Résumé

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.  

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