Igor Borisovich Frenkel (russian: Игорь Борисович Френкель; born April 22, 1952) is a Russian-American mathematician at

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

working in

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

and

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

. Frenkel emigrated to the United States in 1979. He received his PhD from

in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras". He held positions at the

IAS IAS may refer to: Science * Institute for Advanced Study, in Princeton, New Jersey, United States * Image Analysis & Stereology, the official journal of the International Society for Stereology & Image Analysis. * Iowa Archeological Society, Uni ...

and MSRI, and a tenured professorship at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

, before taking his current job of tenured professor at

. He was elected to the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

in 2018. He is also a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

Mathematical work

In collaboration with

James Lepowsky James "Jim" Lepowsky (born July 5, 1944, in New York City) is a professor of mathematics at Rutgers University, New Jersey. Previously he taught at Yale University. He received his Ph.D. from M.I.T. in 1970 where his advisors were Bertram Kostant ...

and

Arne Meurman Arne Meurman (born 6 April 1956) is a Swedish mathematician working on finite groups and vertex operator algebras. Currently, he is a professor at Lund University. He is best known for constructing the monster vertex algebra The monster vertex a ...

, he constructed the

monster vertex algebra The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applyi ...

, 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 The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, Frenkel worked on the mathematical

theory of knots In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

, 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 Mikhail Khovanov (russian: Михаил Гелиевич Хованов; born 1972) is a Russian-American professor of mathematics at Columbia University who works on representation theory, knot theory, and algebraic topology. He is known for int ...

, and their collaboration ultimately led to the discovery of

Khovanov homology In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov, then at ...

, a refinement of the Jones polynomial, in 2002. A detailed description of Igor Frenkel's research over the years can be found in

References

External links

Home page
* 1952 births Living people 20th-century American mathematicians Rutgers University faculty Yale University faculty Mathematicians from Saint Petersburg Fellows of the American Academy of Arts and Sciences Members of the United States National Academy of Sciences {{US-mathematician-stub