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LASER: Lightweight And SEcure Remote keyless entry protocol (Extended version)May 14 2019May 15 2019Since Remote Keyless Entry (RKE) systems started to be widely used, several vulnerabilities in their protocols have been found. Attacks such as jamming-and-replay attacks and relay attacks are still effective against most recent RKE systems, even when ... More

LASER: Lightweight And SEcure Remote keyless entry protocol (Extended version)May 14 2019Since Remote Keyless Entry (RKE) systems started to be widely used, several vulnerabilities in their protocols have been found. Attacks such as jamming-and-replay attacks and relay attacks are still effective against most recent RKE systems, even when ... More

Multi Web Audio Sequencer: Collaborative Music MakingMay 16 2019Recent advancements in web-based audio systems have enabled sufficiently accurate timing control and real-time sound processing capabilities. Numerous specialized music tools, as well as digital audio workstations, are now accessible from browsers. Features ... More

Higher spin algebras as higher symmetriesApr 06 2007Aug 23 2007The exhaustive study of the rigid symmetries of arbitrary free field theories is motivated, along several lines, as a preliminary step in the completion of the higher-spin interaction problem in full generality. Some results for the simplest example (a ... More

Clusters, Graphs, and Networks for Analysing Internet-Web-Supported Communication within a Virtual CommunityJul 10 2007The proposal is to use clusters, graphs and networks as models in order to analyse the Web structure. Clusters, graphs and networks provide knowledge representation and organization. Clusters were generated by co-site analysis. The sample is a set of ... More

Geometry of the Feigenbaum mapNov 15 1997Aug 11 1998We show that the Feigenbaum-Cvitanovic equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which ... More

Asymptotically safe weak interactionsDec 26 2010We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak ... More

Very Light Cosmological Scalar Fields from a Tiny Cosmological ConstantMay 03 2007Jun 28 2007We discuss a mechanism which generates a mass term for a scalar field in an expanding universe. The mass of this field turns out to be generated by the cosmological constant and can be naturally small if protected by a conformal symmetry which is however ... More

Softening the Naturalness ProblemFeb 07 2003Mar 17 2003It was observed by Veltman a long time ago that a special value for the Higgs boson mass could lead to a cancellation of the quadratically divergent corrections to the Higgs boson's squared mass which appear at one loop. We present a class of low energy ... More

Requirements Management for Service Providers: the Case of Services for CitizensJan 19 2013Take the Internet of Things, a piece of cloud computing, a handful of smart cities, don't forget social platforms, flavour it with mobile technologies and ever-changing environments, shake it up and... voila! What a wonderful service! Oops! Wait a minute, ... More

Essential spectrum of local multi-trace boundary integral operatorsAug 03 2015Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does ... More

Quantum Mechanics, Gravity and Modified Quantization RelationsApr 29 2015In this paper we investigate a possible energy scale dependence of the quantization rules and in particular, from a phenomenological point of view, an energy scale dependence of an effective $\hbar$. We set a bound on the deviation from the value of $\hbar$ ... More

A new light on the breaking of uniaxial symmetry in nematicsJul 01 2013Sep 18 2013Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that energy minimizers among uniaxially symmetric configurations ... More

Random matrix over a DVR and LU factorizationDec 03 2012Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting a LU decomposition, it could happen that the entries of the factors L and U do not lie in R, but just in K. Having a good control on the valuations ... More

Hadronic B Decays to Charm and Charmonium With the BaBar ExperimentSep 17 2008Oct 17 2008The {\it BaBar} experiment has recorded the decays of more than 465$\times 10^6 B\bar{B}$ pairs since 1999, and is reaching an unprecedented precision in the measurement of hadronic B decays. The following results are presented: tests of QCD factorization ... More

Renormalized stress tensor in one-bubble spacetimesApr 08 1999We compute the two-point function and the renormalized expectation value of the stress tensor of a quantum field interacting with a nucleating bubble. Two simple models are considered. One is the massless field in the Vilenkin-Ipser-Sikivie spacetime ... More

On concrete models for local operator spacesOct 28 2008In this short note, we propose a concrete analogue of the space $\cL(H)$ for local operator spaces, the multinormed $C^*$-algebra $\displaystyle\prod_{\alpha} \cL(H_{\alpha})$.

