Spectral networks and character varieties- Andrew Neitzke

Conference Title: GEAR Retreat 2012 Theme: Higgs Bundles (4 of 5) Title: Spectral networks and character varieties Speaker: Andrew Neitzke, University of Texas at Austin; Date and Time: Tuesday August 7, 14:40 Description: A spectral network is a network of paths drawn on a punctured surface, satisfying certain combinatorial rules. I will explain how spectral networks induce coordinate systems on (finite covers of) character varieties for the group GL(K). Conjecturally, these coordinate systems are those in the cluster atlas for the character variety, as described by Fock-Goncharov. Spectral networks are also a key ingredient in a new description of the hyperkahler structure on the character variety. This is joint work with Davide Gaiotto and Greg Moore. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Andrew Neitzke, in this GEAR Retreat 2012 session on Higgs Bundles, will explain how spectral networks induce coordinate systems on (finite covers of) character varieties for the group GL(K), and related topics.