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Differential Geometry: "Exotic components of representation varieties for surface groups, and their Higgs bundle avatars"

Dr. Steven Bradlow, University of Illinois at Urbana-Chanpaign

Friday, June 9, 2017
  11:10 a.m.–Noon


Location: Surge Building 268
  Parking Information

Category: Seminar

Description: Moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. For representations into complex semisimple Lie groups, these spaces have just one connected component. This is no longer true if one restricts to real forms of the complex groups. Obvious topological invariants separate the spaces in all such cases, but in some cases other factors lead to the existence of extra `exotic' components. Formerly, all known instances of such exotic components were attributable to one of two distinct mechanisms. Recent Higgs bundle results for the groups SO(p,q) shed new light on this dichotomy and reveal new examples outside the scope of the two known mechanisms. This talk will survey what is known about the exotic components and describe the new SO(p,q) results.

Additional Information: Math Semianrs

Open to: General Public
Admission: Free
Sponsor: Mathematics

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