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Some Dipole Shower StudiesOct 01 2017Mar 30 2018Parton showers have become a standard component in the description of high-energy collisions. Nowadays most final-state ones are of the dipole character, wherein a pair of partons branches into three, with energy and momentum preserved inside this subsystem. ... More

A Monte-Carlo Simulation of Double Parton ScatteringJun 11 2019In this work, a new Monte-Carlo simulation of double parton scattering (DPS) at parton level is presented. The simulation is based on the QCD framework developed recently by M. Diehl, J. R. Gaunt and K. Sch\"{o}nwald. With this framework, the dynamics ... More

Equivalences between blocks of cohomological Mackey algebrasJun 24 2014Let $G$ be a finite group and $(K,\mathcal{O},k)$ be a $p$-modular system "large enough". Let $R=\mathcal{O}$ or $k$. There is a bijection between the blocks of the group algebra $RG$ and the central primitive idempotents (the blocks) of the so-called ... More

On the zero-field orbital magnetic susceptibility of Bloch electrons in graphene-like solids: Some rigorous resultsApr 02 2012Jul 04 2012Starting with a nearest-neighbors tight-binding model, we rigorously investigate the bulk zero-field orbital susceptibility of a non-interacting Bloch electrons gas in graphene-like solids at fixed temperature and density of particles. In the zero-temperature ... More

A perturbation result for the Riesz transformMay 30 2011Apr 10 2013We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_0$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$, which are isometric outside a compact set, and if the Riesz transform on $M_0$ ... More

The Weil-étale fundamental group of a number field IJun 02 2010Sep 16 2010Lichtenbaum has conjectured the existence of a Grothendieck topology for an arithmetic scheme $X$ such that the Euler characteristic of the cohomology groups of the constant sheaf $\mathbb{Z}$ with compact support at infinity gives, up to sign, the leading ... More

On hyperbolicity and Gevrey well-posedness. Part one: the elliptic caseNov 22 2016In this paper we prove that the Cauchy problem for first-order quasi-linear systems of partial differential equations is ill-posed in Gevrey spaces, under the assumption of an initial ellipticity. The assumption bears on the principal symbol of the first-order ... More

On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitionsNov 24 2016For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears on the principal symbol of the first-order operator. Under such an assumption, ... More

Polarization in Low Frequency Radio AstronomyJan 11 2019This chapter introduces the concepts of polarimetry in the case of low frequency radio astronomy. In this regime radio waves are usually not the signature of atomic or molecular transitions lines, but rather that of unstable particle distribution functions ... More

Double Burnside algebra via evaluations of biset functorsNov 10 2015For a non-vanishing group, we show that the evaluation functor induces an equivalence between the category of modules over the double Burnside algebra and a certain category of biset functors. Using this equivalence, we deduce that over a field of characteristic ... More

A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transformNov 23 2010Apr 10 2013Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive and the Ricci ... More

Lagrangian concordance of Legendrian knotsNov 28 2006Aug 21 2013In this article we define Lagrangian concordance of Legendrian knots, the analogue of smooth concordance of knots in the Legendrian category. In particular we study the relation of Lagrangian concordance under Legendrian isotopy. The focus is primarily ... More

Lagrangian concordance is not a symmetric relationJan 16 2013Aug 16 2013We provide an explicit example of a non trivial Legendrian knot $\Lambda$ such that there exists a Lagrangian concordance from $\Lambda_0$ to $\Lambda$ where $\Lambda_0$ is the trivial Legendrian knot. We then use the map induced in Legendrian contact ... More

Applications of an Equivariant Etale Cohomology to Arithmetic TopologyFeb 03 2006Jun 02 2010A. Sikora has shown results which confirm the analogy between number fields and 3-manifolds. However, he has given proofs of his results which are very different in the arithmetic and in the topological case. In this paper, we show how to provide a unified ... More

Hardy spaces and heat kernel regularityAug 27 2013In this paper, we show the equivalence between the boundedness of the Riesz transform $d\Delta^{-1/2}$ on $L^p$, $p\in (2,p_0)$, and the equality $H^p=L^p$, $p\in(2,p_0)$, in the class of manifold whose measure is doubling and for which the scaled Poincar\'{e} ... More

