Igor Frenkel
Encyclopedia
Igor Borisovich Frenkel is a mathematician at Yale University
working in representation theory
and mathematical physics
.
, USSR (Now St. Petersburg, Russia), Frenkel emigrated to the United States in 1979. He received his Ph.D. from Yale University
in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras." He held positions in IAS
and MSRI, and a tenured professorhip at Rutgers University
, before taking his current job of tenured professor at Yale University
.
and Arne Meurman
, he constructed the monster vertex algebra
, a vertex algebra which provides a representation of the monster group
.
Around the year 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.
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
working in representation theory
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 studiesmodules over these abstract algebraic structures...
and mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
.
Biography
Born in LeningradSaint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
, USSR (Now St. Petersburg, Russia), Frenkel emigrated to the United States in 1979. He received his Ph.D. from Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
in 1980 with a dissertation on the "Orbital Theory for Affine Lie Algebras." He held positions in IAS
IAS
- Accounting, Auditing :*International Accounting Standards*Internal Audit Service - Science :*Institute for Advanced Study**IAS computer, built at the Institute for Advanced Study*Indian Academy of Sciences...
and MSRI, and a tenured professorhip at Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
, before taking his current job of tenured professor at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
.
Mathematical work
In collaboration with James LepowskyJames Lepowsky
James Lepowsky 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 advisor was Bertram Kostant. Lepowsky graduated from Stuyvesant High School in 1961, 16 years after Kostant...
and Arne Meurman
Arne Meurman
Arne Meurman is a Swedish mathematician working on finite groups and vertex operator algebras. Currently he is a professor at Lund University....
, he constructed the monster vertex algebra
Monster vertex algebra
The monster vertex algebra is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R...
, a vertex algebra which provides a representation of the monster group
Monster group
In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...
.
Around the year 1990, as a member of the School of Mathematics at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
, 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
Mikhail Khovanov
Mikhail Khovanov is a professor of mathematics at Columbia University. He earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel. His interests include knot theory and algebraic topology...
, and their collaboration ultimately led to the discovery of Khovanov homology
Khovanov homology
In mathematics, Khovanov homology is an invariant of oriented knots and links that arises as the homology of a chain complex. It may be regarded as a categorification of the Jones polynomial....
, a refinement of the Jones polynomial, in 2002.