Hamiltonian description of the isomonodromic deformations with irregular singularities
Ilia Gaiur
IHES
Wed, Dec. 01st 2021, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
My talk will be mostly about my recent results obtained in collaboration with M. Mazzocco and V. Roubtsov (arXiv:2106.13760). We study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-adjoint orbits of the Takiff algebra (i.e. truncated current algebra). In my talk I will explain how to choose the isomonodromic times in irregular situations and how this choice may be explained from the Poisson point of view. Such choice covers a wide class of isomonodromic systems and is related to the classical Painlev'e transcendents as well as to higher order and matrix Painlev'e systems. I will also introduce a general formula for the Hamiltonians of the isomonodromic flows. In the end of the talk I wish to discuss some questions about quantization of obtained systems and its connection with isomonodromic tau-function


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