Speaker: Nikita Nikolaev (University of Birmingham)

Abstract: I will recall the WKB method for Schrödinger equations and explain how to make sense of it in more invariant and geometric terms. I will then explain how to prove that Schrödinger equations on compact Riemann surfaces have the so-called quantum resurgence property: the Borel transform of a formal WKB solution is a holomorphic germ that extends to a global holomorphic function on an infinite Riemann surface with exponential bounds at infinity. This infinite Riemann surface has a rich geometry that is built out of the geometry of the spectral curve and completely governs the Stokes phenomenon in the WKB method. Based on arXiv:2410.17224.