Citizenship American Role Mathematician Nationality Russian | Name Igor Frenkel | |
 | ||
Alma mater Saint Petersburg State University (Sankt-Peterburgskii gosudarstvennii universitet)Yale University Doctoral students Pavel EtingofMikhail KhovanovAlexander Kirillov, Jr. Residence New Haven, Connecticut, United States Books Vertex Operator Algebras and the Monster, On Axiomatic Approaches to Vertex Operator Algebras and Modules Education Yale University (1980), Saint Petersburg State University Awards Guggenheim Fellowship for Natural Sciences, US & Canada | ||
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
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.
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.
A detailed description of Igor Frenkel's research over the years can be found in "Perspectives in Representation Theory".