Resumen de KP integrability through the swap relation

Alexander Alexandrov, V. D. Bychkov, P. Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin

• We discuss a universal relation that we call the x − y swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the x −y swap relation and KP integrability. As an application, we prove a recent conjecture that relates some particular instances of topological recursion to the Mironov–Morozov– Semenoff matrix integrals.