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Igor Frenkel

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Igor Frenkel
Born (1952-04-22) April 22, 1952 (age 72)
NationalityRussian
CitizenshipAmerican
Alma materSaint Petersburg State University
Yale University
Scientific career
FieldsMathematics
InstitutionsYale University
Doctoral advisorHoward Garland
Doctoral studentsPavel 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. He was elected to the National Academy of Sciences in 2018.[1] He is also a Fellow of the American Academy of Arts and Sciences.[2]

Mathematical work

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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.[3][4]

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.[5]

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

References

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  1. ^ "Six Yale professors elected to National Academy of Sciences". May 2018.
  2. ^ "Six Yale professors elected to National Academy of Sciences". May 2018.
  3. ^ Frenkel, Igor; Lepowsky, James; Meurman, Arne (1988). Vertex operator algebras and the Monster. Pure and Applied Mathematics. Vol. 134. Boston: Academic Press. ISBN 0-12-267065-5.
  4. ^ 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.
  5. ^ Witten, Edward (Spring 2011), "Knots and Quantum Theory" (PDF), The Institute Letter, archived from the original (PDF) on 27 September 2011, retrieved 17 August 2011
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