Joseph Loubert, Affine cellularity of KLR algebras.

Affine cellular algebras are a nice class of (usually infinite-dimensional) algebras having strong representation-theoretic properties. Given a Lie type \Gamma, there is defined a Khovanov-Lauda-Rouquier algebra whose representations categorify half of the corresponding quantum group. It is suspected that all KLR algebras are affine cellular, and that if \Gamma is of finite type, then the KLR algebra satisfies an additional property which one might call affine quasi-heredity. In this talk I will discuss these objects and explain the current state of knowledge regarding this problem.