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The solutions of Painlevé equations in terms of Fredholm determinants and consequences.

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ARA2 - Applicable resurgent asymptotics: towards a universal theory

Painlevé equations can be expressed as a system of differential equations called the Lax pair. In this talk, I will present a construction of Fredholm determinants using the Lax matrices and show that they are related to the solutions of Painlevé equations. Such a construction also proves useful to study the asymptotics of the solutions at critical points.

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

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