Abstract: |
For a Landau-Ginzburg model with the superpotential a quasi-homogenous polynomial singularity, there are two mathematical theories with very difference geometric flavor. The A-model is the FJRW theory of the singularity, which describes the moduli problem of the corresponding Witten equations and its intersection theory; while the B-model is the Saito-Givental theory, where the genus zero part comes from the universal unfolding of the singularity and the theory of primitive forms. I will talk about a mirror theorem between these two Landau-Ginzburg models at all genera, i.e., the FJRW theory of an invertible quasi-homogenous polynomial is equivalent to the Saito-Givental theory of the mirror polynomial. This work is joint with Weiqiang He, Si Li, and Rachel Webb. |