In the first part of the talk I will review some aspects of the Painlevé/gauge correspondence. In particular I will show how we can construct generic and explicit solutions to such nonlinear ODEs by using the Nekrasov partition function in the (epsilon1=- epsilon2) phase of the Omega background (Kiev construction). In the second part I will show how we can systematically associate a set of quantum systems to such nonlinear ODEs and how their spectral properties are completely determined by the Kiev formula and thus by the (epsilon1=- epsilon2) phase of the Omega background. This is based on work in progress with M.Bershtein and P. Gavrylenko.
