Homological mirror symmetry for local Calabi-Yau manifolds via SYZ

Abstract

This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of papers of the author and his collaborators Daniel Pomerleano and Kazushi Ueda where we show how Strominger-Yau-Zaslow (SYZ) transforms can be applied to understand the geometry of Kontsevich's homological mirror symmetry (HMS) conjecture for certain local Calabi-Yau manifolds.Comment: 19 pages, 10 figures; v2: minor revision, references added; to appear in a special issue of TJM for the proceedings of "Algebraic Geometry in East Asia 2016