Igor Frenkel

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Igor Frenkel
Born (1952-04-22) April 22, 1952 (age 63)
Leningrad, Soviet Union (present-day Russia)
Residence New Haven
Citizenship American
Nationality Russian
Fields Mathematics
Institutions Yale University
Alma mater Saint Petersburg State University (Санкт-Петербургский государственный университет)
Yale University
Doctoral advisor Howard Garland
Doctoral students Pavel Etingof
Mikhail Khovanov
Alexander Kirillov, Jr.

Igor Borisovich Frenkel (born April 22, 1952) is a Russian-American mathematician at Yale University working in representation theory and mathematical physics.

Frenkel emigrated to the United States in 1979. He received his PhD from Yale University in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras". He held positions at the IAS and MSRI, and a tenured professorship at Rutgers University, before taking his current job of tenured professor at Yale University.

Mathematical work[edit]

In collaboration with James Lepowsky and Arne Meurman, he constructed the monster vertex algebra, a vertex algebra which provides a representation of the monster group.[1][2]

Around 1990, as a member of the School of Mathematics at the Institute for Advanced Study, Frenkel worked on the mathematical theory of knots, hoping to develop a theory in which the knot would be seen as a physical object. He continued to develop the idea with his student Mikhail Khovanov, and their collaboration ultimately led to the discovery of Khovanov homology, a refinement of the Jones polynomial, in 2002.[3]

A detailed description of Igor Frenkel's research over the years can be found in "Perspectives in Representation Theory". 


  1. ^ Frenkel, Igor; Lepowsky, James; Meurman, Arne (1988). Vertex operator algebras and the Monster. Pure and Applied Mathematics 134. Boston: Academic Press. ISBN 0-12-267065-5. 
  2. ^ Ogg, Andrew (1991). "Review: Igor Frenkel, James Lepowsky and Arne Meurman,Vertex operator algebras and the Monster". Bull. Amer. Math. Soc. (N.S.) 25 (2): 425–432. doi:10.1090/s0273-0979-1991-16086-6. 
  3. ^ Witten, Edward (Spring 2011), "Knots and Quantum Theory" (PDF), The Institute Letter, retrieved 17 August 2011 

External links[edit]