3:30 pm Tuesday, May 10, 2016
Student Geometry Seminar: The Exact WKB Method and Abelianisation by Nikita Nikolaev in RLM 12.166
The exact WKB method, as initiated by Voros in 1983, is a powerful tool in singular perturbation theory. More recently, Gaiotto, Moore, and Neitzke (2012) laid foundation for the theory of Spectral Networks; amongst their many applications, a procedure called abelianisation of connections was discovered. This procedure appears to exhibit all the same phenomena as the WKB method. I will give a brief description of the exact WKB method and abelianisation, and I will hint at why they are probably the same. I will describe my most recent approach to establishing this fact. This approach -- which I refer to as the "motivic description" -- involves exponential Gauss-Manin connections: given a family of algebraic varieties with an extra data of a regular function, there is a natural connection on the sheaf of fibrewise twisted algebraic de Rham cohomology. Submitted by
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