Brieskorn Complete Intersections and Automorphic Forms.
Chern forms and the Riemann tensor for the moduli space ofcurves.
Complex algebraic curves with real moduli.
Complex geometry of the universal Teichmüller space.
Connected components of the strata of the moduli spaces of quadratic differentials
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
Coordinates for Teichmüller spaces of -groups with torsion.
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Déformation localisée de surfaces de Riemann.
Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.
Deformations and moduli of Riemann Surfaces with nodes and signatures.
Deformations of Holomorphic Seifert Fiber Spaces.
Deformations of Strictly Pseudoconvex Domains.
Deforming real projective structures.
Déviations de moyennes ergodiques, flots de Teichmüller et cocycle de Kontsevich-Zorich
Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...
Die 3-Weierstrass Punkte über dem Teichmüller-Raum T2.
Die Automorphismensgruppe der universellen Familie kompakter Riemannscher Flächen vom Geschlecht g...3.
Die Jacobi-Abbildung über dem Raum der Mumfordkurven.
Differentiability and rigidity of Möbius groups.
Differentials of the second kind for families of Mumford curves
Dimension vs. genus: A surface realization of the little k-cubes and an operad
We define a new operad based on surfaces with foliations which contains suboperads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes (thus making contact with string topology), by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new Ω spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension k of the little...
Dirchlet's energy on Teichmüller's moduli space and the Nielsen realization problem.