It has been known for roughly 30 years that the Knizhnik–Zamolodchikov connection (KZ) can be obtained from the quantisation of the Schlesinger system: KZ controls correlation functions in conformal field theory, and Schlesinger governs isomonodromic deformations of meromorphic connections with tame/regular singularities, encompassing e.g. the sixth Painlevé equation.The talk will aim at reviewing part of this story, and presenting results about the wild/irregular case, encompassing e.g. all the other Painlevé equations. It is joint work with P. Boalch, J. Douçot, G. Felder and M. Tamiozzo. 

https://indico.math.cnrs.fr/event/9430/