Integrable Systems and Random Matrix Theory Seminar

Title: Irregular isomonodromic deformations: Hamiltonian aspects

Abstract: We study 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 (aka truncated current algebra). In my talk I will explain how to choose 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 such as classical Painlevé transcendents as well as higher order ones and matrix Painlevé systems. I will also introduce a general formula for Hamiltonians of isomonodromic flows. Talk is based on the thesis of the speaker and the results obtained in a collaboration with M. Mazzocco and V. Roubtsov (arXiv:2106.13760).