Representations semi-stables de torsion dans le cas peu ramifieJul 17 2004Oct 24 2004Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the residual field). ... More

A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decompositionFeb 25 2000Given a doubling measure $\mu$ on $R^d$, it is a classical result of harmonic analysis that Calderon-Zygmund operators which are bounded in $L^2(\mu)$ are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes ... More

Painleve's problem and the semiadditivity of analytic capacityApr 02 2002Let $\gamma(E)$ be the analytic capacity of a compact set $E$ and let $\gamma_+(E)$ be the capacity of $E$ originated by Cauchy transforms of positive measures. In this paper we prove that $\gamma(E)\approx\gamma_+(E)$ with estimates independent of $E$. ... More

A priori estimates for solutions of a nonlinear dispersive equationAug 24 2005Mar 19 2010This paper has been withdrawn by the author due to a crucial error.

Sharp global well-posedness for a higher order Schrödinger equationApr 28 2005Apr 30 2005Using the theory of almost conserved energies and the ``I-method'' developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher order Schr\"odinger equation is globally well-posed in Sobolev spaces of ... More

Principal values for Riesz transforms and rectifiabilityAug 01 2007Let $E\subset R^d$ with $H^n(E)<\infty$, where H^n stands for the $n$-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit $$\lim_{\ve\to0}\int_{y\in E:|x-y|>\ve} \frac{x-y}{|x-y|^{n+1}} dH^n(y)$$ exists ... More

Cosmological Evolution of the Higgs Boson's Vacuum Expectation ValueJul 21 2017We point out that the expansion of the universe leads to a cosmological time evolution of the vacuum expectation of the Higgs boson. Within the standard model of particle physics, the cosmological time evolution of the vacuum expectation of the Higgs ... More

The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approachNov 15 2016We numerically study an Asset Liability Management problem linked to the decommissioning of French nuclear power plants. We link the risk aversion of practitioners to an optimization problem. Using different price models we show that the optimal solution ... More

Computations with p-adic numbersJan 24 2017This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts: first, we ... More

The Dual Standard Model and the 750 GeV Events at the LHCApr 21 2016The aim of this short paper is to discuss the recently observed excess at 750 GeV by both CMS and ATLAS in the light of the dual standard model. Within this framework it is natural to introduce neutral spin 0 and/or spin 2 $SU(2)$ glue mesons which could ... More

On the bit-size of non-radical triangular setsOct 17 2017We present upper bounds on the bit-size of coefficients of non-radical lexicographical Groebner bases in purely triangular form (triangular sets) of dimension zero. This extends a previous work [Dahan-Schost, Issac'2004], constrained to radical triangular ... More

Rigid covariance, equivalence principle and Fermi rigid coordinates:gravitational wavesJul 17 2018Jan 21 2019For a given space-time and for an arbitrary time-like geodesic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigid covariant. We then apply these conditions to linear plane gravitational waves.

Improved Low-qubit Hidden Shift AlgorithmsJan 31 2019Hidden shift problems are relevant to assess the quantum security of various cryptographic constructs. Multiple quantum subexponential time algorithms have been proposed. In this paper, we propose some improvements on a polynomial quantum memory algorithm ... More

Rectifiability of measures and the $β_p$ coefficientsAug 07 2017Jan 19 2018In some former works of Azzam and Tolsa it was shown that $n$-rectifiability can be characterized in terms of a square function involving the David-Semmes $\beta_2$ coefficients. In the present paper we construct some counterexamples which show that a ... More

Courants dynamiques pluripolairesMar 08 2010We show the existence of birational self-maps f of P^k which are algebraically stable with algebraic degree d, for which there is a unique positive closed (1,1) current T satisfying f^*T=d T and ||T||=1 and for which the current T gives total mass to ... More

