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Variations on the Petersen colouring conjectureMay 20 2019The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with $5$ colours such that for every edge $e$, the set of colours assigned to the edges adjacent to $e$ has cardinality either $2$ or $4$, but not $3$. ... More

Strong chromatic index and Hadwiger numberMay 15 2019We investigate the effect of a fixed forbidden clique minor upon the strong chromatic index, both in multigraphs and in simple graphs. We conjecture for each $k\ge 4$ that any $K_k$-minor-free multigraph of maximum degree $\Delta$ has strong chromatic ... More

Colouring powers and girthNov 27 2015Aug 08 2016Alon and Mohar (2002) posed the following problem: among all graphs $G$ of maximum degree at most $d$ and girth at least $g$, what is the largest possible value of $\chi(G^t)$, the chromatic number of the $t$th power of $G$? For $t\ge 3$, we provide several ... More

Distance colouring without one cycle lengthJan 26 2017We consider distance colourings in graphs of maximum degree at most $d$ and how excluding one fixed cycle length $\ell$ affects the number of colours required as $d\to\infty$. For vertex-colouring and $t\ge 1$, if any two distinct vertices connected by ... More

Fractional chromatic number, maximum degree and girthApr 11 2019We prove new lower bounds on the independence ratio of graphs of maximum degree $\Delta \in \{3,4,5\}$ and girth $g\in \{6,\dotsc,12\}$, establishing notably that $i(4,10)\ge 1/3$ and $i(5,8)\ge 2/7$. We also demonstrate that every graph $G$ of girth ... More

Fractional chromatic number, maximum degree and girthApr 11 2019Apr 21 2019We prove new lower bounds on the independence ratio of graphs of maximum degree $\Delta \in \{3,4,5\}$ and girth $g\in \{6,\dotsc,12\}$, notably $1/3$ when $(\Delta,g)=(4,10)$ et $2/7$ when $(\Delta,g)=(5,8)$. We also demonstrate that every graph of girth ... More

Strong cliques and forbidden cyclesMar 14 2019Given a graph $G$, the strong clique number $\omega_2'(G)$ of $G$ is the cardinality of a largest collection of edges every pair of which are incident or connected by an edge in $G$. We study the strong clique number of graphs missing some set of cycle ... More

Occupancy fraction, fractional colouring, and triangle fractionDec 28 2018Given $\varepsilon>0$, there exists $f_0$ such that, if $f_0 \le f \le \Delta^2+1$, then for any graph $G$ on $n$ vertices of maximum degree $\Delta$ in which the neighbourhood of every vertex in $G$ spans at most $\Delta^2/f$ edges, (i) an independent ... More

Colouring triangle-free graphs with local list sizesDec 04 2018We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs. In both our results, we permit the amount of colour made available to ... More

Bipartite induced density in triangle-free graphsAug 07 2018Aug 17 2018Any triangle-free graph on $n$ vertices with minimum degree at least $d$ contains a bipartite induced subgraph of minimum degree at least $d^2/(2n)$. This is sharp up to a logarithmic factor in $n$. We also provide a related extremal result for the fractional ... More

Random walk driven by the simple exclusion processApr 16 2014Oct 30 2015We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if the asymptotic ... More

An Alternative Matting LaplacianMay 16 2016Cutting out and object and estimate its transparency mask is a key task in many applications. We take on the work on closed-form matting by Levin et al., that is used at the core of many matting techniques, and propose an alternative formulation that ... More

Eigenvalue varieties of Brunnian linksDec 10 2015In this article, it is proved that the eigenvalue variety of the exterior of a nontrivial, non-Hopf, Brunnian link in $\mathbb{S}^{3}$ contains a nontrivial component of maximal dimension. This generalises, for Brunnian links, the nontriviality of the ... More

A new family of posets generalizing the weak order on some Coxeter groupsAug 25 2015Oct 22 2015We construct a poset from a simple acyclic digraph together with a valuation on its vertices, and we compute the values of its M\"obius function. We show that the weak order on Coxeter groups of type A, B, affine A, and the flag weak order on the wreath ... More

