Appears in collection : Wall-Crossing Structures, Analyticity, and Resurgence

In the first half of the talk, I’ll give a review of the topological recursion and how it is related to WKB, Painlevé equations and BPS structures (I 2019, Eynard--Garcia-Failde-Marchal-Orantin 2019, 2021, I—Kidwai 2020, 2021). In the latter half, I’ll discuss a resurgence property of the topological recursion partition function based on several conjectures which are expected to hold from the view-point of the exact WKB analysis. In particular, I’ll explain how the cluster transformation is related to the non-linear Stokes phenomena for the Painlevé transcendents.