CEO Topological recursion and KP integrability

Chekhov-Eynard-Orantin topological recursion (TR)  is a remarkable universal recursive procedure that has been found in many enumerative problems, from combinatorics of maps, to random matrices, Gromov-Witten invariants, Hurwitz numbers, Mirzakhani’s hyperbolic volumes of moduli spaces, knot polynomials. Kadomtsev–Petviashvili (KP) hierarchy represents an infinite system of nonlinear partial differential equations, whose solutions often correspond to enumerative invariants. For instance, Witten's conjecture (proved by Kontsevich) asserts that the generating function for intersection numbers of psi classes on the moduli space of algebraic curves is a solution to the KP hierarchy. I will talk about the recent progress in the understanding of integrability in topological recursion: KP integrability property of the TR differentials for genus zero spectral curves, providing applications from Hurwitz numbers theory and Hodge integrals.

The talk is based on the joint works with Alexander Alexandrov, Petr Dunin-Barkowski, Maxim Kazarian and Sergey Shadrin.