arXiv research

Investigates nearly Kähler and parallel G2 manifolds using Hitchin functionals.

Study automorphism equivariant Hitchin index for Riemann surfaces.

Study on Hitchin index for cohomogeneity one nearly Kähler structures.

In this note we study some analytic properties of the linearized self-duality equations on a family of smooth Riemann surfaces $Σ_R$ converging for $R\searrow0$ to a surface $Σ_0$ with a finite number of nodes. It is shown that the linearization along the fibres of the Hitchin fibration gives rise to a graph-continuous…

Strict plurisubharmonicity proven for Teichmüller energy on Hitchin representations.

We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new ingredient of independent interest is homotopy density of the subspace of metrics with c…

New minimal surface theory disproves a conjecture in symmetric spaces.

New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.

We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature to construct a secondary index map from the space of positive scalar metrics to a suitable spa…

Recently, Atiyah and LeBrun proved versions of the Gauss-Bonnet and Hirzebruch signature Theorems for metrics with edge-cone singularities in dimension four, which they applied to obtain an inequality of Hitchin-Thorpe type for Einstein edge-cone metrics. Interestingly, many natural examples of edge-cone metrics in dim…

Surveying Hitchin representations of Fuchsian groups.

Defines and parametrizes $\mathfrak{sl}(2)$-type singular fibres in symplectic and odd orthogonal Hitchin systems.

Real projective surfaces with Hitchin holonomy can be related via grafting.

Study asymptotics of hyperkähler geometry on singular fibers of Hitchin moduli space.

Generic Hitchin representations generate dense subgroups.

New estimates for Hitchin's equations at high energy.

Study shows rapid decay of Hitchin metric from semi-flat metric on Higgs bundles.

Study of a basic Hitchin equation on Sasakian 3-folds, showing hyperKähler metric.

Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.

Study pressure metrics for cusped Hitchin representations.

Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.

The paper studies sequences of solutions to Hitchin-Simpson equations on Kähler manifolds.

We study hyperkahler metrics and hyperholomorphic connections of Hitchin's moduli spaces after Gaiotto, Moore and Neitzke. Their construction via the twistor technique produces intricate wall crossing behaviors. For certain four dimensional Hitchin's moduli spaces local models and degeneration to local models near sing…

We survey some recent developments in the asymptotic geometry of the Hitchin moduli space, starting with an introduction to the Hitchin moduli space and hyperkähler geometry.

Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.

We consider Hitchin's hyperkähler metric $g_{L^2}$ on the $SU(n)$-Hitchin moduli space moduli space over a compact Riemann surface. We prove that the difference between the metric $g_{L^2}$ and a simpler "semiflat" hyperkähler metric $g_{\mathrm{sf}}$ is exponentially-decaying along generic rays in the Hitchin moduli s…

We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the intersection function on Hitchin components of dimension 3 and on the self-dual Hitchin components in all dimensions. As an important tool in t…

This paper proves Hitchin moduli spaces are ALG gravitational instantons.

This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is…

In this paper we construct a Hitchin connection in a setting, which significantly generalizes the setting covered by the first author previously, which in turn was a generalisation of the moduli space case covered by Hitchin in his original work on the Hitchin connection. In fact, our construction provides a Hitchin co…

The abstract discusses rational approximations for Hitchin representations on surfaces.

Generic Hitchin representations avoid hyperplanes in Lie algebras.

Describes spectral data for singular fibres of a specific Hitchin system.

In this paper we calculate the curvature of the Hitchin connection. We further show that a slight (possibly trivial) modification of the Hitchin connection has curvature equal to an explict given multiple of the Weil-Petersen symplectic form on Teichmüller space.

Study on Higgs bundles and hyperpolygon spaces using Hitchin metrics.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

New metrics derived from Hölder distortion on Hitchin components.

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies Hitchin's moduli space with the moduli space of flat $K^\mathbb{C}$-connections,…

Study on projective structures linked to Hitchin representations.

Goldman symplectic form and complex structure compatible on $\mathrm{SL}(3,\mathbb R)$ Hitchin component.

This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and $L$-twisted Hitchin pairs on nodal curves. In particular, we survey on the relation between representations of the fundamental group of a nodal curve and the moduli spaces of generalised parabolic …

In this article we give a geometric interpretation of the Hitchin component for PSL(4,R) in the representation variety of a closed oriented surface of higher genus. We show that representations in the Hitchin component are precisely the holonomy representations of properly convex foliated projective structures on the u…

New insights into currents of Hitchin representations with combinatorial restrictions.

We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root flow, derive a Liouville volume rigidity result, and construct a Liouville pressure metric on the Hitchin component.

Characterizes flag geometries for Hitchin representations in SL3(R).

We study a natural functional on the space of holomorphic sections of the Deligne-Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We give a link to a natural meromorphic connection on the hyperholomorphic line bundle recently constr…

Paper studies compactifications of Higgs bundles and self-duality equations.

Explicit computation of symplectic form for $\mathrm{PGL}_n(\mathbb{R})$-Hitchin component.