Categorified Quantum Groups

Abstract:

Quantum groups are objects that first arose in mathematical physics, and in subsequent times have found applications in fields as diverse as constructing knot invariants and studying algebraic groups in positive characteristic. The process of categorification is an art which considers objects one step up on the categorical ladder (e.g. numbers --> vector spaces --> additive categories --> ... ) with a view to improving our understanding of their shadows on the lower categorical rung. We will talk about this process of categorification as it pertains to quantum groups.