A far reaching correspondence from physics suggests that the Gromov-Witten theory of a Calabi-Yau hypersurface of weight projective space (more generally a toric variety) can be computed by the singularity theory of its defining polynomial. In this talk, I will present some of works (jointly with Alessandro Chiodo) towards establishing this correspondence mathematically as well as some of surprises and speculations.\\ Talk time runs to 10:30 AM.