Wednesday, December 6, 2023
12/06/2023 - 10:30am
Abstract: Given a proper CY A-infinity category C, a notion closely related to that of a 2d extended TQFT, I explain how the Loday-Quillen-Tsygan map fits into a commutative diagram of dg-BV algebras. The first two corners are built from the cyclic cohomology of C, respectively from a cyclic L-infinity algebra associated to C. The other two corners are of a more geometric nature, given by chains on the moduli space of Riemann surfaces with corners, free boundaries decorated by objects of C, respectively chains on the moduli space of metric graphs. I indicate how this generalizes an observation by Kontsevich producing cocycles on M_g,n. Further I compare this to the story of closed SFT developed by Costello, Caldararu-Tu, which led to the definition of categorical Gromov-Witten invariants for categories C as above that are also smooth.
12/06/2023 - 4:00pm
I will describe some recent results on the first order rigidity of homeomorphism groups of compact manifolds, and their applications to dynamics of group actions on manifolds. I will also describe how to find “syntactic” invariants of manifolds, and how these can be used to give a conjectural model-theoretic characterization of the genus of a surface.