Quantum Painlevé monodromy manifolds and Sklyanin–Painlevé algebra, I

In this talk, I will discuss the Painlevé monodromy manifolds as a special class of del Pezzo surfaces. I will discuss the natural Poisson structure on these manifolds and the Riemann–Hilbert correspondence in terms of a map between Okamoto and Looijenga pairs. Finally, I will related introduce the generalised Sklyanin–Painlevé algebra.