Igor Frenkel
| Igor Frenkel | |
|---|---|
| Born |
April 22, 1952 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
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".
References
- ↑ 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.
- ↑ 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.
- ↑ Witten, Edward (Spring 2011), "Knots and Quantum Theory" (PDF), The Institute Letter, retrieved 17 August 2011