Mathematics

I will give an introduction to Homological Mirror Symmetry. One of the main hurdles in establishing HMS is that the Fukaya category is notoriously hard to compute in general. In the case of exact symplectic manifolds, however, the Fukaya category has good local-to-global properties. This allows us to apply powerful sheaf-theoretic methods to symplectic geometry. I will  explain applications of this point of view to Hori-Vafa mirror symmetry for toric Calabi-Yau threefolds.