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


Teaching. Spring 2007

Topics in the Geometric Langlands Program


New Book "Langlands Correspondence for Loop Groups"

has been published by Cambridge University Press in June 2007.


Research Project "Geometric Langlands Program"

I am 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 am co-managing this project together with Kari Vilonen of Northwestern University. This site contains links to our activities, such as the workshops that we have organized, and various resources on the Langlands Program.


Book "Vertex Algebras and Algebraic Curves"

(joint with David Ben-Zvi ) A new edition, substantially improved and expanded, has been published in August of 2004.


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.


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


More papers...


Complete bibliography


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

If you wish to submit a paper to any of these journals, you may do that electronically, by e-mailing me the Postsript file of your paper (in the case of IMRN, you should also e-mail your paper to the editorial office).


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