Speaker
Pavlo Gavrylenko
(Birmingham University)
Description
q-Painlevé III₃ equation is related to the N=1 5d gauge theory. We reformulate its linear problem as the Riemann-Hilbert problem on a circle. Then, we express its tau function as the Fredholm determinant related to this Riemann-Hilbert problem. This expression allows us to study the global properties of the q-Painlevé solution, and so of the partition function of the 5d gauge theory. The talk will be based on https://arxiv.org/abs/2501.01419.