Magneto-electric coupling in a two-dimensional ballistic Josephson junction with in-plane magnetic textureAug 20 2014We study a Josephson junction made with a spin-textured bridge, when both Rashba and Zeeman interactions combine to generate a magneto-electric coupling between the superconducting current and the in-plane magnetic texture in the normal region. In particular, ... More

Cyclic surfaces and Hitchin components in rank 2Jun 18 2014Jul 05 2016We prove that given a Hitchin representation in a real split rank 2 group $\mathsf G_0$, there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a ... More

Continuous inverse regressionSep 02 2014Jun 01 2015We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the central subspace. ... More

Can LHC observe an anomaly in ttZ production?Apr 12 2013The cross section for production at the 7 TeV LHC has been measured. For the first time it therefore becomes possible to measure Z couplings to top quarks. Interpreting the notorious LEP1 anomaly on Z couplings to b quarks in terms of an extra-dimension ... More

Bifurcation currents in holomorphic families of rational mapsJul 03 2012The aim of these lectures is the study of bifurcations within holomorphic families of polynomials or rational maps by mean of ergodic and pluripotential theoretic tools.

Reduced Joule heating in nanowiresFeb 16 2011Feb 28 2011The temperature distribution in nanowires due to Joule heating is studied analytically using a continuum model and a Green's function approach. We show that the temperatures reached in nanowires can be much lower than that predicted by bulk models of ... More

Quantitative concentration inequalities on sample path space for mean field interactionNov 30 2005We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure ... More

Optimal coupling for mean field limitsSep 20 2010We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence ... More

Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified caseDec 05 2014Nov 12 2015In parametric estimation of covariance function of Gaussian processes, it is often the case that the true covariance function does not belong to the parametric set used for estimation. This situation is called the misspecified case. In this case, it has ... More

Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecificationJan 18 2013May 31 2013The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the estimation of ... More

Implementing the asymptotically fast version of the elliptic curve primality proving algorithmFeb 04 2005The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time cannot be proven rigorously, but heuristic arguments show that it should run in time ... More

Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for $K3$ surfaces, and the Tate conjectureJul 02 2014Aug 24 2014We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli spaces of stable ... More

Progrès récents sur les fonctions normales (d'après Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...)Jan 30 2013Given a family of smooth complex projective varieties, the Hodge conjecture predicts the algebraicity of the locus of Hodge classes. This was proven unconditionnally by Cattani, Deligne and Kaplan in 1995. In a similar way, conjectures on algebraic cycles ... More

Quantum Reidemeister torsion, open Gromov-Witten invariants and a spectral sequence of OhMar 02 2015May 08 2015We adapt classical Reidemeister torsion to monotone Lagrangian submanifolds using the pearl complex of Biran and Cornea. The definition involves generic choices of data and we identify a class of Lagrangians for which this torsion is invariant and can ... More

On Zagier's conjecture for base extensions of elliptic curvesApr 02 2012Let E be an elliptic curve over Q, and let F be a finite abelian extension of Q. Using Beilinson's theorem on a suitable modular curve, we prove a weak version of Zagier's conjecture for L(E/F,2), where E/F is the base extension of E to F.

On the ramification of modular parametrizations at the cuspsJun 12 2012Jun 02 2015We investigate the ramification of modular parametrizations of elliptic curves over $\mathbf{Q}$ at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular ... More

Relative Entropy and StatisticsAug 29 2008Apr 03 2010Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical measure of ... More

Source Spaces and Perturbations for Cluster ComplexesDec 12 2012We define objects made of marked complex disks connected by metric line segments and construct nonsymmetric and symmetric moduli spaces of these objects. This allows choices of coherent perturbations over the corresponding versions of the Floer trajectories ... More

On Lorentz spacetimes of constant curvatureJun 18 2015We describe in parallel the Lorentzian homogeneous spaces $G=\mathrm{PSL}(2,\mathbb{R})$ and $\mathfrak{g}=\mathfrak{psl}(2,\mathbb{R})$, and review some recent results relating the geometry of their quotients by discrete groups.

