9400908 Frenkel This award supports research in algebra and quantum field theory. The principle investigator will study the connections among vertex operator algebras, quantum groups and modular tensor categories. He will also work on the categorification of these algebraic structures, as well as, problems related to their q-deformations. Conformal field theory is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory also has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera, and knot theory, is revealed in the study of conformal field theory.
