The Z-hat invariant, proposed by Gukov, Pei, Putrov, and Vafa, is a fascinating q-series invariant of three-manifolds related to various areas of mathematics and physics. We want to find a topological quantum field theory (TQFT) that computes this invariant to understand it better. This invariant cannot come from TQFT in the sense of Atiyah, as it depends on an additional structure on the three-manifold, viz. spin-c structures. We need decorated TQFTs, TQFTs that compute invariants that depend on additional structures. In this talk, we’ll discuss decorated TQFTs, cutting and gluing rules in decorated TQFTs, and propose vector spaces assigned to two-dimensional surfaces in the decorated TQFT for Z-hat.

Speaker’s webpage: https://pma.caltech.edu/people/mrunmay-jagadale

Zoom link: https://ncsu.zoom.us/j/91276544366?pwd=dzVRL2pFVytMQlRVMjB6amlERks4QT09