Integral structures and HMS for toric varieties

The mirror of a toric variety is a Landau-Ginzburg model. The solution space to the quantum connection is equipped with a natural integral structure. I will describe how this integral strucuture arises from oscillatory integration on Lagrangian cycles in the mirror LG model, and its relation to homological mirror symmetry. As a consequence, we can show the Gamma II conjecture for toric varieties — which says a particular basis in the solution space comes from an exceptional collection.