Equivalences between blocks of p-local Mackey algebrasMay 02 2013Jun 24 2014Let $G$ be a finite group and $(K,\mathcal{O},k)$ be a $p$-modular system. Let $R=\mathcal{O}$ or $k$. There is a bijection between the blocks of the group algebra and the blocks of the so-called $p$-local Mackey algebra $\mu_{R}^{1}(G)$. Let $b$ be a ... More

Variants of a-T-menability for actions on non-commutative Lp spacesApr 20 2013We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on non-commutative Lp spaces. We introduce a variant (H_Lp) for orthogonal representations ... More

Property (T) with respect to non-commutative Lp-spacesJul 07 2011We show that a group with Kazhdan's property $(T)$ has property $(T_{B})$ for $B$ the Haagerup non-commutative $L_{p}(\mathcal{M})$-space associated with a von Neumann algebra $\mathcal{M}$, $1

On the finiteness of the Morse Index for Schrödinger operatorsNov 15 2010Mar 11 2011Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the existence of a function $\phi$ solution of $H\phi=0$ outside ... More

Index of the critical catenoidSep 08 2016In this article, we show that the critical catenoid, as a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, has index $4$. We also prove that a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, that is not a flat disk, ... More

A spectral result for Hardy inequalitiesFeb 13 2013Jan 08 2014Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to several well-known ... More

The Weil-étale fundamental group of a number field IIJun 02 2010Sep 30 2010We define the fundamental group underlying to Lichtenbaum's Weil-\'etale cohomology for number rings. To this aim, we define the Weil-\'etale topos as a refinement of the Weil-\'etale sites introduced in \cite{Lichtenbaum}. We show that the (small) Weil-\'etale ... More

Milne's correcting factor and derived de Rham cohomology IIOct 25 2016Milne's correcting factor, which appears in the Zeta-value at $s=n$ of a smooth projective variety $X$ over a finite field $\mathbb{F}_q$, is the Euler characteristic of the derived de Rham cohomology of $X/\mathbb{Z}$ modulo the Hodge filtration $F^n$. ... More

On the Weil-étale cohomology of number fieldsJun 02 2010We give a direct description of the category of sheaves on Lichtenbaum's Weil-\'etale site of a number ring. Then we apply this result to define a spectral sequence relating Weil-\'etale cohomology to Artin-Verdier \'etale cohomology. Finally we construct ... More

Heat Kernel And Riesz Transform Of Schrodinger OperatorsMar 02 2015The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{\"o}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result ... More

Sur l'analogie entre le système dynamique de Deninger et le topos Weil-étaleJun 02 2010Oct 17 2010We express some basic properties of Deninger's conjectural dynamical system in terms of morphisms of topoi. Then we show that the current definition of the Weil-\'etale topos satisfies these properties. In particular, the flow, the closed orbits, the ... More

Simple formulas for constellations and bipartite maps with prescribed degreesApr 10 2019We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, $2k$-angulations), and constellations. These formulas are the fastest known way of computing these numbers. Our work is a natural ... More

Milne's correcting factor and derived de Rham cohomologyJul 09 2014Nov 20 2014Milne's correcting factor is a numerical invariant playing an important role in formulas for special values of zeta functions of varieties over finite fields. We show that Milne's factor is simply the Euler characteristic of the derived de Rham complex ... More

Trace maps for Mackey algebrasMar 19 2014Jun 17 2014Let $G$ be a finite group and $R$ be a commutative ring. The Mackey algebra $\mu_{R}(G)$ shares a lot of properties with the group algebra $RG$ however, there are some differences. For example, the group algebra is a symmetric algebra and this is not ... More

A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limitMar 12 2014Oct 01 2015The original formulation of the Bohr-van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical ... More

On the atomic orbital magnetism: A rigorous derivation of the Larmor and Van Vleck contributionsFeb 05 2013Apr 24 2014The purpose of this paper is to rigorously investigate the orbital magnetism of core electrons in 3-dimensional crystalline ordered solids and in the zero-temperature regime. To achieve that, we consider a non-interacting Fermi gas subjected to an external ... More

Quasi-hereditary property of double Burnside algebrasNov 10 2015In this short note we investigate some consequences of the vanishing of simple biset functors. As corollary, if there is no non-trivial vanishing of simple biset functors (e.g. if the group is commutative), then we show that the double Burnside algebra ... More

On gradient estimates for the heat kernelMar 27 2018Aug 12 2018We study pointwise and $L^p$ gradient estimates of the heat kernel, on manifolds that may have some amount of negative Ricci curvature, provided it is not too negative (in an integral sense) at infinity. We also prove uniform boundedness results on $L^p$ ... More

