Yongbin Ruan

A quantum cohomology theory of singularity

By solving the moduli problem of Witten equation (topic of another talk in IAS), we construct a quantum cohomology theory of singularity. This theory is computationally friendly and is conjectured to have many beautiful properties. We will first present a solution to Witten's conjectures in ADE-case. Then, we will discuss mirror symmetry and its role as a phase of Calabi-Yau geometry.