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Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…
Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to…
This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…
Let $M$ be the moduli space of rank 3 parabolic vector bundles over a Riemann surface with several punctures. By the Mehta-Seshadri correspondence, this is the space of rank 3 unitary representations of the fundamental group of the…
In the theory of Teichm\"uller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally…
We generalise to the genus one case several results of Thurston concerning moduli spaces of flat Euclidean structures with conical singularities on the two dimensional sphere. More precisely, we study the moduli space of flat tori with $n$…
We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…
We present a geometric mechanism for the emergence of spherical $3$-manifolds from the superspace of Riemannian metrics associated with flat ${\rm{SU}}(2)$-bundles over closed orientable hyperbolic surfaces. Our main result shows that any…
In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics…
The aim of this paper is to construct the parabolic version of the Donaldson--Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing…
This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2,C) representations of a surface group. Specifically, we find an asymptotic correspondence between the…
It is shown that the space of null geodesics of a causally simple Lorentzian manifold is Hausdorff if it admits an open conformal embedding into a globally hyperbolic spacetime. This provides an obstruction to conformal embeddings of…
We study Selberg zeta functions $Z(s,\sigma)$ associated to locally homogeneous vector bundles over the unit-sphere bundle of a complete odd-dimensional hyperbolic manifold of finite volume. We assume a certain condition on the fundamental…
We construct the moduli space of smooth hypersurfaces with level $N$ structure over $\mathbb{Z}[1/N]$. As an application we show that, for $N$ large enough, the stack of smooth hypersurfaces over $\mathbb{Z}[1/N]$ is uniformisable by a…
We present a simple description of moduli spaces of torsion-free D-modules (``D-bundles'') on general smooth complex curves X, generalizing the identification of the space of ideals in the Weyl algebra with Calogero-Moser quiver varieties.…
We study complex hyperbolic disc bundles over closed orientable surfaces that arise from discrete and faithful representations H_n->PU(2,1), where H_n is the fundamental group of the orbifold S^2(2,...,2) and thus contains a surface group…
We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…
We introduce and study a novel uniformization metric model for the quasi-Fuchsian space QF(S) of a closed oriented surface S, defined through a class of C-valued bilinear forms on S, called Bers metrics, which coincide with hyperbolic…
We characterize which cobounded quasigeodesics in the Teichmueller space T of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path gamma in T, we show that gamma is a quasigeodesic with…
We show that every $\mathbb R$-linear surjective isometry between the cotangent spaces to the Teichm\"uller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces, which is an analogue…