Geometry and Resurgence of WKB Solutions of Schrödinger Equations

Nikita Nikolaev (University of Birmingham)

Tuesday 21st October 16:00-17:00
Maths 311B

Abstract

I will recall the WKB method for Schrödinger equations and explain how to make sense of it in geometric terms. I will then explain some ingredients of my proof of the so-called Quantum Resurgence Conjecture, a longstanding open problem in mathematical physics. The upshot is that the Borel transform of a formal WKB solution naturally defines a holomorphic family of infinite Riemann surfaces with very interesting geometry that encodes the singularities and the Stokes phenomenon of exact WKB solutions using the periods of a spectral curve. Based on arXiv:2410.17224.

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