  This is an informal (and mostly conjectural) discussion of some aspects of
Fukaya categories. We start by looking at exact symplectic manifolds which are
obtained from a closed Calabi-Yau by removing a hyperplane section. We look at
the possible geometric significance of Hochschild cohomology in this situation,
and how one can try to get from the Fukaya category of the exact manifold to
that of the closed Calabi-Yau. Also included is a brief discussion of the role
of Lefschetz pencils, and a bit of general deformation theory. To appear in the
Proceedings of the Beijing ICM.
