My recent essays:
The Perils of Hacking Math in Slate
The Nobel Prize in Physics Is Really a Nobel Prize in Math
in The Atlantic
On the Rosetta stone of mathematics in Scientific
Prime numbers, Internet
security, and Pierre Fermat who was such a tease in Slate
Republicans Should Love 'Common Core'
(with Hung-Hsi Wu)
Op-Ed in The Wall Street Journal
Common Core Standards for Mathematics: The Real Issues
(with Hung-Hsi Wu)
in The Huffington Post
Don't Listen to E.O. Wilson in Slate
Don't Let Economists and Politicians Hack Your Math in
Math is more than the sum of its parts (with Ronald Ross) Op-Ed
in New York Daily News
My review of in Probably Approximately Correct The
New York Times
My review of in Our Mathematical Universe The
New York Times
San Francisco Book Review
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 Quantum Physics.
Here are the videos of my lectures
"An overview of the geometric Langlands Program" (at the Fields
Medal Symposium, Toronto, 2012)
"What Do Fermat's Last Theorem and Electro-magnetic Duality Have in
Common?" (at KITP, Santa Barbara, 2011) in which these topics are
And here is a
video summary of
my Seminaire Bourbaki on this subject.
I spent the Spring semester of 2012 at Columbia University as
the Samuel Eilenberg Visiting Professor, giving a series of lectures
The Langlands Program and Quantum Field Theory.
Videos of these lectures are
Video of the Q&A after the
screening at the Berkeley Film Festival, where the film won a
Grand Festival Award
For more information, visit
this Web site.
A newly revised version has been published
Buy it on Amazon.com
Staged Reading of the theatrical adaptation, directed by Barbara
Oliver, was held at the Aurora Theater in Berkeley on November 14,
Article in The Daily Californian
Cambridge University Press in June 2007. Fully hyperlinked
electronic version of the book is
) Second Edition was published by the American Mathematical
Society in August of 2004.
Research Project "Geometric Langlands Program"
In 2003-2013 I was involved in running a Research Project dedicated to
the investigation of the geometric Langlands Program, its relationship
to other areas of mathematics, and its relationship to physics. It was
funded by DARPA through its "Focus Areas in Theoretical Mathematics"
Program. I was co-managing this project together with Kari Vilonen of
site contains links to some of our past activities, such as the
workshops that we have organized, and various resources on the
As part of this project, I co-organized a
"Gauge Theory and Langlands Duality" and a
"Dualities in Physics and Mathematics" at
the Kavli Institute for
Theoretical Physics (KITP) in Santa Barbara in 2008 and 2009. The
talks are available
The next conference in this series was
"Langlands-Type Dualities in Quantum Field Theory", held at
KITP in August 2010. Here is the
video of my opening lecture. All talks are available here.
The most recent Program at KITP,
"Nonperturbative Effects and Dualities in QFT and Integrable
Systems", ran from July 5 to August 26, 2011.
More than the Sum of His
Parts -- interview on "Indoor Boys".
Article in the Berkeley Science Matters on the Grand Unified
Theory of Mathematics.
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
Text of my lecture on the occasion
of receiving the 2002 Hermann Weyl Prize
at the XXIV
Colloquium on Group Theoretical Methods in Physics .
Seminaire Bourbaki talk on vertex
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.
My recent papers
Baxter's Relations and Spectra of Quantum Integrable Models
Geometric Langlands Correspondence Near Opers
The Langlands Program, Trace Formulas, and their
Geometrization of Trace Formulas
Formule des Traces et Fonctorialite: le Debut d'un Programme
Soliton equations, vertex operators, and simple singularities
Gauge Theory and Langlands Duality
Gromov-Witten Gauge Theory I
Langlands duality for finite-dimensional representations of quantum
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
D-modules on the affine flag variety and representations of affine
Local Geometric Langlands Correspondence: the Spherical Case
Geometric Endoscopy and Mirror Symmetry
I am a member of the editorial boards of the following journals:
Bulletin of the American Mathematical Society
International Mathematics Research
Algebra and Number Theory
Annales mathematiques du Quebec
My Ph.D. students:
Ben-Zvi (Ph.D. 1999)
Peter Pribik (Ph.D. 2004)