Topological chaos: what may this mean ?May 02 2008We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch ... More

A non-trivial example of a free-by-free group with the Haagerup propertyAug 23 2010May 16 2011The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies ... More

Steinberg representations for groups of parahoric types: the special caseFeb 17 2011In this paper, we define and study a kind of Steinberg representation for linear algebraic groups of a particular kind, called groups of parahoric type, defined overa finite field; in particular, when G is the group of F-points of a connected reductive ... More

Linear drift and entropy for regular coversOct 08 2009We consider a regular Riemannian cover $\M$ of a compact Riemannian manifold. The linear drift $\ell$ and the Kaimanovich entropy $h$ are geometric invariants defined by asymptotic properties of the Brownian motion on $\M$. We show that $\ell^2 \leq h$. ... More

On the cohomology ring of narrow Lagrangian 3-manifolds, quantum Reidemeister torsion, and the Landau-Ginzburg superpotentialMar 17 2016Jul 18 2016Let $L$ be a closed, orientable, monotone Lagrangian 3-manifold of a symplectic manifold $(M, \omega)$, for which there exists a local system such that the corresponding Lagrangian quantum homology vanishes. We show that its cohomology ring satisfies ... More

Quantum Reidemeister torsion, open Gromov-Witten invariants and a spectral sequence of OhMar 02 2015Jul 26 2017We adapt classical Reidemeister torsion to monotone Lagrangian submanifolds using the pearl complex of Biran and Cornea. The definition involves generic choices of data and we identify a class of Lagrangians for which this torsion is invariant and can ... More

Extrema of the dynamic pressure in a solitary waveDec 23 2016Jan 11 2017We study the dynamic pressure in an irrotational solitary wave propagating at the surface of water over a flat bed, under the influence of gravity. We consider the nonlinear regime, that is, the case of waves of moderate to large amplitude. We prove that, ... More

The Mean-Field Limit for a Regularized Vlasov-Maxwell DynamicsNov 07 2011The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and Dobrushin [Func. Anal. Appl. ... More

Instability of an integrable nonlocal NLSDec 09 2016Jan 27 2017In this note we discuss the global dynamics of an integrable nonlocal NLS on $\mathbb{R}$, which has been the object of recent investigation by integrable systems methods. We prove two results which are in striking contrast with the case of the local ... More

Eulerian graphs and local complementationJan 15 2007We define pure graphs, invertible graphs, and the notion of complementation of bicoloured graphs. The study of pure graphs is motivated by two conjectures about the transition systems of eulerian graphs and by the Cycle Double Cover Conjecture. We show ... More

Functions of degree 4e that are not APN infinitely oftenFeb 02 2016We prove a necessary condition for some polynomials of degree 4e (e an odd number) to be APN over F q n for large n, and we investigate the polynomials f of degree 12.

Open Access and Discovery Tools: How do Primo Libraries Manage Green Open Access Collections?Sep 15 2015Feb 28 2016Scholarly Open Access repositories contain lots of treasures including rare or otherwise unpublished materials and articles that scholars self-archive, often as part of their institution's mandate. But it can be hard to discover this material unless users ... More

Fourier-based schemes for computing the mechanical response of composites with accurate local fieldsDec 21 2014We modify the Green operator involved in Fourier-based computational schemes in elasticity, in 2D and 3D. The new operator is derived by expressing continuum mechanics in terms of centered differences on a rotated grid. Use of the modified Green operator ... More

A natural generalization of Balanced TableauxJul 23 2014Mar 10 2016We introduce the notion of "type" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any permutation. We then generalize ... More

Présentation des groupes de tresses purs et de certaines de leurs extensionsNov 27 2015Jan 07 2016This paper dates back to 1999 but was never published. The major part of it was included in the joint paper [Digne-Gomi, Presentation of pure braid groups, J. Knot Theory and its Ramifications 10 (2001) 609--623]. Sections 2 and 6 were not included there. ... More

