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Isomonodromic deformations: confluence, reduction and quantization

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Marta Mazzocco
Birmingham University
Tue, 2021-07-06 14:00 - 15:30


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.


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