaire Bourbaki about my joint work with D. Gaitsgory and K. Vilonen on the proof of the geometric Langlands conjecture.
Gauge Theory and Langlands Duality
Langlands duality for finite-dimensional representations of quantum affine algebras
A rigid irregular connection on the projective line
Any flat bundle on a punctured disc has an oper structure
Gerbal Representations of Double Loop Groups
Langlands duality for representations of quantum groups
Instantons beyond topological theory II
On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level
Opers with irregular singularity and spectra of the shift of argument subalgebra
D-modules on the affine flag variety and representations of affine Kac-Moody algebras
Local Geometric Langlands Correspondence: the Spherical Case
Geometric Endoscopy and Mirror Symmetry
Letters in Mathematical Physics
Bulletin of the American Mathematical Society
International Mathematics Research Notices
David Ben-Zvi (Ph.D. 1999)
Matthew Szczesny (Ph.D. 2002)
Peter Pribik (Ph.D. 2004)
A.J. Tolland (Ph.D. 2009)
Xinwen Zhu (Ph.D. 2009)