Title: WKB and Topological Spectral Networks
Abstract: A spectral network is a graph on a Riemann surface subordinate to a branched covering, with many applications in geometry and mathematical physics. In this talk I will introduce the notions of a WKB spectral network and its topological generalization. I will briefly indicate the physical ideas behind WKB spectral networks and explain the geometric motivation for topological spectral networks via non-abelianization of flat connections. I will also discuss how spectral networks give natural coordinate systems on moduli spaces of flat connections on the surface.