Edward Frenkel

Contributor to the Langlands Program and its connections to representation theory, integrable systems, geometry, and quantum physics. Made important contributions such as the construction of the free field realizations of affine Lie algebras, semi-infinite flag manifolds, and the center of affine Kac-Moody algebras at the critical level (also known as the Feigin-Frenkel isomorphism), and quantum Drinfeld-Sokolov reduction. Proved the geometric Langlands conjecture for GL(N) (jointly with Gaitsgory and Vilonen). Broke new ground in the theory of quantum groups by constructing quantum W-algebras and defining q-characters of quantum affine algebras. Formulated the local geometric Langlands correspondence (with Gaitsgory), presented in his influential book Langlands Correspondence for Loop Groups (2007). Jointly with Witten, obtained new results linking dualities in quantum field theory and the Langlands Program. Proposed, with Langlands and Ngô Bao Châu, a new approach to the Langlands functoriality conjecture using trace formulas, and a novel concept of geometrization of the trace formulas.

Author of the New York Times bestselling book Love and Math, the winner of the 2015 Euler Book Prize that has been translated into 18 languages.