Topological Recursion, Painlevé Equation, Exact WKB and Resurgence

Explore a comprehensive lecture on topological recursion and its connections to various mathematical concepts. Delve into the relationship between topological recursion and WKB method, Painlevé equations, and BPS structures. Examine recent developments in the field, including works by Iwaki (2019), Eynard-Garcia-Failde-Marchal-Orantin (2019, 2021), and Iwaki-Kidwai (2020, 2021). Investigate the resurgence property of the topological recursion partition function, based on conjectures derived from exact WKB analysis. Discover the intriguing link between cluster transformation and non-linear Stokes phenomena for Painlevé transcendents. Gain insights from Kohei Iwaki, a researcher from The University of Tokyo, as he presents this advanced mathematical topic at the Institut des Hautes Etudes Scientifiques (IHES).