| Abstract: |
Recently, Bozec–Calaque–Scherotzke have articulated a noncommutative version of the AKSZ construction, which associates to a smooth Calabi–Yau category a fully extended TQFT valued in a category of iterated Calabi–Yau cospans. In this talk, I will study a class of examples of such theories motivated by conjectures of Costello and Li describing “twists” of Type II strings as topological strings. These TQFTs capture structural features of the BPS physics of D-branes that are in some sense "universal in Chan–Paton factors". Conjecturally, the commutative counterparts of the values of such theories on closed manifolds can sometimes be quantized to yield algebraic structures with Hall-type products. Examples of this paradigm include CoHAs associated to Calabi–Yau 3-folds, CoHAs attached to local systems on 3-manifolds, and the categorified Hall algebras of Porta–Sala. |
