KP integrability of Topological Recursion

Topological recursion is a powerful tool in mathematical physics with pplications to various problems in enumerative geometry, including intersection theory on moduli spaces and Hurwitz numbers. In this talk, I will discuss the KP integrability of topological recursion, which arises naturally in the context of the x-y swap relation. I will explain how this KP integrability can be described via certain integral transforms, leading to Kontsevich-type matrix models.