Zeta functions of regular arithmetic schemes at s=0Mar 30 2011Oct 21 2013Lichtenbaum conjectured the existence of a Weil-\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme $\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\'e characteristics. Assuming ... More

Some non-collarable slices of Lagrangian surfacesAug 15 2011Jan 16 2012In this note we define the notion of collarable slices of Lagrangian submanifolds. Those are slices of Lagrangian submanifolds which can be isotoped through Lagrangian submanifolds to a cylinder over a Legendrian embedding near a contact hypersurface. ... More

A note on exact Lagrangian cobordisms with disconnected Legendrian endsJan 29 2013Jul 08 2013We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian cobordism on ... More

The preparation of states in quantum mechanicsSep 28 2014The important problem of how to prepare a quantum mechanical system, $S$, in a specific initial state of interest - e.g., for the purposes of some experiment - is addressed. Three distinct methods of state preparation are described. One of these methods ... More

Optimal $L^p$ Hardy inequalitiesDec 21 2013Let $\mathcal{Q}(\varphi):=\int_\Omega \big(|\nabla \varphi|^p+V|\varphi|^p\big)\dnu$ on $\core$, and assume that $\mathcal{Q}\geq 0$. The aim of the paper is to obtain ''as large as possible" nonnegative (optimal) Hardy-type weight $W$ satisfying $$\mathcal{Q}(\varphi)\geq ... More

Moduli of Stokes Torsors and Singularities of Differential EquationsFeb 01 2018Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the restrictions to D of ... More

On the affine random walk on the torusFeb 27 2017Let $\mu$ be a borelian probability measure on $\mathbf{G}:=\mathrm{SL}_d(\mathbb{Z}) \ltimes \mathbb{T}^d$. Define, for $x\in \mathbb{T}^d$, a random walk starting at $x$ denoting for $n\in \mathbb{N}$, \[ \left\{\begin{array}{rcl} X_0 &=&x\\ X_{n+1} ... More

The speed of convergence in the renewal theoremJun 25 2015In this article we study a diophantine property of probability measures on R. We will always assume that the considered measures have an exponential moment and a drift. We link this property to the points in C close to the imaginary axis where the Fourier-Laplace ... More

Goussarov-Habiro theory for string links and the Milnor-Johnson correspondenceFeb 03 2004Nov 14 2005We study the Goussarov-Habiro finite type invariants theory for framed string links in homology balls. Their degree 1 invariants are computed: they are given by Milnor's triple linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and ... More

Branching brownian motion seen from its left-most particuleMay 19 2013This paper is a review of the recent progresses on the branching brownian motion seen from its left-most particule. We describe in particular the recent works by Arguin-Bovier-Kistler and A\"id\'ekon-Berestycki-Brunet-Shi. This is the text in french of ... More

Borromean surgery formula for the Casson invariantSep 15 2005Apr 22 2008It is known that every oriented integral homology 3-sphere can be obtained from S^3 by a finite sequence of Borromean surgeries. We give an explicit formula for the variation of the Casson invariant under such a surgery move. The formula involves simple ... More

On Vassiliev invariants of order two for string linksFeb 04 2004Nov 10 2004We show that the Casson knot invariant, linking number and Milnor's triple linking number, together with a certain 2-string link invariant $V_2$, are necessary and sufficient to express any string link Vassiliev invariant of order two. Explicit combinatorial ... More

Conformal symplectic geometry of cotangent bundlesJun 02 2016May 31 2017We prove a version of the Arnol'd conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian $L$ which has non-zero Morse-Novikov homology for the restriction of the Lee form $\beta$ cannot be disjoined from itself by a $C^0$-small ... More

Generalized blocks of unipotent characters in the finite general linear groupSep 01 2006Dec 04 2007In a paper of 2003, B. K\"ulshammer, J. B. Olsson and G. R. Robinson defined $\ell$-blocks for the symmetric groups, where $\ell >1$ is an arbitrary integer, and proved that they satisfy an analogue of the Nakayama Conjecture. Inspired by this work and ... More

The Machine Learning Algorithm as Creative Musical ToolNov 01 2016Machine learning is the capacity of a computational system to learn structures from datasets in order to make predictions on newly seen data. Such an approach offers a significant advantage in music scenarios in which musicians can teach the system to ... More

