Higgs bundles and representations of fundamental groups- Tony Pantev

Conference Title: GEAR Retreat 2012 Theme: Higgs Bundles (1 of 5) Title: Higgs bundles and representations of fundamental groups Speaker: Tony Pantev, Univ. of Pennsylvania; Date and Time: Tuesday August 7, 09:30 Description: I will review the notion of a Higgs bundle on a Riemann surface and will discuss the nonabelian Hodge theorem which relates representations of fundamental groups to Higgs bundles. I will explain how the non-abelian Hodge dictionary can be used to convert difficult existence questions for special representations to projective geometry. I will present samples of standard construction techniques, including the spectral cover construction and Katz's middle convolution algorithm. I will also explain how this formalism can be applied to construct rigid representations, representations with prescribed arithmetic properties, and representations of geometric origin. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Tony Pantev, in this GEAR Retreat 2012 session on Higgs Bundles, will review the notion of a Higgs bundle on a Riemann surface and will discuss the nonabelian Hodge theorem which relates representations of fundamental groups to Higgs bundles, and other topics.