Jump formulas for singular integrals and layer potentials on rectifiable setsNov 19 2018Nov 28 2018In this paper the jump formulas for the double layer potential and other singular integrals are proved for arbitrary rectifiable sets, by defining suitable non-tangential limits. The arguments are quite straightforward and only require some Calder\'on-Zygmund ... More

Virial expansion with Feynman diagramsSep 22 2011We present a field theoretic method for the calculation of the second and third virial coefficients b2 and b3 of 2-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b3 in terms of the ... More

Estimation des dimensions de certaines variétés de KisinMay 13 2010Jan 30 2011In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the dimension we ... More

The Transverse SpinJul 25 2002Sep 30 2002Contents : 1. Pre-history 2. Transversity versus helicity 3. The massless limit. "Cardan" and "see-saw" transformations 4. Transversity distribution delta q(x). The diquark spectator model 5. Soffer inequality 6. Tensor charge sum rule 7. t-channel analysis ... More

Construction optimale d'images bolometriques - Contribution a l'etude du milieu interstellaire et du rayonnement fossileOct 02 2002This work takes part of the development of far-infrared and millimeter astrophysics. We have worked on the data processing and analysis in the fields of the Galactic interstellar medium, through the dust thermal emission, and cosmology through the observation ... More

Iterative map-making methods for Cosmic Microwave Background data analysisSep 27 2001The map-making process of Cosmic Microwave Background data involves linear inversion problems which cannot be performed by a brute force approach for the large timelines of most modern experiments. We present optimal iterative map-making methods, both ... More

Planck Length and CosmologyApr 11 2007We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length. Furthermore we give ... More

Radiative Lepton Decays and the Substructure of LeptonsAug 08 2001The leptons are viewed as composite objects, exhibiting anomalous magnetic moments and anomalous flavor-changing transition moments. The decay \mu \to e \gamma is expected to occur with a branching ratio of the same order as the present experimental limit. ... More

Equivalence Principle and the Gauge Hierarchy ProblemAug 21 2007Mar 19 2008We show that the gauge hierarchy problem can be solved in the framework of scalar-tensor theories of gravity very much in the same way as it is solved in the Randall-Sundrum scenario. Our solution involves a fine-tuning of the gravitational sector. However ... More

On the Precision of a Length MeasurementJan 09 2007We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime ... More

Space-Time Symmetries of Noncommutative SpacesNov 15 2004Apr 13 2005We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz ... More

Hedging Swing contract on gas marketsAug 27 2012Swing options on the gas market are american style option where daily quantities exercices are constrained and global quantities exerciced each year constrained too. The option holder has to decide each day how much he consumes of the quantities satisfying ... More

Handel's fixed point theorem revisitedAug 10 2012Michael Handel proved in [7] the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. ... More

Resultants and subresultants of p-adic polynomialsJul 23 2015We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are highly unstable ... More

Some non monotone schemes for Hamilton-Jacobi-Bellman equationsDec 18 2013Feb 11 2015We extend the theory of Barles Jakobsen to develop numerical schemes for Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation. We give ... More

Some non monotone schemes for time dependent Hamilton-Jacobi-Bellman equations in stochastic controlOct 23 2013Jan 21 2015We introduce some approximation schemes for linear and fully non-linear diffusion equations of Bellman-Isaacs type. Although they are not monotone one can prove their convergence to the viscosity solution of the problem. Effective implementation of these ... More

Model selection and estimation of a component in additive regressionSep 28 2012Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or Gaussian hypothesis. ... More

Classes of semigroups modulo Green's relation HMar 16 2012Inverses semigroups and orthodox semigroups are either defined in terms of inverses, or in terms of the set of idempotents E(S). In this article, we study analogs of these semigroups defined in terms of inverses modulo Green's relation H, or in terms ... More

Hyperelliptic curves covering an elliptic curve twiceMar 18 2013We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also show that, if ... More

Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regressionJul 16 2008Dec 30 2008Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent copies of ... More

