Geometry and Dynamics Seminar | Riemann-Hilbert problems from rank 3 WKB spectral networks

Abstract

A class of Riemann-Hilbert problems arising in Donaldson-Thomas theory has been investigated by Bridgeland. These problems concern mappings from the complex plane to an algebraic torus that exhibit prescribed discontinuities along a set of rays. In this talk, I will begin by reviewing some basics of these Riemann-Hilbert problems, as well as the WKB spectral networks introduced by Gaiotto, Moore, and Neitzke. Building on the techniques for solving these Riemann-Hilbert problems from quadratic differentials, as developed by Allegretti and Bridgeland, I will next outline a strategy for constructing solutions to the Riemann-Hilbert problems from some rank 3 WKB spectral networks.