PSF and field of view characteristics of imaging and nulling interferometersApr 01 2010In this communication are presented some complements to a recent paper entitled "Simple Fourier optics formalism for high angular resolution systems and nulling interferometry", dealing with imaging and nulling capacities of a few types of multi-aperture ... More

Noisy data clusters are hollowJun 10 2015Mar 10 2016A new vision in multidimensional statistics is proposed impacting severalareas of application. In these applications, a set of noisy measurementscharacterizing the repeatable response of a process is known as a realizationand can be seen as a single point ... More

Thermoelectric efficiency in the space-charge-limited transport regime in semiconductorsSep 27 2012The thermoelectric efficiency of semiconductors is usually considered in the ohmic electronic transport regime, which is achieved through high doping. Here we consider the opposite regime of low doping where the current-voltage characteristics are nonlinear ... More

On parametric extensions over number fieldsFeb 22 2016Mar 07 2016Given a number field $F$, a finite group $G$ and an indeterminate $T$, {\it{a $G$-parametric extension over $F$}} is a finite Galois extension $E/F(T)$ with Galois group $G$ and $E/F$ regular that has all the Galois extensions of $F$ with Galois group ... More

Hilbert specialization results with local conditionsDec 24 2014Feb 15 2016Given a field $k$ of characteristic zero and an indeterminate $T$, the main topic of the paper is the construction of specializations of any given finite extension of $k(T)$ of degree $n$ that are degree $n$ field extensions of $k$ with specified local ... More

Asymptotic direction for random walks in random environmentsDec 16 2005Dec 11 2007In this paper we study the property of asymptotic direction for random walks in random i.i.d. environments (RWRE). We prove that if the set of directions where the walk is transient is non empty and open, the walk admits an asymptotic direction. The main ... More

An introduction to finite volumes for gas dynamicsJan 22 2011We propose an elementary introduction to the finite volume method in the context of gas dynamics conservation laws. Our approach is founded on the advection equation, the exact integration of the associated Cauchy problem, and the so-called upwind scheme ... More

Frobenius distribution for pairs of elliptic curves and exceptional isogeniesNov 11 2014Let E and E' be two elliptic curves over a number field. We prove that the reductions of E and E' at a finite place p are geometrically isogenous for infinitely many p, and draw consequences for the existence of supersingular primes. This result is an ... More

A remark on the Torelli theorem for cubic fourfoldsSep 20 2012In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.

Information-theoretical label embeddings for large-scale image classificationJul 19 2016We present a method for training multi-label, massively multi-class image classification models, that is faster and more accurate than supervision via a sigmoid cross-entropy loss (logistic regression). Our method consists in embedding high-dimensional ... More

Xception: Deep Learning with Depthwise Separable ConvolutionsOct 07 2016Oct 11 2016We present an interpretation of Inception modules in convolutional neural networks as being an intermediate step in-between regular convolution and the \textit{depthwise separable convolution} operation (a depthwise convolution followed by a pointwise ... More

Edwards curves and CM curvesApr 15 2009Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves ... More

Coarse Lipschitz embeddings of James spacesJun 07 2016We prove that, for $1 < p \neq q < \infty$, there does not exist any coarse Lipschitz embedding between the two James spaces $J_p$ and $J_q$, and that, for $1 < p < q < \infty$ and $1 < r < \infty$ such that $r \notin \{p,q\}$, $J_r$ does not coarse Lipschitz ... More

The $L^1$ gradient flow of a generalized scale invariant Willmore energy for radially non increasing functionsNov 13 2014Jul 06 2016We use the minimizing movement theory to study the gradient flow associated with a non-regular relaxation of a geometric functional derived from the Willmore energy. Thanks to the coarea formula, one can define a Willmore energy on regular functions of ... More

An inverse scattering problem for short-range systems in a time-periodic electric fieldJun 20 2005We consider the time-dependent Hamiltonian $H(t)= {1 \over 2} p^2 -E(t) \cdot x + V(t,x)$ on $L^2(R^n)$, where the external electric field $E(t)$ and the short-range electric potential $V(t,x)$ are time-periodic with the same period. It is well-known ... More

