Representation theory is the study of vector spaces with prescribed symmetries. Replacing vector spaces by more complicated structures (of categorical, topological or geometrical origin) leads to new directions in algebra. This sheds a new light on geometric representation theory. More general moduli spaces constructions and enumerative invariants should fit in that framework. An additional motivation is the construction of invariants of low-dimensional manifolds from quantum field theories.

Raphaël Rouquier is currently professor at UCLA. He was previously Directeur de Recherche at CNRS in France and Waynflete professor at Oxford University. Professor Rouquier has initiated a new field in mathematics “higher representation theory”. He constructed novel categories of geometric and representation-theoretic interest and applied these to problems in the theory of finite groups, Lie theory, algebraic geometry and mathematical physics. He was invited speaker at the ICM in Madrid in 2006 and winner of several distinguished prizes.