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Painlevé I and exact WKB: studying Stokes phenomenon analytically and numerically

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ARA2 - Applicable resurgent asymptotics: towards a universal theory

I discuss recent work with Alexander van Spaendonck in which we study the Stokes phenomenon of two-parameter solutions to the Painlevé I equation, both analytically and numerically. On the analytical side we use the idea of isomonodromic deformation, as studied by e.g. Takei and collaborators and Iwaki. We recover the exact expressions for the Stokes data that were recently found by Baldino, Schwick, Schiappa and Vega, explain several ambiguities in relating parameter choices for transseries solutions to actual Painlevé transcendents, and study the monodromy of formal solutions. In the talk I also explain how one can numerically solve the Painlevé I equation, using ideas of Fornberg and Weideman, to check analytic results in part of the full two-dimensional parameter space.

This talk is part of the Isaac Newton Institute Seminar Series series.

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