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Learning and Querying Fast Generative Models for Reinforcement LearningFeb 08 2018A key challenge in model-based reinforcement learning (RL) is to synthesize computationally efficient and accurate environment models. We show that carefully designed generative models that learn and operate on compact state representations, so-called ... More

Towards Conceptual CompressionApr 29 2016We introduce a simple recurrent variational auto-encoder architecture that significantly improves image modeling. The system represents the state-of-the-art in latent variable models for both the ImageNet and Omniglot datasets. We show that it naturally ... More

The dipole representation of vector meson electroproduction beyond leading twistApr 10 2012We link the recent computation beyond leading twist of the impact factor of the transition gamma*T -> rhoT performed in the light-cone collinear approach, to the dipole picture by expressing the hard part of the process through its Fourier transform in ... More

Convolution by Evolution: Differentiable Pattern Producing NetworksJun 08 2016In this work we introduce a differentiable version of the Compositional Pattern Producing Network, called the DPPN. Unlike a standard CPPN, the topology of a DPPN is evolved but the weights are learned. A Lamarckian algorithm, that combines evolution ... More

Simplicite de groupes d'automorphismes d'espaces a courbure negativeDec 04 1998We prove that numerous negatively curved simply connected locally compact polyhedral complexes, admitting a discrete cocompact group of automorphisms, have automorphism groups which are locally compact, uncountable, non linear and virtually simple. Examples ... More

Linear groups in Galois fields. A case study of tacit circulation of explicit knowledgeFeb 14 2012This preprint is the extended version of a paper that will be published in the proceedings of the Oberwolfach conference "Explicit vs tacit knowledge in mathematics" (January 2012). It presents a case study on some algebraic researches at the turn of ... More

Solving 3-SAT and 3-dimensional matching in polynomial timeOct 07 2013Feb 04 2014We show how the implementation of conservative logic gates on flow networks suggests a way to solve 3SAT and 3-dimensional matching problems in polynomial time by using standard minimum-cost flow methods.

The 2200 A bump and the UV extinction curveAug 31 2012The 2200 A bump is a major figure of interstellar extinction. Extinction curves with no bump however exist and are, with no exception, linear from the near-infrared down to 2500 A at least, often over all the visible-UV spectrum. The duality linear versus ... More

Providing better confidentiality and authentication on the Internet using Namecoin and MinimaLTJul 24 2014In this paper, we introduce a duo of improvements for the Internet that would lead to better security. The authentication model on the Internet is broken and TLS connections have a considerable overhead. We try to address those issues with changes in ... More

Shifted versions of the Bailey and well-poised Bailey lemmasJun 10 2009The Bailey lemma is a famous tool to prove Rogers-Ramanujan type identities. We use shifted versions of the Bailey lemma to derive $m$-versions of multisum Rogers-Ramanujan type identities. We also apply this method to the Well-Poised Bailey lemma and ... More

A critical evaluation of PCA detection of polarized signatures using real stellar dataJun 22 2012The general context of this study concerns the post-processing of multiline spectropolarimetric observations of stars, and in particular these numerical analysis techniques aiming at the detection and the characterization of polarized signatures. Hereafter, ... More

Non-Supersymmetric SO(3)-Invariant Deformations of N=1* Vacua and their Dual String Theory DescriptionJul 11 2000Jul 20 2000We study the SO(3)-invariant relevant deformations of N=4 SU(N) gauge theory using the methods of Polchinski and Strassler. We present the region of parameter space where the non-supersymmetric vacuum is still described by stable ``dielectric'' five branes ... More

On the Operator Product Expansion in Noncommutative Quantum Field TheoryApr 11 2000May 01 2000Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we find that the ... More

Star formation in galaxy interactions and mergersJun 09 2011This lecture reviews the fundamental physical processes involved in star formation in galaxy interactions and mergers. Interactions and mergers often drive intense starbursts, but the link between interstellar gas physics, large scale interactions, and ... More

Looking for New Physics in b-decays with LHCbOct 18 2010This article is a short and non-exhaustive summary of the prospects to find New Physics with LHCb as was presented at the HCP conference at Toronto on August 26th 2010.

