Isomonodromic Deformations Painlevé Equations, and Integrable Systems

8 Jun 2022

The conference Isomonodromic Deformations Painlevé Equations, and Integrable Systems, will take place online from June 27–July 1, 2022. Pavlo Gavrylenko is on the Organizing Committee & Alba Grassi (UNIGE) is amongst the speakers.

Introduction

"Integrable systems played an extremely important role in mathematical physics over the last 50 years. Their physical applications include gauge theories and conformal field theories, as well as statistical models. Mathematically, this area has deep connections with complex and algebraic geometry, geometry of algebraic curves and various types of moduli problems. Among the key tools of the modern theory of integrable system is the notion of a Lax Pair representation or, equivalently, of an isospectral deformation of some linear problem – the associated spectral curve then encodes the integrals of motion of the system. The non-autonomous analogue of this representation is the notion of an isomonodromic deformation. Classical theory of isomonodromic deformations goes back over a hundred years to the works of Fuchs and Schlesinger. It was revived in mid-1980s by the Japanese school, and at present it is yet again attracting a lot of attention. Classical connections between isomonodromic deformations and differential Painlevé equations have been generalized to the discrete case. There are deep connections of this area to new exciting mathematical objects such as Integrable Probability, Cluster Varieties and Dimer Models, as well as the relations between tau-functions of differential Painlevé equations and Conformal Blocks, and its generalization to q-Painlevé equations. And the list goes on. The goal of our conference is to discuss some of the recent progress and results in this exciting area of Mathematical Physics."

Phase I & II research project(s)

2022 Dubrovin Medal

SwissMAP Research Fellows