Landau-Ginzburg/Calabi Yau correspondence and the Crepant Transformation Conjecture
I will discuss current work with Y.P. Lee and Mark Shoemaker, in which prove the Landau--Ginzburg/Calabi--Yau correspondence in genus zero for certain hypersurfaces in weighted projective space. The LG/CY correspondence is a relationship between the Gromov-Witten theory of a Calabi--Yau and the Landau-Ginzburg model, given by FJRW theory, for the corresponding potential and group of symmetries. This correspondence is proved via the Crepant Tranformation Conjecture.