Princeton Symplectic Geometry Seminar

Abstract: In this talk, I will report our recent work on the construction of Quantum singularity theory by using Witten equation. This theory corresponds to the orbifold Landau-Ginzburg A model. We constructed the virtual cycles for the general quasi-homogeneous polynomial $W$ and proved they satisfy a series of axioms analogous to GW theory for pseudo-holomorphic curves. We also proved the mirror symmetry between the Frobenius structures of LG A model and B model(Saito's singularity theory) for DE case. At last I will report the progress of the hierarchy problems for D E cases and mention the relation to Calabi-Yau