Bifurcation analysis in a frustrated nematic cellOct 25 2013Nov 13 2013Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the cell width ... More

Calderon-Zygmund capacities and Wolff potentials on Cantor setsJan 18 2010Jan 31 2013We show that, for some Cantor sets in R^d, the capacity g_s associated to the s-dimensional Riesz kernel x/|x|^{s+1} is comparable to the capacity C_{2(d-s)/3,3/2} from non linear potential theory. It is an open problem to show that, when s is positive ... More

Fano surfaces with 12 or 30 elliptic curvesJan 27 2010Feb 05 2010Curves of low genus on a surface carry important informations on that surface. We study the Fano surfaces of lines of cubic threefolds that contain 12 or 30 elliptic curves. We determine their Picard number and compute a basis of the N\'eron-Severi group ... More

On generalized inverses and Green's relationsMar 10 2009We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose ... More

Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonalityMay 07 2008In this paper we study some questions in connection with uniform rectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are ... More

On generalized Kummer surfaces and the orbifold Bogomolov-Miyaoka-Yau inequalityAug 30 2017Dec 29 2017A generalized Kummer surface $X=Km(T,G)$ is the resolution of a quotient of a torus $T$ by a finite group of symplectic automorphisms $G$. We complete the classification of generalized Kummer surfaces by studying the two last groups which have not been ... More

$n+1$ formalism of $f($Lovelock$)$ gravityDec 09 2017May 02 2018In this note we perform the $n+1$ decomposition, or Arnowitt Deser Misner (ADM) formulation of $f($Lovelock$)$ gravity theory. The hamiltonian form of Lovelock gravity was known since the work of C. Teitelboim and J. Zanelli in 1987, but this result had ... More

BMO, H^1, and Calderon-Zygmund operators for non doubling measuresFeb 18 2000Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in this paper, ... More

Abelian varieties with many endomorphisms and their absolutely simple factorsFeb 04 2011We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties A/k satisfying that $\End_k^0(A)$ is a ... More

Regularity of C^1 and Lipschitz domains in terms of the Beurling transformJan 25 2012Let D be a bounded planar C^1 domain, or a Lipschitz domain "flat enough", and consider the Beurling transform of 1_D, the characteristic function of D. Using a priori estimates, in this paper we solve the following free boundary problem: if the Beurling ... More

Bounded negativity, Miyaoka-Sakai inequality and elliptic curve configurationsNov 25 2014Mar 14 2015Similarly to the linear Harbourne constant recently defined, we study the elliptic $H$-constants of $\mathbb{P}^{2}$ and Abelian surfaces. We exhibit configurations of smooth plane cubic curves whose Harbourne index is arbitrarily close to $-4$. As a ... More

Squares in arithmetic progression over number fieldsSep 09 2009We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to $k$-powers ... More

Mass transport and uniform rectifiabilityMar 08 2011Aug 29 2011In this paper we characterize the so called uniformly rectifiable sets of David and Semmes in terms of the Wasserstein distance $W_2$ from optimal mass transport. To obtain this result, we first prove a localization theorem for the distance $W_2$ which ... More

Polynomial parametrizations of length $4$ Büchi sequencesAug 18 2010B\"uchi's problem asks whether there exists a positive integer $M$ such that any sequence $(x_n)$ of at least $M$ integers, whose second difference of squares is the constant sequence $(2)$, satisifies $x_n^2=(x+n)^2$ for some $x\in\Z$. A positive answer ... More

Sobolev and isoperimetric inequalities with monomial weightsOct 16 2012Apr 20 2015We consider the monomial weight $|x_1|^{A_1}...|x_n|^{A_n}$ in $\mathbb R^n$, where $A_i\geq0$ is a real number for each $i=1,...,n$, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue ... More

Regularity of stable solutions up to dimension 7 in domains of double revolutionFeb 06 2012We consider the class of semi-stable positive solutions to semilinear equations $-\Delta u=f(u)$ in a bounded domain $\Omega\subset\mathbb R^n$ of double revolution, that is, a domain invariant under rotations of the first $m$ variables and of the last ... More

