Calogero-Painlevé systems, their isomonodromic formulation and non-commutative monodromy data

I present our recent results on the isomonodromic formulation of the so-called Calogero-Painlev? systems. We will also discuss, for the case of Painlev? II, how the associated monodromy data can be interpreted, to some extent, as a sort of quantization of the classical cubic associated to the “classical” Painlev? II equation (joint work with Marco Bertola and Vladimir Roubtsov)