Hodge-GUE Correspondence
By Di Yang
Appears in collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data
An explicit relationship between certain cubic Hodge integrals on the Deligne–Mumford moduli space of stable algebraic curves and connected GUE correlators of even valencies, called the Hodge–GUE correspondence, was recently discovered. In this talk, we prove this correspondence by using the Virasoro constraints and by deriving the Dubrovin–Zhang loop equation. The talk is based on a series of joint work with Boris Dubrovin, Si-Qi Liu and Youjin Zhang.
