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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

Machine Learning at Microsoft with ML .NETMay 14 2019May 15 2019Machine Learning is transitioning from an art and science into a technology available to every developer. In the near future, every application on every platform will incorporate trained models to encode data-based decisions that would be impossible for ... More

The HPS electromagnetic calorimeterOct 14 2016Feb 02 2017The Heavy Photon Search experiment (HPS) is searching for a new gauge boson, the so-called "heavy photon." Through its kinetic mixing with the Standard Model photon, this particle could decay into an electron-positron pair. It would then be detectable ... More

Flavor-dependent EMC effect from a nucleon swelling modelJun 24 2018Aug 22 2018We present the flavor-dependent EMC effect from nIMParton nuclear PDFs, of which the $x$-dependence is described with a nucleon swelling model. The nuclear correction originated from the nucleon swelling is considered through modifying the initial valence ... More

The HPS electromagnetic calorimeterOct 14 2016The Heavy Photon Search experiment (HPS) is searching for a new gauge boson, the so-called "heavy photon". Through its kinetic mixing with the Standard Model photon, this particle could decay into an electron-positron pair. It would then be detectable ... 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

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

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.

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

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

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

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

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

Natural generalized inverse and core of an element in semigroups, rings and Banach and Operator AlgebrasMar 16 2012Using the recent notion of inverse along an element in a semigroup, and the natural partial order on idempotents, we study bicommuting generalized inverses and define a new inverse called natural inverse, that generalizes the Drazin inverse in a semigroup, ... More

Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: a surveyJul 16 2015Oct 19 2015We present the proof of several inequalities using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, we give a new and simple proof of a lower bound of Berestycki, Nirenberg, and Varadhan concerning the ... More

Characterization of $n$-rectifiability in terms of Jones' square function: Part IJan 07 2015Jan 19 2015In this paper it is shown that if $\mu$ is a finite Radon measure in $\mathbb R^d$ which is $n$-rectifiable and $1\leq p\leq 2$, then $$\int_0^\infty \beta_{\mu,p}^n(x,r)^2\,\frac{dr}r<\infty \quad {for $\mu$-a.e. $x\in\mathbb R^d$,}$$ where $$\beta_{\mu,p}^n(x,r) ... More

Diffractive Rho Meson Electroproduction at High Q^2 and High |t|Jul 02 2002The electroproduction of rho mesons is studied at HERA with the H1 detector at high Q^2 and high |t|. Cross sections are measured as a function of Q^2, W and t. The W dependence of the gamma*-p cross section is observed to increase with Q^2 from values ... More

Canonical bases of higher-level q-deformed Fock spacesJun 09 2006We show that the transition matrices between the standard and the canonical bases of infinitely many weight subspaces of the higher-level q-deformed Fock spaces are equal.

Hadronic and rare B decays with the BaBar and Belle experimentsMay 16 2012We review recent experimental results on Bd and Bs mesons decays by the BaBar and Belle experiments. These include measurements of the color-suppressed decays B0bar to D(*)0h0, h0=pi0, eta, etaprime, omega, observation of the baryonic decay B0bar to Lambdac+ ... More

A conjecture for q-decomposition matrices of cyclotomic v-Schur algebrasMay 18 2005Apr 27 2006The Jantzen sum formula for cyclotomic v-Schur algebras yields an identity for some q-analogues of the decomposition matrices of these algebras. We prove a similar identity for matrices of canonical bases of higher-level Fock spaces. We conjecture then ... More

The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than oneJan 23 2019Jan 26 2019Let $\Omega\subset\mathbb R^{n+1}$ be open and let $E\subset \partial\Omega$ with $0<H^s(E)<\infty$, for some $s\in(n,n+1)$, satisfy a local capacity density condition. In this paper it is shown that the harmonic measure cannot be mutually absolutely ... More

Fibre derivatives: some applications to singular lagrangiansJul 27 2000The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric construction useful ... More

Well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indicesJul 31 2003We prove that, the initial value problem associated to u_{t} + i\alphau_{xx} + \beta u_{xxx} + i\gamma |u|^{2}u = 0, x,t \in R, is locally well-posed in Sobolev spaces H^{s} for s>-1/4.

Variance optimal hedging with application to Electricity marketsNov 10 2017Aug 28 2018In Electricity markets, illiquidity, transaction costs and market price characteristics prevent managers to replicate exactly contracts. A residual risk is always present and the hedging strategy depends on a risk criterion chosen. We present an algorithm ... More

Elliptic curve configurations on Fano surfacesApr 11 2008Jan 27 2010The elliptic curves on a surface of general type constitute an obstruction for the cotangent sheaf to be ample. In this paper, we give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That ... More

Dualité de Cartier et modules de BreuilNov 16 2005Let O\_K be a complete discrete valuation ring. Denote by K its fractions field and by k its residue field. Assume that k is of characteristic p>0 and perfect. Breuil gives an anti-equivalence between the category of finite flat O\_K-group schemes killed ... More

Expected number of critical points of random holomorphic sections over complex projective spaceJan 24 2017Jan 25 2017We study the high dimensional asymptotics of the expected number of critical points of a given Morse index of Gaussian random holomorphic sections over complex projective space. We explicitly compute the exponential growth rate of the expected number ... More

Phragmén's sequential method with a variance criterionNov 18 2016A variant of Phragm\'en's method for proportional representation via approval voting is briefly explored. Instead of D'Hondt's rule, this variant generalizes Sainte-Lagu\"e's rule.

