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 the series of papers [16, 23-25] where the author and his collaborators Daniel Pomerleano and Kazushi Ueda 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.
"Homological Mirror Symmetry for Local Calabi-Yau Manifolds via SYZ." Taiwanese J. Math. 21 (3) 505 - 529, 2017. https://doi.org/10.11650/tjm/7901