No Arabic abstract
We extend a result of Matucci on the number of conjugacy classes of finite order elements in the Thompson group $T$. According to Liousse, if $ gcd(m-1,q)$ is not a divisor of $r$ then there does not exist element of order $q$ in the Brown-Thompson group $T_{r,m}$. We show that if $ gcd(m-1,q)$ is a divisor of $r$ then there are exactly $varphi(q). gcd(m-1,q)$ conjugacy classes of elements of order $q$ in $T_{r,m}$, where $varphi$ is the Euler function phi. As a corollary, we obtain that the Thompson group $T$ is isomorphic to none of the groups $T_{r,m}$, for $m ot=2$ and any morphism from $T$ into $T_{r,m}$, with $m ot=2$ and $r ot= 0$ $mod (m-1)$, is trivial.
In this article, we consider the links between parabolic induction and the local Langlands correspondence. We enunciate a conjecture about the (enhanced) Langlands parameters of supercuspidal representation of split reductives $p$-adics groups. We are able to verify this in those known cases of the local Langlands correspondence for linear groups and classical groups. Furthermore, in the case of classical groups, we can construct the cuspidal support of an enhanced Langlands parameter and get a decomposition of the set of enhanced Langlands parameters a la Bernstein. We check that these constructions match under the Langlands correspondence and as consequence, we obtain the compatibility of the Langlands correspondence with parabolic induction.
We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $lambda$. We prove that if $lambda$ is uniquely integrable and if both structures of the pair are tight, then the integral foliation of $lambda$ doesnt contain any Reeb component whose core curve is homologous to zero. Moreover, the ambient manifold carries a Reebless foliation. We also show a stability theorem `a la Reeb for positive pairs of tight contact structures.
3D mapping of matter distribution in the universe through the 21 cm radio emission of atomic hydrogen is a complementary approach to optical surveys for the study of the Large Scale Structures, in particular for measuring the BAO (Baryon Acoustic Oscillation) scale up to redshifts z <~ 3 and constrain dark energy. We propose to carry such a survey through a novel method, called intensity mapping, without detecting individual galaxies radio emission. This method requires a wide band instrument, 100 MHz or larger, and multiple beams, while a rather modest angular resolution of 10 arcmin would be sufficient. The instrument would have a few thousand square meters of collecting area and few hundreds of simultaneous beams. These constraints could be fulfilled with a dense array of receivers in interferometric mode, or a phased array at the focal plane of a large antenna.
This article is the detailed version of a paper on dark matter, dark energy, and modified gravity, published in the December 2015-January 2016 special issue of La Recherche (in French)
This paper contains results concerning a conjecture made by Lang and Silverman predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition. We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curves.