Joint IAS/Princeton University Symplectic Geometry Seminar

The Gross-Siebert program suggests that mirror symmetry is mediated by the combinatorial data of a dual pair of integral affine manifolds with singularities and polyhedral decomposition. Much is now understood about the passage from the combinatorial data to complex spaces "near the large complex structure limit" - a toric degeneration and its smoothing. In this talk, we discuss the mirror procedure for moving from the combinatorial data to symplectic spaces "near the large volume limit" - a Weinstein symplectic manifold and its compactification -- and we will explain a proof of homological mirror symmetry between the complex and symplectic manifold associated to local pieces of the combinatorial data. This is part of a program with Vivek Shende to prove homological mirror symmetry over a global SYZ base.