|| Photo by Elizabeth Lippman |
Math 110. Linear Algebra
Math 113. Abstract Algebra
Under the Command of Algorithms my interview with the Brazilian weekly VEJA (English translation is at the end)
My New York Times bestselling book Love and Mathhas won the 2015 Euler Book Prize from the Mathematical Association of America
My tribute to Alexander Grothendieck in The New York Times
Is the Universe a Simulation? my Op-Ed in The New York Times (it was No. 1 "most viewed")
How our 1,000-year-old math curriculum cheats America's kids my Op-Ed in The Los Angeles Times
Math: Your Secret Weapon Against Wall Street and the NSA interview in Mother Jones
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
order e-book on Amazon (for Kindle), on Apple's iBooks (for iPad and iPhone), or on Google Books;
The Perils of Hacking Math in Slate
Don't Let Economists and Politicians Hack Your Math in Slate
A Day in the Life of a Mathematician in the Argentinian bilingual magazine Labor
Prime numbers, Internet security, and Pierre Fermat who was such a tease in Slate
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 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.
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)