Virtual Workshop on Recent Developments in Geometric Representation Theory

Categorification of integrable representations of quantum Kac--Moody algebras is a relatively well-developed subject nowadays, which has found several applications, in particular to low-dimensional topology. The story outside of the integrable world is far less well-known. In the first part of this talk, we'll explain the ideas behind categorification of Verma modules, and how our construction is related to other known structures in higher representation theory. In the second part, we'll discuss how to extend the construction to tensor products involving Verma modules, and some connections with low-dimensional topology.