Supercritical bifurcation of a hula hoopNov 18 2002The motion of a hoop hung on a spinning wire provides an illustrative and pedagogical example of a supercritical bifurcation. Above a certain angular velocity threshold Omega_c, the hoop rises, making an angle theta = (Omega-Omega_c)^(1/2) with the vertical. ... More

Les incompatibilites entre la theorie standard de l'extinction interstellaire et l'observationMay 09 2002May 17 2002The standard interpretation of the extinction curve does not agree with some observations. The light we receive from a reddened star must be contaminated by starlight scattered at very small angular distances from the star. The true extinction curve is ... More

Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliersNov 22 2012May 01 2013In this work, we describe several results exhibited during a talk at the El Escorial 2012 conference. We aim to pursue the development of a multi-frequency Calderon-Zygmund analysis introduced in [9]. We set a definition of general multi-frequency Calderon-Zygmund ... More

A T(1)-Theorem in relation to a semigroup of operators and applications to new paraproductsMay 27 2010In this work, we are interested to develop new directions of the famous T(1)-theorem. More precisely, we develop a general framework where we look for replacing the John-Nirenberg space BMO (in the classical result) by a new BMO_{L}, associated to a semigroup ... More

Uniform estimates for paraproducts and related multilinear multipliersJun 03 2008In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on R^d. We are looking for uniformity with respect to parameters, which allow us to disturb the geometry and ... More

Geometry of genus 9 Fano 4-foldJan 08 2009Jan 11 2009References to the works of Iliev-Ranestad and Kuznetsov added. ----- In a first part we detail the construction, on a general Fano 4-fold of genus 9, of a canonical set of four stable vector bundles of rank 2, and prove that they are rigid. Those results ... More

Control of Nonholonomic Systems and Sub-Riemannian GeometrySep 19 2012Jan 08 2013Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon, 2012

On the Coxeter transformations for Tamari posetsFeb 03 2005On obtient une relation entre la transformation de Coxeter agissant sur le groupe de Grothendieck de la categorie derivee des modules sur un poset de Tamari d'une part et la structure de l'operade anticyclique dendriforme d'autre part. A relation between ... More

Pfaffian bundles on cubic surfaces and configurations of planesOct 05 2012Apr 20 2013We give a canonical birational map between the moduli space of pfaffian vector bundles on a cubic surface and the space of complete pentahedra inscribed in the cubic surface. The universal situation is also considered, and we obtain a rationality result. ... More

Cohomology rings of toric varieties assigned to cluster quivers: the case of unioriented quivers of type AMar 04 2005The theory of cluster algebras of S. Fomin and A. Zelevinsky has assigned a fan to each Dynkin diagram. Then A. Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov have generalized this construction using arbitrary quivers on Dynkin diagrams. In the ... More

Quantum Metric Spaces and the Gromov-Hausdorff PropinquityJun 14 2015Mar 08 2016We present a survey of the dual Gromov-Hausdorff propinquity, a noncommutative analogue of the Gromov-Hausdorff distance which we introduced to provide a framework for the study of the noncommutative metric properties of C*-algebras. We first review the ... More

Approximation of Quantum Tori by Finite Quantum Tori for the Quantum Gromov-Hausdorff DistanceOct 15 2003Oct 18 2005The statement that one can approximate a quantum torus by some twisted convolution C*-algebra of a (finite) quotient of Z^d can be found in the physics literature dealing with quantum field theory and M-theory. In this paper, we show that indeed the quantum ... More

Three examples of noncommutative boundaries of Shimura varietiesOct 10 2004Dec 16 2004We study the noncommutative modular curve (which was already studied by Connes, Manin and Marcolli), and the space of geodesics on the usual modular curve, from the viewpoint of algebraic groups, linear algebra and class field theory. This allows us, ... More

Local in time results for local and non-local capillary Navier-Stokes systems with large dataJun 10 2013Jun 13 2013In this article we study three capillary compressible models (the classical local Navier-Stokes-Korteweg system and two non-local models) for large initial data, bounded away from zero, and with a reference pressure state $\bar{\rho}$ which is not necessarily ... More

Feuilletages holomorphes admettant une mesure transverse invarianteSep 11 2014Let $\cal{F}$ be a regular codimension 1 holomorphic foliation on a compact K\" ahler manifold. One assumes in addition that $\cal{F}$ possesses a transverse invariant positive current. The aim of this paper is to establish the following alternative: ... More

La fonte algébrique des Méthodes nouvelles de la mécanique céleste d'Henri PoincaréOct 09 2012Poincar\'e's approach to the three body problem has often been celebrated as a starting point of chaos theory in relation to the investigation of dynamical systems. Yet, Poincar\'e's strategy can also be analyzed as molded on - or casted in - some specific ... More

