Igor Frenkel named the Sol Goldman Family Professor of Mathematics

Igor B. Frenkel, newly named as the Sol Goldman Family Professor of Mathematics, is a leading representation theorist and mathematical physicist.

Frenkel studies finite and infinite dimensional symmetries and their realizations in algebraic, geometric, and analytic structures. This field of mathematics is called representation theory of groups and algebras. His research has also resulted in numerous applications to other areas of mathematics and mathematical physics. In particular, his work was fundamental in the development of two-dimensional quantum field theory, which is a prototype of the theory that describes elementary particles; it also has important applications to string theory.

In a series of research papers and in his book “Vertex Operator Algebras and the Monster,” Frenkel found a realization of the group known as the “Monster Group” as a symmetry of a special two-dimensional quantum field theory. He also discovered a new class of difference equations based on representation theory that play a key role in statistical physics; these results were described in his second book “Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations” and several papers. Frenkel also initiated a program of representation theoretic approach to construction of four-dimensional topological field theories and published a number of results in this direction. These areas of research are now being actively developed by mathematicians and mathematical physicists.

A graduate of St. Petersburg University (Russia), Frenkel earned his Ph.D. in mathematics from Yale in 1980. He began his academic career as a Gibbs Instructor at the university, eventually serving as a full professor and chair of the Department of Mathematics. Frenkel obtained his first tenured position at Rutgers University, and has held visiting faculty positions at the Institute for Advanced Study at Princeton University, the Research Institute for Mathematical Sciences (Berkeley), and the Institut des Hautes Etudes Scientifiques (Paris).

Frenkel is the recipient of fellowships from the Sloan Foundation and the Guggenheim Foundation. He is an elected fellow of the National Academy of Sciences and the American Academy of Arts and Sciences.