Joint IAS/Princeton University Symplectic Geometry Seminar

A very affine hypersurface is the vanishing locus of a Laurent polynomial in a complex torus; its complement is also a very affine hypersurface, but in two subtly-different ways. The (partially) wrapped Fukaya categories of the hypersurface and its complement are closely related: Auroux sketched the definitions of several new acceleration and restriction functors between them. I'll explain how we can define these functors in terms of Liouville sectors and how this implies conjectures of Auroux about their mirror counterparts, building on work of Gammage-Shende. On the way, I'll explain how the different realizations of the complement lead to very different Fukaya categories, related by a non-geometric equivalence mediated by derived Knorrer periodicity.