Related papers: On Codazzi tensors on a hyperbolic surface and fla…
In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…
This paper is a survey on the role of Higgs bundle theory in the study of higher Teichm\"uller spaces. Recall that the Teichm\"uller space of a compact surface can be identified with a certain connected component of the moduli space of…
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
We identify a new class of closed smooth manifolds for which there exists a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit cotangent disk bundle, settling a well-known conjecture of…
In this note we prove infinite dimensionality of the Teichm\"uller space of a hyperbolic Riemann surface lamination of a compact space having a simply connected leaf.
We study the moduli space of constant scalar curvature K\"ahler surfaces around the toric ones. To this aim, we introduce the class of foldable surfaces : smooth toric surfaces whose lattice automorphism group contain a non trivial cyclic…
The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…
We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that…
Take a Teichm\"uller disc whose corresponding flat surface has a Veech-Group that contains a parabolic element. We look at its image in Schottkyspace and show that we can always construct a Schottky covering such that this image is not a…
We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using…
This thesis mainly treats two developments of the classical theory of hypersurfaces inside pseudo-Riemannian space forms. The former - a joint work with Francesco Bonsante - consists in the study of immersions of smooth manifolds into…
Identifying parallel sides of a collection of Euclidean polygons yields a flat surface with cone points of angles multiples of 2 pi, naturally a compact Riemann surface but also an algebraic curve, and a hyperbolic surface. In general two…
This paper develops a novel approach to functorial quantum field theories (FQFTs) in the context of Lorentzian geometry. The key challenge is that globally hyperbolic Lorentzian bordisms between two Cauchy surfaces cannot change the…
We compute the cohomology spaces for the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme H of subschemes of length n of a smooth projective surface X. We show that for L and A invertible vector bundles on X,…
From a view point of the moment map, we shall introduce the notion of Einstein-Hermitian generalized connections over a generalized K\"ahler manifold of symplectic type. We show that moduli spaces of Einstein-Hermitian generalized…
The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\mathbb{P}^1 \times…
We study the following question: Let $(X,g)$ be a compact Gauduchon surface, $(E,h)$ be a differentiable rank $r$ vector bundle on $X$, ${\mathcal{D}}$ be a fixed holomorphic structure on $D:=\det(E)$ and $a$ be the Chern connection of the…
We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real…
We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…
In the genus one case, we make explicit some constructions of Veech on flat surfaces and generalize some geometric results of Thurston about moduli spaces of flat spheres as well as some equivalent ones but of an analytico-cohomological…