Basar, Gokce2016-05-182016-05-182016-05-14http://hdl.handle.net/11299/180388The theory of resurgence connects high order terms of perturbative series to low order terms in non-perturbative sectors. In this talk I will present a different type of resurgent relation that connects perturbative and non-perturbative sectors in a term-by-term fashion in certain quantum mechanical systems. This relation is valid for everywhere in the spectrum and has a geometric interpretation in terms of quantization of Riemann surfaces. Notably, the spectra of these quantum mechanical examples encode the vacua of certain N=2 supersymmetric gauge theories in the Nekrasov-Shatashvili limit.enFTPIQCDPresentation