Categorification of Verma modules and q-series invariants of 3-manifolds
Dec. 7, 2026 – Dec. 11, 2026
This workshop, sponsored by AIM and the NSF, 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
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
For more information email workshops@aimath.org