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactionsMar 15 2012Apr 16 2014We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously ... More

Classical and quantum systems: transport due to rare eventsJan 20 2017We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum ... More

Présentations duales des groupes de tresses de type affine $\tilde A$Feb 07 2004Sep 06 2005In the present paper we define dual monoids for all Artin-Tits groups and we prove that for the type $\tilde A_n$ we get a (quasi)-Garside structure. Such a structure provides normal forms for the Artin-Tits group elements and allows to solve some questions ... More

Régulateurs modulaires explicites via la méthode de Rogers-ZudilinFeb 09 2016We compute the regulator of Beilinson-Deninger-Scholl elements in terms of special values of L-functions of modular forms, using the Rogers-Zudilin method.

Equivalent partial differential equations of a lattice Boltzmann schemeJun 08 2018We show that when we formulate the lattice Boltzmann equation with a small time step $\Delta$t and an associated space scale $\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish macroscopic fluid equations ... More

Recent Results on the Periodic Lorentz GasJun 01 2009Jun 25 2009The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some appropriate scaling ... More

On the Periodic Lorentz Gas and the Lorentz Kinetic EquationMar 27 2007We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence ... More

Jacobi's bound and normal forms computations. A historical surveyNov 13 2009May 01 2010Jacobi is one of the most famous mathematicians of his century. His name is attached to many results in various fields of mathematics and his complete works in seven volumes have been available since the end of the XIXth century and are very often quoted ... More

The radiation condition at infinity for the high-frequency Helmholtz equation with source term: a wave packet approachMar 16 2005We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter $\a>0$. The high-frequency (or: semi-classical) parameter is $\eps>0$. We let $\eps$ and $\a$ go to zero simultaneously. We assume that the zero ... More

Thermoplasticity as a nonsmooth phenomenonDec 16 2017Feb 20 2018This paper develops the multisymplectic formulation of nonsmooth elastoplastic phenomena, where the plastic deformation and the associated thermodynamic entropy evolve by jumps.

Efficient tensor tomography in fan-beam coordinates. II: Attenuated transformsApr 26 2017Nov 02 2017This article extends the author's past work [Inv. Probl. Imaging, 10:2 (2016), 433--459] to attenuated X-ray transforms, where the attenuation is complex-valued and only depends on position. We give a positive and constructive answer to the attenuated ... More

Numerical implementation of geodesic X-ray transforms and their inversionSep 24 2013Apr 16 2014We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in \cite{Pestov2004,Krishnan2010} ... More

An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equationOct 05 2011An inhomogeneous nonlinear Schr\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the stationary equation. ... More

On the Dynamics of Large Particle Systems in the Mean Field LimitJan 23 2013This course explains how the usual mean field evolution partial differential equations (PDEs) in Statistical Physics - such as the Vlasov-Poisson system, the vorticity formulation of the two-dimensional Euler equation for incompressible fluids, or the ... More

De Newton à Boltzmann et Einstein: validation des modèles cinétiques et de diffusionNov 30 2014The kinetic theory of Maxwell and Boltzmann has been the subject of major scientific controversies. The alleged incompatibility between the reversible nature of the equations of classical mechanics and the increase of entropy, which, in the kinetic theory ... More

From the Kinetic Theory of Gases to Continuum MechanicsSep 22 2010Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like that of an ... More

Borne sur le degré des polynômes presque parfaitement non-linéairesMay 09 2006May 02 2008The vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect non-linearity (APN) ... More

Lengthening deformations of singular hyperbolic toriJun 18 2015Let $S$ be a torus with a hyperbolic metric admitting one puncture or cone singularity. We describe which infinitesimal deformations of $S$ lengthen (or shrink) all closed geodesics. We also study how the answer degenerates when $S$ becomes Euclidean, ... More

