This week Yale is hosting a conference on Perspectives in Representation Theory, in honor of Igor Frenkel’s 60th birthday. I’m planning to take the train up there and attend some of the talks tomorrow and Wednesday. Frenkel has been a pioneer in the field of representation theory, especially in the area of infinite-dimensional algebras whose representations are significant for understanding low-dimensional QFT, string theory and topological QFT. He started his career in the early 1980s, with many important results relevant to understanding affine Lie algebras. These became central in the explosion of interest among physicists in 2d conformal QFTs after 1984 due to their importance in string theory. Frenkel’s later work has covered a wide variety of topics, with one theme that of trying to understand higher-dimensional generalizations of affine Lie algebras and their potential application to QFTs in higher space-time dimensions than 2. He has also promoted the themes of “categorification” and geometric incarnation of representations that are now central to much research in this area.
Pavel Etingof and other students and collaborators of Frenkel have put together a wonderful document, On the work of Igor Frenkel, which gives much more detail about the many topics of his mathematical research.
Update: Videos of the talks are now available here.