Primordial Black Holes and a Large Hidden SectorJul 17 2010Nov 01 2010In this note we point out that primordial black holes could be much shorter lived than usually assumed if there is a large hidden sector of particles that only interacts gravitationally with the particles of the standard model. The observation of the ... More

Cosmological Constant and Noncommutative SpacetimeOct 19 2005We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra ... More

An algorithm for computing the canonical bases of higher-level q-deformed Fock spacesSep 14 2006Dec 12 2006We derive a straightening-free algorithm that computes the canonical bases of any higher-level q-deformed Fock space.

Barycentric Subspace Analysis on ManifoldsJul 11 2016This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and more general type of family of subspaces in manifolds that we call barycen-tric subspaces. They are implicitly defined ... More

Determination of the best optimal estimation parameters for validation of infrared hyperspectral sounding retrievalsMay 14 2012The availability of hyperspectral infrared remote sensing instruments, like AIRS and IASI, on board of Earth observing satellites opens the possibility of obtaining high vertical resolution atmospheric profiles. We present an objective and simple technique ... More

Uniaxial symmetry in nematic liquid crystalsFeb 05 2014Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied, except in very ... More

Quantum black holes and effective quantum gravity approachesDec 21 2014This is the text of the invited talk I have given at the Karl Schwarzschild Meeting in Frankfurt in 2013.

Dispersive and dissipative effects in quantum field theory in curved space-time to model condensed matter systemsNov 06 2014The two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with ... More

The Lightest of Black HolesOct 10 2014In this paper we consider general relativity in the large $N$ limit, where $N$ stands for the number of particles in the model. Studying the resummed graviton propagator, we propose to interpret its complex poles as black hole precursors. Our main result ... More

On lexicographic Groebner bases of radical ideals in dimension zero: interpolation and structureJul 17 2012Oct 01 2012Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for radical ideals of ... More

Comments on higher-spin symmetriesJul 28 2008Nov 14 2010The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the torsion constraints, ... More

Représentations galoisiennes p-adiques et (phi,tau)-modulesOct 23 2010Oct 01 2012Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible system of p^n-th ... More

About Inverse 3-SATMar 18 2013Aug 26 2013The Inverse 3-SAT problem is known to be coNP Complete. This article shows a new interesting way to solve directly the problem by using closure under resolution and partial assignment properties. An algorithm is proposed which lets solve the (co)Inverse ... More

Conjecture de l'inertie modérée de SerreSep 29 2005Let K be a local field of mixte characteristics. We assume that the residue field is perfect. Let X\_K be a proper smooth scheme over K admitting an integer model X which is proper and semi-stable. In this article, we prove a period isomorphism linking ... More

Schémas en groupes et poids de Diamond-SerreMay 09 2007This note is a correction of (statement and proof of) proposition 3.3.1 of Toby Gee's preprint intitled *On the weights of mod p Hilbert modular forms*. The aim is to compare Galois representations arising from extensions of some group schemes (over the ... More

Genus 2 curve configurations on Fano surfacesFeb 24 2010We study the configurations of genus 2 curves on the Fano surfaces of cubic threefolds. We establish a link between some involutive automorphisms acting on such a surface S and genus 2 curves on S. We give a partial classification of the Fano surfaces ... More

Adaptive sparse grids for time dependent Hamilton-Jacobi-Bellman equations in stochastic controlAug 19 2014We introduce some sparse grids interpolations used in Semi-Lagrangian schemes for linear and fully non-linear diffusion Hamilton Jacobi Bellman equations arising in stochastic control. We prove that the method introduced converges toward the viscosity ... More

Vanishing of Quantum Gravitational Corrections to Vacuum Solutions of General Relativity at Second Order in CurvatureOct 23 2018In this note we prove that quantum gravitational corrections to vacuum solutions of Einstein's equations vanish at second order in curvature.