Sur la topologie de l'espace des operateurs pseudodifferentiels inversibles d'ordre 0Oct 19 2006May 12 2007The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the subgroup of invertible ... More

Galaxy formation hydrodynamics: From cosmic flows to star-forming cloudsSep 01 2010Major progress has been made over the last few years in understanding hydrodynamical processes on cosmological scales, in particular how galaxies get their baryons. There is increasing recognition that a large part of the baryons accrete smoothly onto ... More

Bounded-Lipschitz Distances on the State Space of a C*-algebraOct 16 2005Metric noncommutative geometry, initiated by Alain Connes, has known some great recent developments under the impulsion of Rieffel and the introduction of the category of compact quantum metric spaces topologized thanks to the quantum Rieffel-Gromov-Hausdorff ... More

On the Impact of Information Technologies on Society: an Historical Perspective through the Game of ChessMar 15 2012The game of chess as always been viewed as an iconic representation of intellectual prowess. Since the very beginning of computer science, the challenge of being able to program a computer capable of playing chess and beating humans has been alive and ... More

Removability of singularities of harmonic maps into pseudo-Riemannian manifoldsMay 15 2003We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times continuously ... More

Commensurability and separability of quasiconvex subgroupsApr 17 2009We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph ... More

Short and long time behavior of the Fokker-Planck equation in a confining potential and applicationsJan 22 2005Jan 23 2008We consider the linear Fokker-Planck equation in a confining potential in space dimension $d \geq 3$. Using spectral methods, we prove bounds on the derivatives of the solution for short and long time, and give some applications.

Efficient erasure decoding of Reed-Solomon codesJan 14 2009We present a practical algorithm to decode erasures of Reed-Solomon codes over the q elements binary field in O(q \log_2^2 q) time where the constant implied by the O-notation is very small. Asymptotically fast algorithms based on fast polynomial arithmetic ... More

Special orbifolds and birational classification: a surveyJan 21 2010We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this special case ... More

Orbifoldes à premi\ere classe de Chern nulleFeb 14 2004Mar 18 2004An orbifold version of Bogomolov decomposition theorem is established for compact K\"ahler spaces with quotient singularities and first Chern class zero.The proof is a direct adaptation of the classical smooth case, using Ricci-flat K\"ahler metrics, ... More

Special Varieties and classification TheoryOct 04 2001Oct 05 2004A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of rational and ... More

Classification of some simple graded pre-Lie algebras of growth oneSep 10 2002We classify a class of infinite-dimensional simple graded pre-Lie algebras on the graded vector space underlying the algebra of Laurent polynomials, with a specific form for the product.

Rooted trees and an exponential-like seriesSep 10 2002This paper deals with a group of generalized power series associated to any augmented operad, focusing on the case of the PreLie operad. The solution of flow equations using the pre-Lie structure on vector fields on an affine space gives rise to an interesting ... More

Hamiltonian formalisms for multidimensional calculus of variations and perturbation theoryDec 11 2002In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to the quantum ... More

Algebraic generality vs arithmetic generality in the controversy between C. Jordan and L. Kronecker (1874)Dec 16 2007Throughout the whole year of 1874, C. Jordan and L. Kronecker were quarrelling over two theorems. On the one hand, Jordan had stated in 1870 a canonical form theorem for substitutions of linear groups; on the other hand, Karl Weierstrass had introduced ... More

Formulas for the Connes-Moscovici Hopf algebraDec 15 2008We give explicit formulas for the coproduct and the antipode in the Connes-Moscovici Hopf algebra $\mathcal{H}_{\tmop{CM}}$. To do so, we first restrict ourselves to a sub-Hopf algebra $\mathcal{H}^1_{\tmop{CM}}$ containing the nontrivial elements, namely ... More

A priori estimates for the 3D quasi-geostrophic systemNov 26 2014The present article is devoted to the 3D dissipative quasi-geostrophic system (QG). This system can be obtained as limit model of the Primitive Equations in the asymptotics of strong rotation and stratification, and involves a non-radial, non-local, homogeneous ... More

Topographic Gromov-Hausdorff quantum Hypertopology for Quantum Proper Metric SpacesJun 02 2014We construct a topology on the class of pointed proper quantum metric spaces which generalizes the topology of the Gromov-Hausdorff distance on proper metric spaces, and the topology of the dual propinquity on Leibniz quantum compact metric spaces. A ... More

