In this paper, we study the geometric and dynamical properties of maximal representations
of surface groups into Hermitian Lie groups of rank 2. Combining tools from Higgs bundle …

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to
study the moduli spaces of surface group representations in a reductive Lie group G. In this …

The space $\mathbf {H}^{4, 2} $ of vectors of norm $-1$ in $\mathbb {R}^{4, 3} $ has a
natural pseudo-Riemannian metric and a compatible almost complex structure. The group of …

In this paper, we study the moduli space of representations of a surface group (that is, the
fundamental group of a closed oriented surface) in the real symplectic group Sp (2 n, ℝ). The …

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures,
when G is a real reductive Lie group, and establish a correspondence between these …

We introduce a type of minimal surface in the pseudo-hyperbolic space H n, n (with n even)
or H n+ 1, n− 1 (with n odd) coming from cyclic SO 0 (n, n+ 1)-Higg bundles. By showing that …

We introduce a new class of $\mathfrak {sl} _2 $-triples in a complex simple Lie algebra
$\mathfrak {g} $, which we call magical. Such an $\mathfrak {sl} _2 $-triple canonically …

This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the
non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in …

The geometry of maximal components of the PSp(4,R) character variety Page 1 msp Geometry
& Topology 23 (2019) 1251–1337 The geometry of maximal components of the PSp.4;R …

We consider the moduli space M (G) of G‐Higgs bundles over a compact Riemann surface
X, where G is a complex semisimple Lie group. This is a hyperkähler manifold …