Quadratic differentials, WKB analysis, and cluster coordinates
Introductory Workshop: Holomorphic Differentials in Mathematics and Physics August 19, 2019 - August 23, 2019
Location: MSRI: Simons Auditorium
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.
If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.
See more of our Streaming videos on our main VMath Videos page.