Feb 09 at 17:30 in 507

Title:  Categorical and geometric enumerative invariants

Abstract: To deduce the enumerative predictions of mirror symmetry from homological mirror symmetry, Kontsevich proposed the construction of a Gromov–Witten-like potential associated to suitable categories. This program was carried out in the work of Costello, with an effective redefinition given in the subsequent work of Costello–Caldararu–Tu. In the first part of the talk, I will sketch its construction and present a simple computation in a toy case. In the second part of the talk, I will describe an extension of this potential to a cohomological field theory (CohFT) which has a precise universal property. In the case of the Fukaya category of a symplectic manifold, this universal property can be used to compare the categorical CohFT with the Gromov–Witten CohFT of the ambient manifold, provided a suitable open-closed chain-level lift of the Gromov–Witten theory exists.