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This paper uses Morse-theoretic techniques to compute the equivariant Betti numbers of the space of semistable rank two degree zero Higgs bundles over a compact Riemann surface, a method in the spirit...
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
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 d...
In the late 1980’s Hitchin [51] and Simpson [71] discovered deep connections between representations of fundamental groups of surfaces and algebraic geometry.
Goldman gratefully acknowledges partial support by NSF grants DMS-9504764, DMS-9803518, DMS-0103889 and a Semester Research Award from the General Research Board of the University of Maryland in Fa...
Consider the moduli space of parabolic Higgs bundles (E,\Phi) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It is equipped with t...
Let $M$ be a compact complex manifold equipped with a Gauduchon metric. If $TM$ is holomorphically trivial, and (V, \theta) is a stable SL(r,{\mathbb C})-Higgs bundle on $M$, then we show that $\thet...
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...

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