Igor B. Frenkel

Biosketch

Igor Frenkel is a mathematician recognized for his work in representation theory and mathematical physics. He is known particularly for his work on representation theory of loop algebras, their quantizations, vertex operator algebras and categorification program. Frenkel was born in St. Petersburg, Russia, and graduated from St. Petersburg State University with Honors Diploma in mathematics. He emigrated to the United States several years later and obtained a Ph. D. degree in mathematics from Yale University in 1980. After assuming postdoctoral positions at Yale, Mathematical Sciences Research Institute and Institute for Advanced Study, Frenkel obtained his first tenure position at Rutgers University. He returned back to Yale University in 1985, where he worked as a Professor of Mathematics for most of his career serving as the Chairman of the Department in 2015/18. Frenkel is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.

Research Interests

Igor Frenkel is interested in representations of various classes of infinite dimensional algebras and groups, and their relations with models in theoretical physics. His results include constructions of representations of loop algebras, Virasoro algebra, vertex operator algebras and establish their connections to two-dimensional conformal field theory and string theory. Frenkel has also contributed to representation theory of quantum groups, their categorification and applications to four-dimensional topological field theories. Frenkel continues to work on the relation of the moonshine module for the Monster group to three dimensional quantum gravity. He conjectured that this relation must yield a geometric explanation of the mysterious genus zero property of the monster elements. Frenkel is also developing the quaternionic analysis as a potential mathematical foundation of the four dimensional quantum field theory. He has shown how certain Feynman integrals naturally appear in this setting and has conjectured that more general Feynman integrals correspond to key structures of the quaternionic analysis.