Global KP integrability

We say that a (formal) solution of KP hierarchy posses a (rational) spectral curve if its associated $n$-point functions extend as global rational functions after a suitable change of variables, one and the same for all $n$. We show that the KP integrability is an internal property of a system of $n$-point functions: the corresponding potential associated with their power expansion at some point in some local coordinate satisfies KP hierarchy if and only if the same holds for any other expansion point and any other local coordinate. As a consequence, we show that potentials govern by the procedure of topological recursion of Chekhov-Eynard-Orantin on a rational spectral curve posses KP integrability property.
The talk is based on a series of joint papers with A.Alexandrov, B.Bychkov, P.Dunin-Barkowsky, and S.Shadrin.