Problemes variationnels invariants par transformation conforme en dimension 2Jan 29 2001This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is given. Second ... More

Spectral symmetries of zeta functionsMar 03 2008Mar 10 2008We define, answering a question of Sarnak in his letter to Bombieri, a symplectic pairing on the spectral interpretation (due to Connes and Meyer) of the zeroes of Riemann's zeta function. This pairing gives a purely spectral formulation of the proof ... More

The algebraic cast of Poincaré's Méthodes nouvelles de la mécanique célesteMay 13 2013This paper aims at shedding a new light on the novelty of Poincar\'e's M\'ethodes nouvelles de la m\'ecanique c\'eleste. The latter's approach to the three-body-problem has often been celebrated as a starting point of chaos theory in relation to the investigation ... More

Autour de pratiques algébriques de Poincaré : héritages de la réduction de JordanOct 15 2012The legacy of Jordan's canonical form on Poincar\'e's algebraic practices. This paper proposes a transversal overview on Henri Poincar\'e's early works (1878-1885). Our investigations start with a case study of a short note published by Poincar\'e on ... More

Global analytic geometryMar 03 2008Jan 08 2013We define a new type of valuation of a ring that combines the notion of Krull valuation with that of multiplicative seminorm. This definition partially restores the broken symmetry between archimedean and non-archimedean valuations. This also allows us ... More

Bulge growth through disk instabilities in high-redshift galaxiesMar 26 2015The role of disk instabilities, such as bars and spiral arms, and the associated resonances, in growing bulges in the inner regions of disk galaxies have long been studied in the low-redshift nearby Universe. There it has long been probed observationally, ... More

Quantization effects for a fourth order equation of exponential growth in dimension fourDec 07 2005We investigate the asymptotic behavior as $k \to +\infty$ of sequences $(u_k)_{k\in\mathbb{N}}\in C^4(\Omega)$ of solutions of the equations $\Delta^2 u_k=V_k e^{4u_k}$ on $\Omega$, where $\Omega$ is a bounded domain of $\mathbb{R}^4$ and $\lim_{k\to ... More

Concentration phenomena for a fourth order equations with exponential growth: the radial caseDec 07 2005We let $\Omega$ be a smooth bounded domain of $\mathbb{R}^4$ and a sequence of fonctions $(V_k)_{k\in\mathbb{N}}\in C^0(\Omega)$ such that $\lim_{k\to +\infty}V_k=1$ in $C^0_{loc}(\Omega)$. We consider a sequence of functions $(u_k)_{k\in\mathbb{N}}\in ... More

A bilinear pseudodifferential calculusFeb 04 2008Feb 21 2008In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the bilinear Hilbert ... More

Local estimates and global continuities in Lebesgue spaces for bilinear operatorsJan 26 2008Feb 08 2008In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle ... More

Slope rational connectedness for orbifoldsJul 26 2016We define, for smooth projective orbifold pairs $(X,D)$ notions of `slope Rational connectedness', and of orbifold `slope Rational quotient' . These notions extend to this larger context the classical notions of rationally connected manifold and `rational ... More

Birational stability of the cotangent bundleAug 28 2010We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent sheaves are birationally ... More

Orbifoldes, variétés spéciales et classification des variétés K\" ahlériennes compactesFeb 14 2004This text is an introduction to math.AG/0110051 (to appear in Ann. Inst. Fourier), and describes a canonical decomposition of compact K\"ahler manifolds $X$ first by means of their "core", the unique fibration on $X$ with fibres special, and orbifold ... More

Free hyperplane arrangements associated to labeled rooted treesJan 31 2003Feb 17 2003Each labeled rooted tree is associated with a hyperplane arrangement, which is free with exponents given by the depths of the vertices of this tree. The intersection lattices of these arrangements are described through posets of forests. These posets ... More

Operades differentielles graduees sur les simplexes et les permutoedresFeb 21 2001We define several differential graded operads, some of them being related to families of polytopes : simplices and permutohedra. We also obtain a presentation by generators and relations of the operad K on associahedra introduced in a previous article. ... More

Sur le nombre de reflexions pleines dans les groupes de Coxeter finisMay 19 2004On etudie divers aspects d'une formule qui compte les reflexions pleines dans les groupes de Coxeter finis. ***** We study several points about a formula which counts reflexions in a finite Coxeter group whose reduced decompositions involve all simple ... More

