Edward Frenkel
Professor of Mathematics
- 819 Evans Hall
- Department of Mathematics
- University of California at Berkeley
- Berkeley, CA 94720-3840
- Tel.: (510) 642-6550
- Fax: (510) 642-8204
- Email address: frenkel AT math.berkeley.edu
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Editorial Boards
I am a member of the editorial boards of the following journals:- Inventiones mathematicae
Letters in Mathematical Physics
Bulletin of the American Mathematical Society
International Mathematics Research Notices
My former and current students:
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)
- Inventiones mathematicae
Office:
I am spending 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 on Tuesdays, 2:40-3:40 pm, at 520 Mathematics Hall. Videos of these lectures are available here.
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 "Symmetry and Duality in Mathematics and Physics" (at Institut Henri Poincare, Paris) and "What Do Fermat's Last Theorem and Electro-magnetic Duality Have in Common?" (at KITP, Santa Barbara) in which these topics are reviewed.
And here is a video summary of my Seminaire Bourbaki on this subject.
Here are the notes of my AMS Colloquium Lectures given at the 2012 Joint Mathematics Meetings in Boston, January 4-6, 2012
My interview about the AMS Colloquium Lectures
Film Rites of Love and Math
For more information, visit this Web site.
Screenplay The Two-Body Problem
The second Staged Reading of the theatrical adaptation, directed by Barbara Oliver, was held at the Aurora Theater in Berkeley on November 14, 2011.
The program of the Staged Reading
Article in The Daily Californian
NEW! State-of-the-art fully hyperlinked electronic version of the book Langlands Correspondence for Loop Groups
Teaching. Fall 2011.
Math 53. Multivariable Calculus
Books
Langlands Correspondence for Loop Groups
has been published by Cambridge University Press in June 2007. Fully hyperlinked electronic version of the book is available here.
Vertex Algebras and Algebraic Curves
(joint with David Ben-Zvi ) Second Edition was published by the American Mathematical Society in August of 2004.Research Project "Geometric Langlands Program"
For the last 7 years I have been 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 is funded by DARPA through its "Focus Areas in Theoretical Mathematics" Program. I have been co-managing this project together with Kari Vilonen of Northwestern University. This site contains links to our past activities, such as the workshops that we have organized, and various resources on the Langlands Program.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 (KITP) in Santa Barbara. 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 latest Program "Nonperturbative Effects and Dualities in QFT and Integrable Systems" has run from July 5 to August 26, 2011.
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.
Review Articles
More than the Sum of His Parts -- interview on "Indoor Boys".
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.
My recent papers
Geometrization of Trace FormulasFormule des Traces et Fonctorialite: le Debut d'un Programme
Soliton equations, vertex operators, and simple singularities
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
More papers...
Complete bibliography