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.