Pavlo Gavrylenko

I will consider the simplest example of isomonodromic deformations on a torus, which corresponds to the non-autonomous Calogero-Moser system. Solution and tau function of this system can be expressed either in terms of conformal blocks/Nekrasov partition functions, or in terms of some block Fredholm determinant. The latter one may also be generalized to the Fredholm determinant of a Riemann-Hilbert problem with arbitrary jump on a torus. The talk will be based on the joint paper with Fabrizio Del Monte and Harini Desiraju https://arxiv.org/pdf/2011.06292.