Abstract: The deep connection between enumerative geometry and integrable hierarchies has been fascinating since early 1990s. In this talk we address our recent progress on two questions: whether an enumerative geometry theory is related to KP-type hierarchy; how to locate such a theory inside the space of KP/BKP hierarchies. Both answers lead to the structure of an underlying Riemann surface, in the sense of “classical” and “quantum” respectively.  

This talk is based on joint works with Shuai Guo, Chenglang Yang and Qingsheng Zhang.