Igor B. Frenkel

For three decades, leader in representation theory and its links to physics. With various co-authors, pioneered representation theory of affine Kac-Moody Lie algebras, including the Fermion-Boson correspondence; creation of vertex operator algebras including remarkable connections with finite sporadic groups, especially the Monster, also the quantum Knizhnik-Zamolodchikov equations. Several of his papers, including the ones with Reshetikhin, with Turaev, and with Crane, have opened substantial new areas of research. In particular, paper with Crane introduced the idea of categorification, which has provided new insights into the relations between physics, affine Lie algebras, and low-dimensional topology.