On the concavity of a sum of elementary symmetric polynomialsDec 12 2017We introduce a new problem on the elementary symmetric polynomials $\sigma_k$, stemming from the constraint equations of some modified gravity theory. For which coefficients is a linear combination of $\sigma_k$ $1/p$-concave, with $0 \leq k \leq p$? ... More

The constraint equations of Lovelock gravity theories: a new $σ_k$-Yamabe problemDec 12 2017Jul 09 2018This paper is devoted to the study of the constraint equations of the Lovelock gravity theories. In the case of an empty, compact, conformally flat, time-symmetric, and space-like manifold, we show that the Hamiltonian constraint equation becomes a generalisation ... More

On the number of equilibria with a given number of unstable directionsSep 12 2017We compute the large-dimensional asymptotics for the average number of equilibria with a fixed number of unstable directions for random Gaussian ODEs on a sphere. We also discuss the effects that the value of the Lagrange multiplier of the vector field ... More

Optimal Transportation of Vector-Valued MeasuresJan 15 2019Given two n-dimensional measures $\mu$ and $\nu$ on Polish spaces, we propose an optimal transportation's formulation, inspired by classical Kan-torovitch's formulation in the scalar case. In particular, we established a strong duality result and as a ... More

Regular graphs of large girth and arbitrary degreeOct 24 2011Sep 21 2013For every integer d > 9, we construct infinite families {G_n}_n of d+1-regular graphs which have a large girth > log_d |G_n|, and for d large enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special set of d+1 generators whose choice ... More

Rectifiable measures, square functions involving densities, and the Cauchy transformAug 29 2014Jan 31 2015This paper is devoted to the proof of two related results. The first one asserts that if $\mu$ is a Radon measure in $\mathbb R^d$ satisfying $$\limsup_{r\to 0} \frac{\mu(B(x,r))}{r}>0\quad \text{ and }\quad \int_0^1\left|\frac{\mu(B(x,r))}{r} - \frac{\mu(B(x,2r))}{2r}\right|^2\,\frac{dr}r< ... More

Trivial points on towers of curvesJan 12 2012We define and study trivial points on towers of curves over number fields, and we show their finiteness in some cases. We relate these to the unboundeness of the gonality of the curves, which we show under some hypothesis. The problem is related to recent ... More

Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEsMay 14 2018We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality and it can be used to solve problems that were out of ... More

Issues in Electric-Magnetic DualitySep 20 2002Chapters : 1. Introduction to electric-magnetic duality 2. Classical duality in bosonic brane electrodynamics 3. Massless spin two gauge theory 4. Duality-symmetric actions and chiral forms 5. BRST quantization of duality-symmetric Maxwell's theory 6. ... More

A matrix phase for the phi^4 scalar field on the fuzzy sphereFeb 27 2004May 13 2004The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is also one of ... More

Grand Unification on Noncommutative SpacetimeMay 12 2006Mar 22 2007We compute the beta-functions of the standard model formulated on a noncommutative spacetime. If we assume that the scale for spacetime noncommutativity is of the order of 2.2 \times 10^{15} GeV we find that the three gauge couplings of the standard model ... More

Quantum Electrodynamics on Noncommutative SpacetimeApr 05 2006Mar 22 2007We propose a new method to quantize gauge theories formulated on a canonical noncommutative spacetime with fields and gauge transformations taken in the enveloping algebra. We show that the theory is renormalizable at one loop and compute the beta function ... More

Symmetries, Microcausality and Physics on Canonical Noncommutative SpacetimeMay 03 2006May 09 2006In this paper we describe how to implement symmetries on a canonical noncommutative spacetime. We focus on noncommutative Lorentz transformations. We then discuss the structure of the light cone on a canonical noncommutative spacetime and show that field ... More

What are the Bounds on Space-Time Noncommutativity?Jan 14 2004In this article we consider the bounds on the noncommutative nature of space-time. We argue that these bounds are extremely model dependent. In the only phenomenologically viable framework, i.e. when the fields are taken to be in the enveloping of the ... More