Igor Borisovich Frenkel (; born 22 April 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. He is also a Fellow of the American Academy of Arts and Sciences.
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