Hodge–GUE correspondence

The Hodge–GUE correspondence describes 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. In this talk, we describe this correspondence and its proof, and discuss its applications.  The talk is based on a series of joint work with Boris Dubrovin, Si-Qi Liu and Youjin Zhang.