Edward Frenkel

Biography

Edward Frenkel was born on May 2, 1968, in Kolomna, Russia, which was then part of the Soviet Union. His father is of Jewish descent and his mother is Russian. As a high school student he studied higher mathematics privately with Evgeny Evgenievich Petrov, although his initial interest was in quantum physics rather than mathematics. He was not admitted to Moscow State University because of discrimination against Jews and enrolled instead in the applied mathematics program at the Gubkin University of Oil and Gas. While a student there, he attended the seminar of Israel Gelfand and worked with Boris Feigin and Dmitry Fuchs. After receiving his degree in 1989, he was first invited to Harvard University as a visiting professor, and a year later he enrolled as a graduate student at Harvard. He received his Ph.D. at Harvard University in 1991, after one year of study, under the direction of Boris Feigin and Joseph Bernstein. He was a Junior Fellow at the Harvard Society of Fellows from 1991 to 1994, and served as an associate professor at Harvard from 1994 to 1997. He has been a professor of mathematics at University of California, Berkeley since 1997.

Mathematical work

Jointly with Boris Feigin, Frenkel constructed the free field realizations of affine Kac–Moody algebras (these are also known as Wakimoto modules), defined the quantum Drinfeld-Sokolov reduction, and described the center of the universal enveloping algebra of an affine Kac–Moody algebra. The last result, often referred to as Feigin–Frenkel isomorphism, has been used by Alexander Beilinson and Vladimir Drinfeld in their work on the geometric Langlands correspondence. Together with Nicolai Reshetikhin, Frenkel introduced deformations of W-algebras and q-characters of representations of quantum affine algebras.

Frenkel's recent work has focused on the Langlands program and its connections to representation theory, integrable systems, geometry, and physics. Together with Dennis Gaitsgory and Kari Vilonen, he has proved the geometric Langlands conjecture for GL(n). His joint work with Robert Langlands and Ngô Bảo Châu suggested a new approach to the functoriality of automorphic representations and trace formulas. He has also been investigating (in particular, in a joint work with Edward Witten) connections between the geometric Langlands correspondence and dualities in quantum field theory.

Awards

Frenkel was the first recipient of the Hermann Weyl Prize in 2002. Among his other awards are Packard Fellowship in Science and Engineering and Chaire d'Excellence from Fondation Sciences mathématiques de Paris.

In 2013 he became a fellow of the American Mathematical Society, for "contributions to representation theory, conformal field theory, affine Lie algebras, and quantum field theory".

In 2014 Frenkel was elected to the American Academy of Arts and Sciences.

Filmmaking

Frenkel has co-produced, co-directed (with Reine Graves) and played the lead in a short film Rites of Love and Math, a homage to the film Rite of Love and Death (also known as Yûkoku) by the Japanese writer Yukio Mishima. The film premiered in Paris in April, 2010 and was in the official competition of the Sitges International Film Festival in October, 2010. The screening of Rites of Love and Math in Berkeley on December 1, 2010 caused some controversy.

He has also written (with Thomas Farber) a screenplay The Two-Body Problem.

He has appeared on the Numberphile YouTube series, created by Brady Haran.

Love and Math

Frenkel's book Love and Math: The Heart of Hidden Reality was published in October 2013. It was a New York Times bestseller was named one of the Best Books of 2013 by Amazon and iBooks, and was the 2015 winner of the Euler Book Prize. As of February 2016, it has been published in 16 languages.

In a review published in The New York Review of Books, Jim Holt called Love and Math a "winsome new memoir" which is "three things: a Platonic love letter to mathematics; an attempt to give the layman some idea of its most magnificent drama-in-progress; and an autobiographical account, by turns inspiring and droll, of how the author himself came to be a leading player in that drama.”

The New York Times review called the book "powerful, passionate and inspiring."

Keith Devlin wrote in The Huffington Post: “With every page, I found my mind's eye conjuring up a fictional image of the book's author, writing by candlelight in the depths of the Siberian winter like Omar Sharif's Doctor Zhivago in the David Lean movie adaptation of Pasternak's famous novel. Love and Math is Edward Frenkel's Lara poems... As is true for all the great Russian novels, you will find in Frenkel's tale that one person's individual story of love and overcoming adversity provides both a penetrating lens on society and a revealing mirror into the human mind.”

Peter Woit, author of Not Even Wrong, wrote in a Sept 2013 blog post:

Edward Frenkel's new book Love and Math is now out.The Love of the title is much more about love of mathematics than love of another person, as Frenkel provides a detailed story of what it is like to fall in love with mathematics, then pursue this deeply, ending up doing mathematics at the highest level. Along the way, there are lots of different things going on in the book, all of them quite interesting.A large part of the book is basically a memoir, recounting Frenkel's eventful career, which began in a small city in the former Soviet Union. He explains how he fell in love with mathematics, his struggles with the grotesque anti-Semitism of the Soviet system of that time, his experiences with Gelfand and others, and how he came to the US and ended up beginning a successful academic career in the West at Harvard.Perhaps the most remarkable part of the book though is the way it makes a serious attempt to tackle the problem of explaining the Langlands program. To anyone who wants to learn more about this subject, the best advice for how to proceed is to read the overview in Love & Math and then try reading some of his more technical surveys, such as the ones cited here, here, and here...

Select publications

E. Frenkel: Langlands Correspondence for Loop Groups, Cambridge Studies in Advanced Mathematics 103, Cambridge University Press 2007, ISBN 978-0-521-85443-6.

E. Frenkel and D. Ben-Zvi: Vertex Algebras and Algebraic Curves, Mathematical Surveys and Monographs 88, Second Edition, American Mathematical Society 2004, ISBN 0-8218-3674-9.

E. Frenkel, D. Gaitsgory and K. Vilonen: On the geometric Langlands conjecture, 2000.

E. Frenkel: Recent Advances in the Langlands Program, 2003.

E. Frenkel: Lectures on the Langlands Program and Conformal Field Theory, Les Houches 2005.

E. Frenkel and E. Witten: Geometric Endoscopy and Mirror Symmetry, 2007.

E. Frenkel: Gauge Theory and Langlands Duality, Séminaire Bourbaki 2009.

E. Frenkel, R. Langlands and B.C. Ngô: Formule des Traces et Fonctorialité: le Début d'un Programme, 2010.

E. Frenkel and B.C. Ngô: Geometrization of Trace Formulas, 2010.

E. Frenkel: Love and Math, The Heart of Hidden Reality, Basic Books, 2013.