Boundedness of stable solutions to semilinear elliptic equations: a surveyApr 20 2017This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known $L^{\infty}$ estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension ... More

Barycentric Subspace Analysis on ManifoldsJul 11 2016Oct 04 2017This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the ... More

What determines the ultimate precision of a quantum computer?Feb 24 2017Apr 12 2019A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one "logical" quantum bits of better quality than the original "physical" ones. QEC theory predicts that the failure probability $p_L$ of logical qubits decreases exponentially ... More

On the number of terms in the Lovelock productsNov 23 2018Mar 22 2019In this short note we wonder about the explicit expression of the expanding of the $p$-th Lovelock product. We use the 1990's works of S. A. Fulling et al. on the symmetries of the Riemann tensor, and we show that the number of independent scalars appearing ... More

Measuring precise radial velocities on individual spectral lines. I. Validation of the method and application to mitigate stellar activitySep 05 2018Oct 22 2018Stellar activity is the main limitation to the detection of Earth-twins using the RV technique. Despite many efforts in trying to mitigate the effect of stellar activity using empirical and statistical techniques, it seems that we are facing an obstacle ... More

Uniform measures and uniform rectifiabilityOct 02 2013Dec 16 2014In this paper it is shown that if $\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\mu$ is uniformly rectifiable. This had already been proved by David and Semmes in ... More

Littlewood-Paley theory and the T(1) theorem with non doubling measuresJun 05 2000Let $\mu$ be a Borel measure on $R^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(B(x,r))\leq C r^n$ for all $x\in R^d$, $r>0$, and for some fixed $0<n\leq d$. In this paper, we develop Littlewood-Paley theory for functions ... More

Weighted norm inequalities for Calderon-Zygmund operators without doubling conditionsJan 23 2001Oct 17 2011In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \mu be a Borel measure on \R^d which may be non doubling. The only condition that \mu must satisfy is \mu(B(x,r))\leq Cr^n for all x\in\R^d, ... More

Characterization of $n$-rectifiability in terms of Jones' square function: Part IJan 07 2015Nov 12 2017In this paper it is shown that if $\mu$ is a finite Radon measure in $\mathbb R^d$ which is $n$-rectifiable and $1\leq p\leq 2$, then $$\int_0^\infty \beta_{\mu,p}^n(x,r)^2\,\frac{dr}r<\infty \quad {for $\mu$-a.e. $x\in\mathbb R^d$,}$$ where $$\beta_{\mu,p}^n(x,r) ... More

The Fano surface of the Klein cubic threefoldJan 27 2010We prove that the Klein cubic threefold $F$ is the only smooth cubic threefold which has an automorphism of order 11. We compute the period lattice of the intermediate Jacobian of $F$ and study its Fano surface $S$. We compute also the set of fibrations ... 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

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

$n+1$ 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

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

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

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

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

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

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

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

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

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

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

An alternative view on the electroweak interactionsAug 23 2010We discuss an alternative to the Higgs mechanism which leads to gauge invariant masses for the electroweak bosons. The key idea is to reformulate the gauge invariance principle which, instead of being applied as usual at the level of the action, is applied ... More

Yang-Mills Theories on Noncommutative Space-TimeJan 27 2004We describe some recent progress in our understanding of Yang-Mills theories formulated on noncommutative spaces and in particular how to formulate the standard model on such spaces.

A review of Quantum Gravity at the Large Hadron ColliderMay 11 2010The aim of this article is to review the recent developments in the phenomenology of quantum gravity at the Large Hadron Collider. We shall pay special attention to four-dimensional models which are able to lower the reduced Planck mass to the TeV region ... More

Minimal Grand Unification Model in an Anthropic LandscapeJun 28 2004It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification ... More

Virtual Black Holes, Remnants and the Information ParadoxDec 19 2014We revisit the question of the contributions of Planckian quantum black holes in general and of remnants in particular to low energy physics observables. As long as quantum gravity preserves the symmetries of the low energy effective field theory, we ... More

On the 1+3 Formalism in General RelativityMay 24 2014We present in this paper the formalism for the splitting of a four-dimensional Lorentzian manifold by a set of time-like integral curves. Introducing the geometrical tensors characterizing the local spatial frames induced by the congruence (namely, the ... More

On the complexity of strongly connected components in directed hypergraphsDec 06 2011Feb 12 2013We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which ... More

Singletons and their maximal symmetry algebrasNov 19 2011Jan 02 2012Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping algebra of the ... More

Effective theory for quantum gravityAug 28 2013In this paper, we discuss an effective theory for quantum gravity and discuss the bounds on the parameters of this effective action. In particular we show that measurement in pulsars binary systems are unlikely to improve the bounds on the coefficients ... More

Some properties of the nematic radial hedgehog in Landau-de Gennes' theoryDec 05 2012In the Landau-de Gennes theoretical framework of a $Q -tensor description of nematic liquid crystals, we consider a radial hedgehog defect with strong anchoring conditions in a ball $B \subset \mathbb{R}^3$ . We show that the scalar order parameter is ... More