Videos

Quadratic Differentials, WKB Analysis, and Cluster Coordinates

Presenter
August 22, 2019
Abstract
The WKB method was originally introduced by Wentzel, Kramers, and Brillouin in 1926 as a way of finding approximate solutions of the Schrodinger equation in the semiclassical limit in quantum mechanics. The modern theory of WKB analysis is a refinement of this method which is deeply related to the theory of quadratic differentials and the associated spectral networks on Riemann surfaces. In this talk, I will review the notion of a Voros symbol from WKB analysis. Voros symbols are non-convergent formal series whose Borel sums define analytic functions under certain conditions. Recently, Iwaki and Nakanishi observed that the wall-crossing behavior of Voros symbols is governed by cluster transformations. I will present an extension of their result, which says that in fact the Borel sums of Voros symbols arise naturally as cluster coordinates on certain moduli spaces.