Bijection: Parking-like structures and Tree-like structuresMar 13 2015We recall the occupancy problem introduced by Konheim & Weiss in 1966 and we consider parking functions as hash maps. Each car $c_i$ prefers parking space $p_i$ (the hash map $c_i \mapsto p_i$ with $c_i$ is a key and $p_i$ an index into an array), if ... More

Numerical study of an anisotropic Vlasov equation arising in plasma physicsOct 05 2016Aug 09 2017Goal of this paper is to investigate several numerical schemes for the resolution of two anisotropic Vlasov equations. These two toy-models arise from a kinetic description of a tokamak plasma confined by strong magnetic fields. The simplicity of our ... More

Push-forwards for Witt groups of schemesJun 03 2008Apr 09 2011We define push-forwards for Witt groups of schemes along proper morphisms, using Grothendieck duality theory. This article is an application of results of the authors on tensor-triangulated closed categories to such structures on some derived categories ... More

Bilinearised Legendrian contact homology and the augmentation categoryOct 27 2012May 13 2013In this paper we construct an $\mathcal{A}_\infty$-category associated to a Legendrian submanifold of jet spaces. Objects of the category are augmentations of the Chekanov algebra $\mathcal{A}(\Lambda)$ and the homology of the morphism spaces forms a ... More

Subcritical regimes in the Poisson Boolean model of continuum percolationNov 13 2006Oct 01 2008We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if $E(R^d)$ is finite, where $R$ denotes the radius of the balls around Poisson points and $d$ denotes the dimension. We also give related ... More

Ellis enveloping semigroup for almost canonical model sets of an Euclidean spaceMay 04 2013Sep 28 2015We consider certain point patterns of an Euclidean space and calculate the Ellis enveloping semigroup of their associated dynamical systems. The algebraic structure and the topology of the Ellis semigroup, as well as its action on the underlying space, ... More

Optimal embedding of Meyer sets into model setsNov 18 2014We give a constructive proof that a repetitive Meyer multiple set of $\mathbb{R}^d$ admits a smallest model multiple set containing it colorwise.

On a motivic invariant of the arc-analytic equivalenceDec 22 2015Apr 15 2016To a Nash function germ, we associate a zeta function similar to the one introduced by J. Denef and F. Loeser. Our zeta function is a formal power series with coefficients in the Grothendieck ring $\mathcal{M}$ of $\mathcal{AS}$-sets up to $\mathbb{R}^*$-equivariant ... More

On the arc-analytic type of some weighted homogeneous polynomialsDec 25 2016Dec 02 2017It is known that the weights of a complex weighted homogeneous polynomial $f$ with isolated singularity are analytic invariants of $(\mathbb C^d,f^{-1}(0))$. When $d=2,3$ this result holds by assuming merely the topological type instead of the analytic ... More

Bases of total Witt groups and lax-similitudeApr 27 2011Dec 24 2012We explain how to work with total Witt groups, more specifically, how to circumvent the classical embarrassment of making choices for line bundles up to isomorphisms and up to squares.

Witt groups of Grassmann varietiesJul 21 2008Dec 24 2012We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, ... More

Homogeneous nearly Kähler manifoldsDec 21 2006We classify six-dimensional homogeneous nearly K\"{a}hler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly K\"{a}hler manifold is a Riemannian 3-symmetric space equipped with its canonical almost Hermitian structure. ... More

Classification des varietes approximativement kahleriennes homogenesJan 14 2004Jan 15 2004We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in ... More

Weil-étale cohomology and Zeta-values of proper regular arithmetic schemesMay 04 2016Mar 01 2017We give a conjectural description of the vanishing order and leading Taylor coefficient of the Zeta function of a proper, regular arithmetic scheme $\mathcal{X}$ at any integer $n$ in terms of Weil-\'etale cohomology complexes. This extends work of Lichtenbaum ... More

Functional optimization of the arterial networkMay 06 2014May 21 2014We build an evolutionary scenario that explains how some crucial physiological constraints in the arterial network of mammals - i.e. hematocrit, vessels diameters and arterial pressure drops - could have been selected by evolution. We propose that the ... More

A rigorous approach to the magnetic response in disordered systemsDec 28 2011Aug 20 2012This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence ... More

Do We Understand Quantum Mechanics - Finally?Mar 16 2012After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator algebras. We ... More

On Morita and derived equivalences for cohomological Mackey algebrasSep 26 2016By results of the second author, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between ... More

