I will report on aspects of work with Sheridan and Ganatra in which we show how homo- logical mirror symmetry for Calabi-Yau manifolds implies equality of Yukawa couplings on the A- and B-sides. On the A-side, these couplings are generating functions for genus-zero GW invariants. On the B-side, one has a degenerating family of CY manifolds, and the couplings are fiberwise integrals involving a holomorphic volume form. We show that the Fukaya category implicitly "knows" the correct normalization of this volume form, as well as the mirror map.[-]

This partly expository talk focuses on the notion of ”symplectic Landau-Ginzburg models”, i.e. symplectic manifolds equipped with maps to the complex plane, ”stops”, or both, as they naturally arise in the context of mirror symmetry. We describe several viewpoints on these spaces and their Fukaya categories, their monodromy, and the functors relating them to other flavors of Fukaya categories. (This touches on work of Abouzaid, Seidel, Ganatra, Hanlon, Sylvan, Jeffs, and others).[-]