Quantum spectral problems and Painlevé equations

by Alba Grassi (CERN)

Monday 19 Apr 2021, 13:30 → 15:30 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Abstract

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.  

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