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Let K be a global field of characteristic not 2. Let Z = H\G be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K is a number field.
Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups A i which are the k-points of maximal (k, σ)-split… (More)
This text is an introduction to lattices in semisimple Lie groups, in five independent lectures. It was given during the first week of the 2004 Summer School at the Fourier Institute in Grenoble. We hope that it will attract young students to this topic and convince them to read some of the many textbooks cited in the references. We illustrate five… (More)
We describe the Zariski closure of the geometric realization of Coxeter groups. When the Coxeter system is irreducible and the Tits form B non positive and non degenerate, this Zariski closure is equal to the orthogonal group of B. 1. Réalisation géométrique d'un groupe de Coxeter Soit (S, M) un système de Coxeter, c'est-` a-dire un couple formé d'un… (More)
The mass colorectal cancer screening program was implemented in 2008 in France, targeting 16 million French people aged between 50 and 74. The current adhesion is insufficient and the participation rate is even lower among the underserved population, increasing health inequalities within our health care system. Patient Navigation programs have proved their… (More)
We prove that a Jordan curve in the 2-sphere is a quasicircle if and only if the closure of its orbit under the action of the conformal group contains only points and Jordan curves.