Speaker: Boris Bychkov (UHaifa, HSE)

Title: KP integrability in topological recursion

Date and time:  26.02.2025, 17:00 (GMT +03:00)

Abstract:  Topological recursion of Chekhov-Eynard-Orantin is a remarkable universal recursive procedure that has been found in many enumerative geometry problems, from combinatorics of maps, to random matrices, Gromov-Witten invariants, Hurwitz numbers, Mirzakhani's hyperbolic volumes of moduli spaces, knot polynomials. A recursion needs an initial data: a spectral curve, and the recursion defines the sequence of invariants of that spectral curve. 

Kadomtsev--Petviashvili hierarchy is an integrable hierarchy of nonlinear PDEs. Except for many important properties, it quite often appears in the applications: a lot of functions from combinatorics, mathematical physics, theory of moduli spaces and Gromov-Witten theory are solutions to the KP hierarchy.

In the talk I will define the KP integrability property for the topological recursion invariants and show that TR invariants are KP integrable if and only if the corresponding spectral curve is rational. If time permits I will discuss the construction of the KP tau function on the TR spectral curve of any genus which can be seen as a non-perturbative generalization of the Krichever's construction of the KP tau function on any elliptic curve.

The talk is based on the series of joint works with A. Alexandrov, P. Dunin-Barkowski, M. Kazarian and S. Shadrin ( https://arxiv.org/abs/2309.12176,  https://arxiv.org/abs/2406.07391,  https://arxiv.org/abs/2412.18592).

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com