Isomonodromic deformations: confluence, reduction and quantization

https://hu-berlin.zoom.us/j/61339297016

In this talk we study the theory of isomonodromic deformations for systems of differential equations with poles of any order on the Riemann sphere. Our initial motivation was to generalise a theorem by Reshetikhin that the quasiclassical solution of the standard  KZ equations (i.e. with simple poles) is expressed via the isomonodromic $\tau$-function arising in the case of Fuchsian systems. Along the way of pursuing this project, we have found a number of interesting results, some of which were already known as folklore (i.e. either done is very specific examples or not really proved formally), others completely original.