Igor Frenkel

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Igor Frenkel
Born (1952-04-22) April 22, 1952 (age 65)
Leningrad, Soviet Union (present-day Russia)
Residence New Haven
Nationality Russian
Citizenship American
Alma mater Saint Petersburg State University
Yale University
Scientific career
Fields Mathematics
Institutions Yale University
Doctoral advisor Howard Garland
Doctoral students Pavel Etingof
Mikhail Khovanov
Alexander Kirillov, Jr.

Igor Borisovich Frenkel (Russian: Игорь Борисович Френкель; 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]