Yongbin Ruan

Almost twenty years ago, the celebrated theorem of Witten-Kontsevich asserted that the intersection theory of Deligne-Mumford space is governed by KdV-hierarchies. Around the same time, Witten proposed a sweeping generalization which leads to the...

Traditionally, we use mirror symmetry to map a difficult problem (A-model) to an easier problem (B-model). Recently, there is a great deal of activities in mathematics to understand the modularity properties of Gromov-Witten theory, a phenomenon...

In early 90's, there are two mathematical theories motivated by physics, Verlinde theory counting the number of generalized theta function on a curve and quantum cohomology counting the number of holomorphic maps. Early explicit computation shows...