Speaker: Catherine Cannizzo (Columbia University)

Title: Wrapping Lagrangians in the Fukaya category of a symplectic fibration

Abstract:  The Fukaya category is an algebraic invariant of symplectic manifolds, with objects given by Lagrangian submanifolds and morphisms given by their intersection points. Mirror symmetry involves a pair of manifolds: given a symplectic manifold, what is its complex mirror manifold? We will show how line bundles on a blow-up of a complex manifold along a submanifold, specifically a deformation to the normal cone, is homologically mirror to the wrapping of Lagrangians around a puncture on the symplectic side in the Fukaya category. This is joint work with Sara Venkatesh.