Abstract: I will discuss a universal relation sometimes called the x−y swap relation, which plays a prominent role in the theory of topological recursion. In particular, the x−y swap relation is very natural for the KP integrability and can be described by certain integral transforms. As an application, I prove a recent conjecture that relates some particular instances of topological recursion to the Mironov-Morozov-Semenoff matrix integrals and derive explicit formulas for the multipoint functions in some enumerative geometry problems. This talk is based on a joint work with Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, and Sergey Shadrin.

Zoom: https://us06web.zoom.us/j/83257513046    Meeting ID: 832 5751 3046   Passcode: EHCGP2024