Speaker:   Yash Deshmukh (Institute for Avanced Study)

Abstract:  Costello introduced categorical enumerative invariants for a smooth and proper Calabi--Yau category equipped with a splitting of the non-commutative Hodge--de Rham spectral sequence. I will discuss an extension of this to a chain-level CohFT structure on the Hochschild homology of the category. This construction will be universal in a precise sense, and I will explain how to exploit this to compare the categorical CohFT of a Fukaya category with the geometric CohFT of the underlying symplectic manifold whenever a chain-level open-closed Gromov--Witten CohFT satisfying suitable properties exists.