Edward Frenkel is a professor of mathematics at the University of California, Berkeley, which he joined in 1997 after being on the faculty at Harvard University. He is a member of the American Academy of Arts and Sciences, a Fellow of the American Mathematical Society, and the winner of the Hermann Weyl Prize in mathematical physics.
In addition to his New York Times bestseller Love and Math, Frenkel has published two other books: Langlands Correspondence for Loop Groups and Vertex Algebras and Algebraic Curves (with David Ben-Zvi). He has also authored 100 scholarly articles in academic journals, and he has lectured on his work around the world.
Frenkel’s research focuses on various aspects of Symmetry in Mathematics and Physics. In a recent series of papers, joint with Pavel Etingof and David Kazhdan, he opened a new chapter of the Langlands Program called the analytic Langlands correspondence (see, for example, this paper). Previously, he has explored links between the Langlands Program and dualities in Quantum Physics (see, for example, this paper). To get a general idea of what the Langlands Program is about, watch Frenkel’s introductory lectures on this subject that were broadcast on the Japanese TV channel NHK in the top video player on the left. Frenkel’s book Love and Math is the first account of the Langlands Program aimed at general audience in a book form.
He has also published a number of surveys aimed at mathematicians. And here’s a set of more technical videos of Frenkel’s Eilenberg Lectures at Columbia University.
Surveys of the Langlands Program:
Seminaire Bourbaki talk on Gauge Theory and Langlands duality.
AMS Colloquium Lectures on the Langlands Program, Trace Formulas, and their Geometrization.
Langlands Program and Physics —Lecture Notes on the Langlands Program and Conformal Quantum Field Theory.
Review of the Langlands Program published in the Bulletin of the American Mathematical Society.
Teaching and Public Lectures:
At UC Berkeley, Frenkel teaches both graduate and undergraduate courses. In the Fall of 2024, he is teaching Abstract Linear Algebra course. For more on his research and teaching, visit his UC Berkeley webpage.
Frenkel has given lectures and made videos for general audience on various mathematical subjects, such as the one about the Riemann Hypothesis on Numberphile YouTube channel in the bottom video player on the left. His most recent Numberphile video is a one-hour pedagogical introduction to the Langlands Program.
Complete bibliography
Selection of recent papers
Extended Baxter relations and QQ-systems for quantum affine algebras (with D. Hernandez)
A general framework for the analytic Langlands correspondence (with P. Etingof and D. Kazhdan)
Weyl group symmetry of q-characters (with D. Hernandez)
Folded quantum integrable systems and deformed W-algebras (with D. Hernandez and N. Reshetikhin)
Analytic Langlands correspondence for PGL(2) on P^1 with parabolic structures over local fields (with P. Etingof and D. Kazhdan)
Hecke operators and analytic Langlands correspondence for curves over local fields (with P. Etingof and D. Kazhdan)
q-Opers, QQ-Systems, and Bethe Ansatz (with P. Koroteev, D. Sage, and Z. Zeitlin)
An analytic version of the Langlands correspondence for complex curves (with P. Etingof and D. Kazhdan)
Is there an analytic theory of automorphic functions for complex algebraic curves?
Quantum Langlands Duality of Representations of W-algebras (with T. Arakawa)
Quantum Langlands Dualities of Boundary Conditions, D-modules, and Conformal Blocks (with D. Gaiotto)
Quantum q-Langlands Correspondence (with M. Aganagic and A. Okounkov)
Spectra of Quantum KdV Hamiltonians, Langlands Duality, and Affine Opers (with D. Hernandez)
Surface Operators and Separation of Variables (with S. Gukov and J. Teschner)
Baxter’s Relations and Spectra of Quantum Integrable Models (with D. Hernandez)
The Langlands Program, Trace Formulas, and their Geometrization (AMS Colloquium Lectures)
Geometrization of Trace Formulas (with B.C. Ngô)
Formule des Traces et Fonctorialité: le Debut d’un Programme (with R. Langlands and B.C. Ngô)
Geometric Endoscopy and Mirror Symmetry (with E. Witten)