Weil-étale cohomology and Zeta-values of proper regular arithmetic schemesMay 04 2016We give a conjectural description of the vanishing order and leading Taylor coefficient of the Zeta function of a proper, regular arithmetic scheme $\mathcal{X}$ at any integer $n$ in terms of Weil-\'etale cohomology complexes. This extends work of Lichtenbaum ... More

Numerical study of an anisotropic Vlasov equation arising in plasma physicsOct 05 2016Goal of this paper is to investigate several numerical schemes for the resolution of two anisotropic Vlasov equations. These two toy-models arise from a kinetic description of a tokamak plasma confined by strong magnetic fields. The simplicity of our ... More

Linking number and Milnor invariantsDec 08 2018This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.

The rate of convergence for the renewal theorem in $\mathbb{R}^d$Mar 23 2016Jul 09 2016Let $\rho$ be a borelian probability measure on $\mathrm{SL}_d(\mathbb{R})$. Consider the random walk $(X_n)$ on $\mathbb{R}^d\setminus\{0\}$ defined by $\rho$ : for any $x\in \mathbb{R}^d\setminus\{0\}$, we set $X_0 =x$ and $X_{n+1} = g_{n+1} X_n$ where ... More

Central limit theorem and law of the iterated logarithm for the linear random walk on the torusFeb 11 2016Feb 25 2016Let $\rho$ be a probability measure on $\mathrm{SL}\_d(\mathbb{Z})$ and consider the random walk defined by $\rho$ on the torus $\mathbb{T}^d = \mathbb{R}^d/\mathbb{Z}^d$. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an assumption on the ... More

Tensor product and irregularity for holonomic D-modulesMar 07 2015Let M be a complex of D-modules with bounded holonomic cohomology on a complex manifold. In this note, we prove that if the derived tensor product of M with itself is regular, then M is regular.

Higgs couplings and BSM physics: Run I Legacy constraintsApr 29 2015We consider the Higgs boson decay processes and its production including all Run I results, through a parametrisation tailored for testing models of new physics beyond the Standard Model, and complementary to the one used by the LHC working groups. Different ... More

The Isaacs-Navarro Conjecture for covering groups of the symmetric and alternating groups in odd characteristicMar 24 2010May 22 2010In this paper, we prove that a refinement of the Alperin-McKay Conjecture for $p$-blocks of finite groups, formulated by I. M. Isaacs and G. Navarro in 2002, holds for all covering groups of the symmetric and alternating groups, whenever $p$ is an odd ... More

Manuscripts in Time and Space: Experiments in Scriptometrics on an Old French CorpusJan 30 2018Witnesses of medieval literary texts, preserved in manuscript, are layered objects , being almost exclusively copies of copies. This results in multiple and hard to distinguish linguistic strata -- the author's scripta interacting with the scriptae of ... More

Fixed-point spectrum for group actions by affine isometries on Lp-spacesOct 01 2014Mar 28 2015The fixed-point spectrum of a locally compact second countable group G on lp is defined to be the set of real numbers p such that every action by affine isometries of G on lp admits a fixed-point. We show that this set is either empty, or is equal to ... More

On the wildness of cambrian latticesApr 06 2017In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite ... More

Extraction de concepts sous contraintes dans des données d'expression de gènesFeb 07 2009In this paper, we propose a technique to extract constrained formal concepts.

Tensor-triangulated categories and dualitiesJun 03 2008In a triangulated symmetric monoidal closed category, there are natural dualities induced by the internal Hom. Given a monoidal functor f^* between two such catgories and adjoint couples (f^*,f_*) and (f_*,f^!), we prove the necessary commutative diagrams ... More

Local limits of uniform triangulations in high genusFeb 01 2019We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the Planar Stochastic Hyperbolic Triangulations (PSHT) defined in arXiv:1401.3297. The ... More

A differential graded Lie algebra approach to non abelian extensions of associative algebrasFeb 13 2018In this paper we show that non abelian extensions of an associative algebra $\mathcal{B}$ by an associative algebra $\mathcal{A}$ can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra $L$. In particular we show that $\mathcal{MC}(L)$, ... More

Quasicrystals and almost periodicityDec 03 2002We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is almost periodic ... More

Geometric description of the connecting homomorphism for Witt groupsJul 21 2008Nov 26 2009We give a geometric setup in which the connecting homomorphism in the localization long exact sequence for Witt groups decomposes as the pull-back to the exceptional fiber of a suitable blow-up followed by a push-forward.

