On q-difference Painlevé equations

Professor Nalini Joshi (University of Sydney)

Tuesday 11th October, 2022 16:00-17:00 Maths 311B


The description of transcendental solutions of the classical differential Painlevé equations was started more than a century ago and a great deal is now known about their properties. The same cannot be said about the discrete Painlevé equations.

In particular, almost nothing is known about the behaviours of transcendental solutions of q-difference Painlevé equations, which arise in mathematical physics. In this talk, I will introduce the background theory of such equations and give some recent results for equations known as the fourth and sixth q-difference Painlevé equations. These rely on a formulation of a q-version of Riemann-Hilbert problems and newly discovered explicit expressions for monodromy manifolds for these equations.

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