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The solutions of Painlevé equations and Fredholm determinants: a Riemann-Hilbert approach

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AR2W02 - Mathematics of beyond all-orders phenomena

In this talk, I will review some recent techniques that enable Fredholm determinant representation of Painlevé tau-functions. The solutions of Painlevé equations are typically logarithmic derivatives of the tau-functions. I will detail the case of the Painlevé II tau-function (associated to the 2 parameter family of solutions), which can be written as a Fredholm determinant of an integrable (IIKS) kernel.  

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

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