QM Research Seminar: Toward a generalization of the Witten conjecture from spectral curve

Speaker: Ce Ji (Peking University)


Abstract:

Over decades of development of the Witten conjecture, many enumerative geometries are related to integrable hierarchies. On the other hand, many of such theories also admit mirror symmetry in the sense of the remodeling conjecture with an underlying object called the spectral curve. In this talk, we propose a generalization of the Witten conjecture from spectral curve, which produce descendent potential functions related to certain reductions of (multi-component) KP integrable hierarchy. Proof for genus zero spectral curve with one boundary will be sketched, which can be applied to deduce the rKdV integrability of deformed negative r-spin theory, conjectured by Chidambaram--Garcia-Falide--Giacchetto. This talk is based on the joint work with Shuai Guo and Qingsheng Zhang.