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Edward Frenkel's UC Berkeley webpage

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Professor of Mathematics

Mailing address:

970 Evans Hall
Department of Mathematics
University of California at Berkeley
Berkeley, CA 94720-3840

Teaching. Spring 2023

Math H53. Honors Multivariable Calculus

Math 261B. Lie Groups and Lie Algebras

2018 Einstein Public Lecture of the American Mathematical Society "Imagination and Knowledge"

Brief Summary of the Einstein Lecture

Elementary Introduction to the Langlands Program

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.

The Reality of Quantum Weirdness Article in The New York Times

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

More Reviews

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

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 "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.

Complete bibliography

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.

Here are the notes of my AMS Colloquium Lectures given at the 2012 Joint Mathematics Meetings in Boston, January 4-6, 2012

Other 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"

In 2003-2013 I was 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 was funded by DARPA through its "Focus Areas in Theoretical Mathematics" Program. I was co-managing this project together with Kari Vilonen of Northwestern University. This site contains links to some of our past activities, such as the workshops that we have organized, and various resources on the Langlands Program.

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.

Survey Articles

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.

My recent papers

Analytic Langlands correspondence for PGL(2) on P^1 with parabolic structures over local fields

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

Complete bibliography

Editorial Boards

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

Bulletin of the American Mathematical Society

International Mathematics Research Notices

Algebra and Number Theory

My Ph.D. 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)

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