Distinction of the Steinberg representation III: the tamely ramified caseAug 28 2014Apr 20 2016Let $F$ be a nonarchimedean local field, let $E$ be a Galois quadratic extension of $F$ and let $G$ be a quasisplit group defined over $F$; a conjecture by Dipendra Prasad states that the Steinberg representation of $G(E)$ is then $\chi$-distinguished ... More

A characterization of groups of parahoric typeFeb 15 2012May 09 2015Let F be a local henselian nonarchimedean field of residual field k, and let G be the group of F-points of a connected reductive group defined over F. It is well-known that the quotient of any parahoric subgroup of G by its first congruence subgroup is ... More

Strip maps of small surfaces are convexJun 26 2015The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of small complexity: ... More

A complete set of multidimensional Bell inequalitiesJul 12 2011Oct 24 2011We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf, and by Zukowski and Brukner, for the two-dimensional case. Our construction applies for the n parties, two-observables case, where ... More

Modular equations for some $η$-productsFeb 08 2011The classical modular equations involve bivariate polynomials that can be seen to be univariate with coefficients in the modular invariant $j$. Kiepert found modular equations relating some $\eta$-quotients and the Weber functions $\gamma_2$ and $\gamma_3$. ... More

Finite volumes and mixed Petrov-Galerkin finite elements : the unidimensional problemJan 04 2014For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some universal function. ... More

Nonlinear Interpolation and Total Variation Diminishing SchemesJun 20 2010The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We prove that ... More

Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemesJan 02 2014We show that an hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes with the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one ... More

Petrov-Galerkin Finite VolumesDec 08 2010For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Raviart-Thomas basis.

Dual Raviart-Thomas mixed finite elementsDec 08 2010For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Raviart-Thomas basis.

FoCaLiZe: Inside an F-IDEApr 26 2014For years, Integrated Development Environments have demonstrated their usefulness in order to ease the development of software. High-level security or safety systems require proofs of compliance to standards, based on analyses such as code review and, ... More

Regularity of the entropy for random walks on hyperbolic groupsOct 14 2011Oct 21 2013We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.

Parametric Galois ExtensionsOct 24 2013Sep 18 2014Given a field $k$ and a finite group $H$, {\it{an $H$-parametric extension over $k$}} is a finite Galois extension of $k(T)$ of Galois group containing $H$ which is regular over $k$ and has all the Galois extensions of $k$ of group $H$ among its specializations. ... More

Specialization results and ramification conditionsOct 08 2013Mar 15 2015Given a hilbertian field $k$ of characteristic zero and a finite Galois extension $E/k(T)$ with group $G$ such that $E/k$ is regular, we produce some specializations of $E/k(T)$ at points $t_0 \in \mathbb{P}^1(k)$ which have the same Galois group but ... More

Approche pédagogique sur l'innocuité des technologies de réseaux sans filNov 07 2007The wireless networks technologies are becoming more prevalent. As part of our courses, we have to deal with the technical aspects of these technologies. However, the experience of mobile telephony has shown fears that these products can lead to the general ... More

Spectroscopy of atomic hydrogen. How is the Rydberg constant determined?Sep 17 2008This article presents a review of the most recent theoretical and experimental results in hydrogen. We particularly emphasize the methods used to deduce the Rydberg constant $R_\infty$ and we consider the prospects for future improvements in the precision ... More

The Tate conjecture for K3 surfaces over finite fieldsJun 18 2012Jul 07 2012Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic ... More

Remarks on the Lefschetz standard conjecture and hyperkähler varietiesFeb 26 2010Jul 06 2010We study the Lefschetz standard conjecture on a smooth complex projective variety X. In degree 2, we reduce it to a local statement concerning deformations of vector bundles on X. When X is hyperk\"ahler, we show that the existence of nontrivial deformations ... More

Conjugate varieties with distinct real cohomology algebrasJun 25 2007Jul 15 2008Using constructions of Voisin, we exhibit a smooth projective variety defined over a number field k and two complex embeddings of k, such that the two complex manifolds induced by these embeddings have non isomorphic cohomology algebras with real coefficients. ... More