Twistors and 3-symmetric spacesApr 18 2006We describe complex twistor spaces over inner 3-symmetric spaces $G/H$, such that $H$ acts transitively on the fibre. Like in the symmetric case, these are flag manifolds $G/K$ where $K$ is the centralizer of a torus in $G$. Moreover, they carry an almost ... More

An inverse mapping theorem for blow-Nash maps on singular spacesJun 25 2014May 12 2015A semialgebraic map $f:X\to Y$ between two real algebraic sets is called blow-Nash if it can be made Nash (i.e. semialgebraic and real analytic) by composing with finitely many blowings-up with non-singular centers. We prove that if a blow-Nash self-homeomorphism ... More

Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approachJun 16 2013May 22 2014In this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic ... More

Finite Chow-Witt correspondencesDec 09 2014We introduce the category of finite Chow-Witt correspondences over a perfect field k of characteristic not 2. We then use them to define bigraded generalized motivic cohomology groups of a smooth scheme over k. We prove that for a finitely generated field ... More

Sur une caractérisation des D-modules holonomes réguliersJan 08 2014Feb 27 2014Let X be a smooth complex manifold. Let Sol denote the solution functor for D-modules on X. Traditionally, the fully-faithfulness of Riemann-Hilbert correspondance is proved by showing that if M_1 and M_2 are regular holonomic D_X modules, then the canonical ... More

Micro-Data Learning: The Other End of the SpectrumOct 04 2016Many fields are now snowed under with an avalanche of data, which raises considerable challenges for computer scientists. Meanwhile, robotics (among other fields) can often only use a few dozen data points because acquiring them involves a process that ... More

A mean field type flowDec 09 2012We consider a gradient flow related to the mean field type equation. First, we show that this flow exists for all time. Next, we prove a compactness result for this flow allowing us to get, under suitable hypothesis on its energy, the convergence of the ... More

Equivariant mean field flowDec 09 2012We consider a gradient flow associated to the mean field equation on $(M,g)$ a compact riemanniann surface without boundary. We prove that this flow exists for all time. Moreover, letting $G$ be a group of isometry acting on $(M,g)$, we obtain the convergence ... More

Monotonicity in first-passage percolationFeb 13 2012Oct 04 2012We consider standard first-passage percolation on $\Z^d$. Let $e_1$ be the first coordinate vector. Let $a(n)$ be the expected passage time from the origin to $ne_1$. In this short paper, we note that $a(n)$ is increasing under some strong condition on ... More

Classification via local multi-resolution projectionsOct 28 2011Dec 13 2011We focus on the supervised binary classification problem, which consists in guessing the label $Y$ associated to a co-variate $X \in \R^d$, given a set of $n$ independent and identically distributed co-variates and associated labels $(X_i,Y_i)$. We assume ... More

Percolation in a multiscale Boolean modelSep 20 2010Mar 11 2011We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the $n^{\textrm{th}}$ copy is $\rho^{-n}$. We prove, under optimal integrability assumptions, ... More

On surgery along Brunnian links in 3-manifoldsMar 17 2006Jul 29 2009We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the each component is 1/k for k in Z. We show that no finite type invariant of degree < 2n-2 can detect such a surgery move. ... More

We are not alone ! (at least, most of us). Homonymy in large scale social groupsJul 24 2017This article brings forward an estimation of the proportion of homonyms in large scale groups based on the distribution of first names and last names in a subset of these groups. The estimation is based on the generalization of the "birthday paradox problem". ... More

Conformal Scale Geometry of SpacetimeNov 13 2018We devise a new approach for the study of the issue of singularities and black holes based on a new mass function on a phase space of the conformal space-time, and on the almost time-independent character of the intrinsic geometry of the Event Horizon. ... More

Cometary topography and phase darkeningJan 18 2019Cometary surfaces can change significantly and rapidly due to the sublimation of their volatile material. Many authors have investigated this evolution; Vincent et al. (2017) have used topographic data from all comets visited by spacecrafts to derive ... More

On the Weil-étale topos of regular arithmetic schemesOct 19 2010We define and study a Weil-\'etale topos for any regular, proper scheme $X$ over $\Spec(Z)$ which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with $R$-coefficients has the expected relation to $\zeta(X,s)$ ... More

Diffraction and Palm measure of point processesAug 08 2002Using the Palm measure notion, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes : stochastic subsets of Z^d, sets obtained by ... More