Related papers: Hyperbolicit\'e des vari\'et\'es complexes

- Synth\`ese des travaux pr\'esent\'es en vue d'une Habilitation \`a Diriger des Recherches - Synthesis of works presented towards the Habilitation degree This is a summary (in French) of my work in number theory, group theory and…

We present a collection of signatures for physics beyond the standard model that need to be explored at the LHC. The signatures are organized according to the experimental objects that appear in the final state, and in particular the number…

We consider groups defined by cyclic presentations where the defining word has length three and the cyclic presentation satisfies the T(6) small cancellation condition. We classify when these groups are hyperbolic. When combined with known…

This is the text of a talk to the study week on \emph{Modular forms and Galois representations} held in Luminy, 1997. We give a survey of $p$-adic modular forms, as developped by Serre, Katz, Hida, Wiles, Coleman and others...

This note contains an attempt to relate Hecke's presentation of an ideal class zeta function in a real quadratic field as an integral of the nonholomorphic Eisenstein series along the loop on modular curve and Zagier's decomposition of this…

This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…

The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional

This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…

Extended version of an article on top-quark physics, to appear in the May 1997 issue of Physics Today.

We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $\mathrm{PO}(n,1)$ with $n>3$. We further show that under an additional assumption (satisfied in all known cases), the covolumes of these…

In this paper, we define two types of partitions of an hyperbolic interval: weak and strong. Strong partitions enables us to define, in a natural way, a notion of hyperbolic valued functions of bounded variation and hyperbolic analogue of…

We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

These are lectures on discrete groups of isometries of complex hyperbolic spaces, aimed to discuss interactions between the function theory on complex hyperbolic manifolds and the theory of discrete groups.

Some conjectures about Heegaard genera and ranks of fundamental groups of 3-manifolds are formulated, and it is shown that they imply new statements about hyperbolic volume.

We survey the known results regarding the boundaries of word-hyperbolic groups.

We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.

New cases of the multiplicity conjecture are considered.

We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…

These notes are based on lectures given in Wuhan (China) in July 2007. Their aim is to provide an introduction to Langlands philosophy.