KP integrability of the non-perturbative tau function

The so called nonperturbative tau function is a kind of one-parameter deformation of the alebraic-geometrical tau function of Krichever construction by means of topological recursion procedure. The talk wil disscuss the proof of a conjecture by Eynard et al claiming that this deformation is a KP tau function as the original tau function of Krichever is. We will explain in details the meaning of all objects entering the formulation of conjecture as well as the nature of KP integrability. The talk is based on a join preprint with A.Alexandrov, B.Bychkov, P.Dunin-Barkowsky, and S.Shadrin.