|| Photo by Elizabeth Lippman |
Math 252. Representation Theory
Brief Summary of the Einstein Lecture
This is the first of my four lectures, aimed at the beginners, that were filmed at MSRI, Berkeley in September 2015 by the crew of the Japanese TV channel NHK. These lectures were broadcast in Japan in the "Luminous Classroom" series.
Tribute to Alexander Grothendieck in The New York Times
Is the Universe a Simulation? Op-Ed in The New York Times
How our 1,000-year-old math curriculum cheats America's kids my Op-Ed in The Los Angeles Times
My book Love and Math was a New York Times bestseller and won the 2015 Euler Book Prize from the Mathematical Association of America.
It has been published in 18 languages.
Brilliance Triumphs Over Rejection review of Love and Math in The New York Times
A Mathematical Romance review in The New York Review of Books
Love and Math: A Modern Russian's Lara Poem review in Huffington Post
Read an excerpt from the book, entitled "The Holy Grail of Quantum Physics on Your Kitchen Table" in Scientific American
Another excerpt in The New Criterion (French translation in the magazine Commentaire)
And another one in The New York Times
Here are the videos of my lectures "An overview of the geometric Langlands Program" (at the Fields Medal Symposium, Toronto, 2012) and "What Do Fermat's Last Theorem and Electro-magnetic Duality Have in Common?" (at KITP, Santa Barbara, 2011) in which these topics are reviewed.
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 available here.
As part of this project, I 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 (KITP) in Santa Barbara in 2008 and 2009. The talks are available online here and here.
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.
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 .
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.
Hecke operators and analytic Langlands correspondence for curves over local fields
q-Opers, QQ-Systems, and Bethe Ansatz
An analytic version of the Langlands correspondence for complex curves
Is there an analytic theory of automorphic functions for complex algebraic curves?
Quantum Langlands Duality of Representations of W-algebras
Quantum Langlands dualities of boundary conditions, D-modules, and conformal blocks
Quantum q-Langlands Correspondence
Spectra of Quantum KdV Hamiltonians, Langlands Duality, and Affine Opers
Surface Operators and Separation of Variables
Baxter's Relations and Spectra of Quantum Integrable Models
Geometric Langlands Correspondence Near Opers
The Langlands Program, Trace Formulas, and their Geometrization
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 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
Algebra and Number Theory
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)