Algebraic solutions of the Painlev\'e equations
Seminar Room 1, Newton Institute
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.