The practical determination of the deficiency (Geschlecht) and adjoint ... curves for a Riemann surface
The Prym variety for a cyclic unramified cover of a hyperelliptic Riemann surface.
The Prym vector bundle and Gunning vector bundle over the Teichmüller space.
The quasihyperbolic metric, growth, and John domains.
The ratio of invariant metrics on the annulus and theta functions
The real genus of the alternating groups.
The return sequence of the Bowen-Series map for punctured surfaces
For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure. ...
The Riemann surface of a uniform dessin.
The Second Homology Group of the Mapping Class Group of an Orientable Surface.
The Serre duality theorem for Riemann surfaces.
The Serre Problem on Riemann Surfaces.
The sympletic nature of the space of projective connections on Riemann surfaces.
The Teichmüller space of an Anosov diffeomorphis of T2.
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
The topology of deformation spaces of Kleinian groups.
The Torelli map at the boundary of the Schottky space.
The virtual cohomological dimension of the mapping class group of an orientable surface.
The visual sphere of Teichmüller space and a theorem of Masur-Wolf.
Théorie de Voronoï géométrique. Propriétés de finitude pour les familles de réseaux et analogues
Nous développons une théorie de Voronoï géométrique. En l’appliquant aux familles classiques de réseaux euclidiens (par exemple symplectiques ou orthogonaux), nous obtenons notamment de nouveaux résultats de finitude concernant les configurations de vecteurs minimaux et les réseaux particuliers (par exemple parfaits) de ces familles. Les méthodes géométriques introduites sont également illustrées par l’étude d’objets voisins (formes de Humbert) ou analogues (surfaces de Riemann).
Theorie der algebraischen Functionen einer Veränderlichen.