Edward Vladimirovich Frenkel (Russian: Эдуáрд Влади́мирович Фре́нкель; born May 2, 1968) is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at the University of California, Berkeley.

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 and instead enrolled 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.

In 1989, upon receiving his undergraduate degree, he was invited to Harvard University and spent a year there as a visiting scholar. In 1990, he enrolled as a graduate student at Harvard. He received his Ph.D. from Harvard University in 1991 after one year of study under the direction of Boris Feigin and Joseph Bernstein.

Frenkel 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.

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, sometimes called the Feigin–Frenkel center. 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.

Together with Pavel Etingof and David Kazhdan, Frenkel introduced the analytic Langlands correspondence, a novel function-theoretic framework for the Langlands Program in the case of Riemann surfaces.

Frenkel was the first recipient of the Hermann Weyl Prize in 2002. Among his other awards are Packard Fellowship for Science and Engineering (1995) and Chaire d'Excellence from Fondation Sciences Mathématiques de Paris [fr].