Speaker: Catherine Cannizzo (Simons Center for Geometry and Physics, Stony Brook University)

Title: Semi-orthogonal decompositions in Fukaya-Seidel mirrors to blowups of abelian varieties

Abstract: Abstract: Homological mirror symmetry (HMS) is an equivalence of categories on pairs of complex and symplectic manifolds: the bounded derived category of coherent sheaves on a complex manifold is equivalent to a symplectic invariant, the Fukaya category, on the mirror symplectic manifold. Three cases where mirrors and HMS have been studied include Calabi-Yau manifolds, Fano manifolds, and those of general type (such as negative first Chern class). In finding a geometric mirror to the genus 2 curve (which is of general type), there are interesting intermediary manifolds with which to check HMS on. We will see an example of this, which makes use of semi-orthogonal decompositions and wrapping in the Fukaya category. This is joint work with S. Venkatesh.