Topological recursion, Painlevé tau-function and exact WKB analysis

I'll show that the solution of the first Painlevé equation (together with the isomonodromic wave function which satisfies the associated linear system) are constructed as the discrete Fourier transform of the topological recursion partition function. Assuming certain conjectures on a resurgence property of the formal series constructed from topological recursion, I'll also explain how the Stokes multipliers of associated linear system are computed from the view point of exact WKB analysis.