course: Spectral networks and their uses Part III
speaker: Andrew Neitzke (The University of Texas at Austin, Mathematics Department)abstract: Spectral networks are certain networks of codimension-1 "walls" on manifolds. Spectral networks on 2-manifolds have appeared in many places, e.g. in the theory of cluster varieties, Teichmuller theory and its higher analogues, Hitchin systems, wall-crossing in Donaldson-Thomas theory, and 4-dimensional supersymmetric quantum field theory. One key idea is that the spectral network gives a way of reducing nonabelian phenomena to abelian ones, e.g. replacing GL(K) connections over some space by GL(1) connections over a K-fold covering space. I will describe what a spectral network is, how they give rise to nice "cluster-like" coordinate systems on moduli spaces of complex flat connections over 2-manifolds (character varieties), and how they can be used to study the solutions of Hitchin equations. Time permitting, I will also briefly discuss an extension of the story to 3-manifolds. The main part of the story is joint work with Davide Gaiotto and Greg Moore, motivated by work of many other people, especially Fock-Goncharov, Kontsevich-Soibelman, Joyce-Song. The extension to 3-manifolds is joint work in progress with Dan Freed, also influenced by work of Thurston, Goncharov, Garoufalidis-Thurston-Zickert.
timetable:
Thu 19 Jun, 9:30 - 10:30, Aula Dini
<< Go back