Edward Frenkel

Professor of Mathematics

Office:

819 Evans Hall

Department of Mathematics

University of California at Berkeley

Berkeley, CA 94720-3840

Tel.: (510) 643-9216

Fax: (510) 642-8204

Email address: frenkel AT math.berkeley.edu

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My research focuses on various aspects of Symmetry in Mathematics and Physics. Recently, I have been exploring fascinating links between the Langlands Program and various dualities in Physics.

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Books

"Langlands Correspondence for Loop Groups"

has been published by Cambridge University Press in June 2007.

"Vertex Algebras and Algebraic Curves"

(joint with David Ben-Zvi ) Second Edition was published by the American Mathematical Society in August of 2004.

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Research Project "Geometric Langlands Program"

For the last 5 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" at the Kavli Institute for Theoretical Physics in Santa Barbara, July 21-August 8, 2008. The talks are available online.

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.

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Review Articles

Article in the Berkeley Science Matters on the Grand Unified Theory of Mathematics.

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.

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My recent papers

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

Weyl modules and opers without monodromy

Quantization of soliton systems and Langlands duality

Notes on instantons in topological field theory and beyond

Gaudin models with irregular singularities

Ramifications of the geometric Langlands Program

Instantons beyond topological theory I

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More papers...

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Complete bibliography

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Editorial Boards

I am a member of the editorial boards of the following journals:

Inventiones mathematicae

Bulletin of the American Mathematical Society

International Mathematics Research Notices

Algebra and Number Theory

Transformation Groups

Letters in Mathematical Physics

Documenta Mathematica

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My former and current students:

David Ben-Zvi (Ph.D. 1999)

Matthew Szczesny (Ph.D. 2002)

Peter Pribik (Ph.D. 2004)

A.J. Tolland

Xinwen Zhu