BKMP remodeling conjecture and its applications

Mirror symmetry predicts Gromov-Witten theory for a Calabi-Yau manifold from the B-model of its mirror. The BKMP (Bouchard-Klemm-Marino-Pasquetti) remodeling conjecture is a mirror symmetry statement predicting all genus open-closed Gromov-Witten theory for a toric CY 3-orbifold from the topological recursion on its mirror curve. Nice features of the topological recursion as B-model give many desired properties of GW invariants, which are usually difficult to prove by other means. I will sketch a proof of BKMP conjecture and a construction of the global mirror curve over the Kahler moduli. Then I will discuss the implications of the BKMP conjecture, including the crepant resolution conjecture and the modularity of GW invariants.