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The Exact WKB Method is Abelianisation

Nikita Nikolaev (University of Toronto)
Mandag, 12 december, 2016, at 16:15-17:15, in Koll. G3 (1532-218)

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    

Organiseret af: QGM
Kontaktperson: Artan Sheshmani