SL(2,C) Higgs bundles with smooth spectral data
Mike Wolf (Rice University)
Aula Beltrami - Wednesday, February 24, 2016 h.14:30
Abstract. Abstract: We show that for every nonelementary representation of a surface group into SL(2,C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the discriminant locus of the Hitchin fibration. Along the way in the argument, we encounter a number of constructions in the geometry of surfaces: complex projective structures, pleated surfaces, harmonic maps to R-trees and the Thurston compactification. Much of the talk will be devoted to explaining the statement and as many of the constructions as time permits. (Joint with Richard Wentworth.)
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