This workshop is sponsored by AIM, NSF, and the Simons Foundation. This activity, which is a part of the New Structures in Low-dimensional topology collaboration, will be devoted to developing an approach to q-series invariants of 3-manifolds and knots via 2-representation theory. Verma modules play a key role in the construction of an analogue for a generic parameter q of the Reshetikhin-Turaev invariants. The workshop will consider the categorification of Verma modules constructed by Naisse-Vaz, their duals and tensor products, as well as braidings and traces. The goal is to apply these constructions to 3-dimensional topology and relate them to known invariants.

Main topics for the workshop are:

• determination of tensor products of 2-Verma modules, braidings and traces
• relation with the Dupont-Naisse construction
• extension to the case of tensor products of 2-Verma modules and their duals
• construction of homological invariants of particular knots and 3-manifolds