Enumerative properties of generalized associahedraJan 19 2004Some enumerative aspects of the fans, called generalized associahedra, introduced by S. Fomin and A. Zelevinsky in their theory of cluster algebras are considered, in relation with a bicomplex and its two spectral sequences. A precise enumerative relation ... More

A Hopf operad of forests of binary trees and related finite-dimensional algebrasSep 04 2002The theme of this article is the algebraic combinatorics of leaf-labeled rooted binary trees and forests of such trees. The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees. An explicit ... More

Empirical evidence for tidal evolution in transiting planetary systemsDec 08 2008Apr 06 2009Most transiting planets orbit very close to their parent star, causing strong tidal forces between the two bodies. Tidal interaction can modify the dynamics of the system through orbital alignment, circularisation, synchronisation, and orbital decay by ... More

Photometric searches for transiting planets: results and challengesOct 31 2005Ground-based photometric surveys have led to the discovery of six transiting exoplanets, five of which were detected by the OGLE survey. The FLAMES multi-object spectrograph on the VLT has permitted a very efficient follow-up of the OGLE transit candidates, ... More

The Cepheid Distance Scale after HipparcosDec 03 1998More than two hundred classical cepheids were measured by the Hipparcos astrometric satellite, making possible a geometrical calibration of the cepheid distance scale. However, the large average distance of even the nearest cepheids measured by Hipparcos ... More

Rare Decays Probing Physics Beyond the Standard TheoryOct 12 2015In the last 50 years we have seen how an initially ad-hoc and not widely accepted theory of the strong and electroweak interactions (Standard Theory: ST) has correctly predicted the entire accelerator based experimental observations with incredible accuracy ... More

Une version feuilletée d'un théorème de BogomolovJan 22 2007On compact K\"{a}hler manifolds, we classify regular holomorphic foliations of codimension 1 whose canonical bundle is numerically trivial.

From dynamical systems to renormalizationFeb 25 2013We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a Lie algebra ... More

Connected components of representation spaces of non-orientable surfacesSep 13 2009Let M be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain Stiefel-Whitney characteristic ... More

A Compactness Theorem for The Dual Gromov-Hausdorff PropinquityJan 25 2015Jan 27 2016We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz compact quantum metric spaces ... More

Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equationMar 17 2005We consider an inhomogeneous linear Boltzmann equation, with an external confining potential. The collision operator is a simple relaxation toward a local Maxwellian, therefore without diffusion. We prove the exponential time decay toward the global Maxwellian, ... More

Convergence of a low order non-local Navier-Stokes-Korteweg system: the order-parameter modelFeb 11 2013In the present article we consider a capillary compressible system introduced by C. Rohde after works of Bandon, Lin and Rogers, called the order-parameter model, and whose aim is to reduce the numerical difficulties that one encounters in the case of ... More

On Jordan's measurementsOct 11 2011The Jordan measure, the Jordan curve theorem, as well as the other generic references to Camille Jordan's (1838-1922) achievements highlight that the latter can hardly be reduced to the "great algebraist" whose masterpiece, the Trait\'e des substitutions ... More

Galois Got his GunNov 02 2011This paper appeals to the figure of \'Evariste Galois for investigating the gates between mathematics and their "publics." The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in turn sketch the ... More

Suppressing nonrevisiting pathsMar 30 2004Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.

On nonimbeddability of topologically trivial domains and Thin Hartogs figures of $P_2(\mathbb{C})$ into Stein spacesNov 04 2004A question of Poletsky was to know if there exists a thin Hartogs figure such that any of its neighborhoods cannot be imbedded in Stein spaces. In \cite{chirka}, Chirka and Ivashkovitch gave such an example arising in an open complex manifold. In this ... More

Tidal Dwarf Galaxies and missing baryonsJul 22 2009Tidal dwarf galaxies form during the interaction, collision or merger of massive spiral galaxies. They can resemble "normal" dwarf galaxies in terms of mass, size, and become dwarf satellites orbiting around their massive progenitor. They nevertheless ... More

Star formation and structure formation in galaxy collisionsSep 09 2009Sep 16 2009A number of theoretical and simulation results on star and structure formation in galaxy interactions and mergers is reviewed, and recent hydrodynamic simulations are presented. The role of gravity torques and ISM turbulence in galaxy interactions, in ... More

Bott Periodicity for Fibred Cusp OperatorsAug 17 2004Mar 04 2006In the framework of fibred cusp operators on a manifold $X$ associated to a boundary fibration $\Phi: \pa X\to Y$, the homotopy groups of the space of invertible smoothing perturbations of the identity are computed in terms of the K-theory of $T^{*}Y$. ... More

