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. 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. He has been a professor of mathematics at University of California, Berkeley, since 1997.
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. at Harvard University in 1991, after one year of study, under the direction of Boris Feigin and Joseph Bernstein. 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. While a student there, he attended the seminar of Israel Gelfand and worked with Boris Feigin and Dmitry Fuchs. 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.
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. His father is of Jewish descent and his mother is Russian.
Edward Frenkel was born on May 2, 1968, in Kolomna, Russia, which was then part of the Soviet Union.
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