This project is concerned with a variety of problems in the area of infinite dimensional Lie algebras. The principal investigator will study infinite-dimensional groups associated to Kac-Moody algebras, representations of the Virasoro algebra, exceptional hierarchies of soliton equations, superintegrable systems, and moduli spaces. The research conducted under this award concerns the topological and algebra-geometric structure of infinite dimensional groups attached to Kac-Moody algebras and their flag varieties. The study of these Kac-Moody algebras have applications throughout mathematics and mathematical physics.
