Title: The Exact WKB Method is Abelianisation
2016.12.06 |
| Date | Mon 12 Dec |
| Time | 16:15 — 17:15 |
| Location | Kol-G3 (1532-218) |
Abstract
The exact WKB method is a powerful tool in singular perturbation theory of differential equations. It is a formal calculation supplemented by a resummation technique: solutions are found as (in general, divergent) power series in the perturbation parameter and subsequently resummed to give true solutions.
I will give a brief introduction to the exact WKB method for second order ODEs on a Riemann surface X, and explain how to use it to construct a flat line bundle on a cover of X which we call the abelianisation of the original system. By considering holonomies of this abelianisation, the exact WKB method produces an explicit Darboux coordinate system on a moduli space of framed SL_2-connections.
Based on joint work in progress with M. Gualtieri, K. Iwaki, A. Neitzke.
AaDAG seminar: Aarhus Differential Algebraic Geometry seminar
