19 Apr/21
13:30 - 15:30 (Europe/Zurich)

Quantum spectral problems and Painlevé equations


4/3-006 at CERN


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=0) 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=0) phase of the Omega background.  

Based on: work in progress with M. Bershtein and P. Gavrylenko.