An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: An Introduction

Algebraic solutions of Painleve VI

14th September 2006

Author: Phil Boalch (ENS)

Abstract

I will survey what is known about the algebraic solutions of the Painleve VI equation. This gives an opportunity to see 'in action' lots of the Painleve/isomonodromy technology: Riemann-Hilbert correspondence, nonlinear monodromy actions, affine Weyl group symmetries, quadratic/Landen/folding transformations and precise asymptotic formulae. Moreover I will try to emphasise some of the mysteries and open problems of the subject.

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