Probleme Plateau complexe dans les varietes KahleriennesMay 11 1999Sep 14 1999The ``complex Plateau problem'' (or boundary problem) in a complexe manifold X is the problem of characterizing the real submanifolds $\Gamma$ of X which are boundaries of analytic sub-varieties of $X \backslash \Gamma$. Our principal result treat the ... More

Ergodic actions of mapping class groups on moduli spaces of representations of non-orientable surfacesJul 10 2008Jan 27 2009The purpose of this paper is to study the action of the mapping class group on the moduli space of representations of the fundamental group of a non-orientable surface into SU(2). The action is shown to be ergodic with respect to a natural measure. This ... More

Orbifoldes speciales et classification bimeromorphe des varietes kaehleriennes compactesMay 05 2007Jul 15 2009This is a sequel to [Ca01]=math.AG/0110051. We define the bimeromorphic {\it category} of geometric orbifolds. These interpolate between (compact K\" ahler) manifolds and such manifolds with logarithmic structure. These geometric orbifolds are considered ... More

Quotients resolubles ou nilpotents des groupes de Kaehler orbifoldesMar 03 2009Aug 28 2010The results known for Green-Lazarsfeld sets and solvable or nilpotent quotients of Kaehler groups are extended to the class of (compact Kaehler) geometric orbifolds with finite and integral multiplicities. The proofs are by reduction to the known case ... More

Sur la conjecture abc, version corps de fonctions d'OesterleMar 16 2007Mar 29 2007We show a weak form of the function field version of Oesterle's abc conjecture. It asserts that, if $B$ is a complex projective connected curve, the number of intersection points, counted without multiplicities, of a fixed divisor $D$ of degree $d>0$ ... More

On a Hopf operad containing the Poisson operadDec 02 2002Jan 01 2004A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by generators and relations ... More

Antichains of positive roots and Heaviside functionsMar 18 2003The ring of locally-constant integer-valued functions on the dominant chamber of the Shi arrangement is endowed with a filtration and a new basis, compatible with this filtration, is found. This basis is compared to the trivial basis. The ring is given ... More

Un theoreme de Cartier-Milnor-Moore-Quillen pour les bigebres dendriformes et les algebres bracesMay 25 2000Jul 11 2000We define an equivalence of categories, quite similar to the classical Cartier-Milnor-Moore-Quillen theorem, between the category of connected dendriform bialgebras and the category of brace algebras. This equivalence is given by the functors "subspace ... More

Real algebraic morphisms on 2-dimensional conic bundlesOct 20 2003Given two nonsingular real algebraic varieties V and W, we consider the problem of deciding whether a smooth map f: V -> W can be approximated by regular maps in the space of smooth maps from V to W. Our main result is a complete solution to this problem ... More

The Modular Gromov-Hausdorff PropinquityAug 17 2016Sep 02 2016We introduce a metric on Hilbert modules equipped with a generalized form of a differential structure, thus extending Gromov-Hausdorff convergence theory to vector bundles and quantum vector bundles --- not convergence as total space but indeed as quantum ... More

The Quantum Gromov-Hausdorff PropinquityFeb 17 2013Nov 30 2013We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative geometry and strengthens Rieffel's quantum Gromov-Hausdorff distance and Rieffel's ... More

Triangle Inequality and the Dual Gromov-Hausdorff PropinquityApr 25 2014Jan 27 2016The dual Gromov-Hausdorff propinquity is a generalization of the Gromov-Hausdorff distance to the class of Leibniz quantum compact metric spaces, designed to be well-behaved with respect to C*-algebraic structures. In this paper, we present a variant ... More

The Dual Gromov-Hausdorff PropinquityNov 01 2013Mar 17 2014Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*-algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named ... More

Un portrait kaléidoscopique du jeune Camille JordanMay 24 2012This paper aims to provide an overview of recent researches studies on Camille Jordan's early works (1860-1870). We especially shed new light on the relation between Galois and Jordan by discussing the collective dimensions of Jordan's works and their ... More

Real rational surfacesMar 04 2015May 27 2015We survey some results on real rational surfaces focused on their topology and their birational geometry.

On the structure of codimension 1 foliations with pseudoeffective conormal bundleApr 28 2014Let $X$ a projective manifold equipped with a codimension $1$ (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus defines a codimension ... More