Abstract

I will start out by discussing a recent conjecture for the complete resurgent Stokes data of the Painlevé I/II equations, which is based upon their resurgent structure [1]. This provides access to an infinite amount of transcedental numbers which completely characterize the global properties of the transseries solutions of Painlevé I/II and the hermitian quartic matrix model. I will then outline how to obtain the exact same data from (off-critical and double-scaled) matrix integral calculations [2]. The full resonant resurgent transseries may be obtained by generalizing physical-sheet eigenvalue tunneling to all (non-physical) sheets of the spectral geometry. This provides the complete semiclassical decoding of resurgent matrix models and minimal strings.I will end by presenting explicit examples. [1] S. Baldino, R. Schiappa, M. S., R. VegaResurgent Stokes Data for Painlevé Equations and Two-Dimensional Quantum (Super) Gravity,(2022), arXiv:2203.13726 [hep-th] [2] M. Mariño, R. Schiappa, M. S.To appear (2022).