Groups arise as sets of symmetries of various structures, perhaps geometric, or physical, or algebraic or analytic. Representation theory deals with how these symmetries give rise to families of operators on a vector space. Associated to groups are Lie algebras, group algebras, and other algebras. The study of representations of these structures arises sometimes from the group setting, and in addition can take a life of its own. This central subject connects with many areas of mathematics, in analysis, geometry, and mathematical physics. Members of our faculty do research on topics in Lie algebras and Lie groups, Kac-Moody algebras, quantum groups, geometric methods in representation theory, Lie combinatorics, and special functions.