On Minkowksi's bound for lattice-packings
We give a new proof of the Minkowski-Hlawka bound on the existence of dense lattices. The proof is based on an elementary method for constructing dense lattices which is almost effective.
The Length of Harmonic Forms on a Compact Riemannian Manifold
We study $n$ dimensional Riemanniann manifolds with harmonic forms of constant length and first Betti number equal to $n-1$ showing that they are 2-steps nilmanifolds with some special metrics. We also characterise, in terms of properties on the product of harmonic forms, the left invariant metrics among them. This allows us to clarify the case of ...
The macroscopic sound of tori
Take a torus with a Riemannian metric. Lift the metric on its universal cover. You get a distance which in turn yields balls. On these balls you can look at the Laplacian. Focus on the spectrum for the Dirichlet or Neumann problem. We describe the asymptotic behaviour of the eigenvalues as the radius of the balls goes to infinity, and characterise ...
Approximation of the Normal Vector Field and the Area of a Smooth Surface
International audience
A Metric Inequality for the Thompson and Hilbert Geometries
There are two natural metrics defined on an arbitrary convex cone: Thompson\'s part metric and Hilbert\'s projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.
Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups
We show that the semi-direct product of a one-ended torsion-free word-hyperbolic group G with Z is a hyperbolic group relative to certain canonical subgroups of G on which the automorphism coming from the action of Z on G acts periodically or with linear growth.
Vers une modélisation d'une géométrie en actes dans les activités de lecture tracé du bâtiment
La recherche présentée ici s'inscrit dans un projet national qui répond à un objectif social de transformations des formations professionnelles. L'activité professionnelle considérée requière des prises de décision dépendant d'une lecture adéquate de plans pour effectuer des tracés dans l'espace du chantier. La modélisation d'une telle activité par...
Chirality and Symmetry Measures: A Transdisciplinary Review
Many quantitative measures of the degree of chirality or symmetry of a set have been proposed in the literature. The main approaches from various areas are reviewed: chemistry, physics, mathematics, computer sciences, biology, and psychophysics. Relations between chirality, symmetry, and other concepts such as similarity, disorder and entropy, are ...
Plusieurs niveaux de généralité en jeu dans l'article de Poincaré.
/ Plusieurs niveaux de généralité en jeu dans l'arti...
Le séminaire "Histoires de Géométries", mis en place à la FMSH par l'équipe F2DS dirigée par Dominique FLAMENT, se veut largement ouvert. Non seulement il est un lieu de rencontre d'excellence entre mathématiciens, philosophes et historiens des sciences, mais il s'ouvre également à un public de "curieux", plus dispersés culturellement. Cet éclateme...
Endomorphisms of Kleinian groups.
We study the co-hopficity of Kleinian groups.
