Results for "Sylvain Lacroix"

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Integrable models with twist function and affine Gaudin modelsSep 18 2018This thesis deals with a class of integrable field theories called models with twist function. The main examples of such models are integrable non-linear sigma models, such as the Principal Chiral Model, and their deformations. A first obtained result ... More
Constrained affine Gaudin models and diagonal Yang-Baxter deformationsJul 10 2019We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging procedure which allows ... More
Cyclotomic Gaudin models, Miura opers and flag varietiesJul 25 2016Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$. Let $\nu \in \text{Aut}\, \mathfrak{g}$ be a diagram automorphism whose order divides $T \in \mathbb{Z}_{\geq 1}$. We define cyclotomic $\mathfrak{g}$-opers over the Riemann sphere $\mathbb{P}^1$ ... More
Cyclotomic Gaudin models, Miura opers and flag varietiesJul 25 2016Feb 23 2017Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$. Let $\nu \in \text{Aut}\, \mathfrak{g}$ be a diagram automorphism whose order divides $T \in \mathbb{Z}_{\geq 1}$. We define cyclotomic $\mathfrak{g}$-opers over the Riemann sphere $\mathbb{P}^1$ ... More
Fitting the Fermi-LAT GeV excess: on the importance of the propagation of electrons from dark matterJan 29 2015An excess of gamma rays at GeV energies has been detected in the Fermi-LAT data. This signal comes from a narrow region around the Galactic Center and has been interpreted as possible evidence for light (30 GeV) dark matter particles. Focussing on the ... More
LHC sensitivity to lepton flavour violating Z boson decaysJul 20 2012Aug 30 2012We estimate that the LHC could set bounds BR(Z -> mu^\pm e^\mp) < 4.1 * 10^{-7} and BR(Z -> tau^\pm mu^\mp)< 3.5 * 10^{-6} (at 95% C.L.) with 20 inverse fb of data at 8 TeV. A similar sensitivity can be anticipated for Z -> tau^\pm e^\mp, because we consider ... More
Local charges in involution and hierarchies in integrable sigma-modelsMar 06 2017Oct 17 2017Integrable $\sigma$-models, such as the principal chiral model, ${\mathbb{Z}}_T$-coset models for $T \in {\mathbb{Z}}_{\geq 2}$ and their various integrable deformations, are examples of non-ultralocal integrable field theories described by (cyclotomic) ... More
Heavy fermion behavior of itinerant frustrated systems: beta-Mn, Y(Sc)Mn_{2} and LiV_{2}O_{4}$Jul 27 2001Jul 31 2001These three metallic systems do not exhibit any magnetic ordering despite experiments show the existence of localized moments with large antiferromagnetic exchange: this is a consequence of the strong geometric frustration (Y(Sc)Mn_{2} and LiV_{2}O_{4} ... More
On the Hamiltonian integrability of the bi-Yang-Baxter sigma-modelDec 08 2015Feb 05 2016The bi-Yang-Baxter sigma-model is a certain two-parameter deformation of the principal chiral model on a real Lie group G for which the left and right G-symmetries of the latter are both replaced by Poisson-Lie symmetries. It was introduced by C. Klimcik ... More
Affine Gaudin models and hypergeometric functions on affine opersApr 04 2018Apr 17 2019We conjecture that quantum Gaudin models in affine types admit families of higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers associated with the Langlands ... More
Cubic hypergeometric integrals of motion in affine Gaudin modelsApr 18 2018We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst themselves and with ... More
Affine Gaudin models and hypergeometric functions on affine opersApr 04 2018We conjecture that quantum Gaudin models in affine types admit families of higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers associated with the Langlands ... More
Integrable coupled sigma-modelsNov 29 2018Jan 07 2019A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realisations of affine Gaudin models. In this language, ... More
On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type modelsJun 06 2016Yang-Baxter type models are integrable deformations of integrable field theories, such as the principal chiral model on a Lie group $G$ or $\sigma$-models on (semi-)symmetric spaces $G/F$. The deformation has the effect of breaking the global $G$-symmetry ... More
Three-parameter integrable deformation of Z_4 permutation supercosetsNov 01 2018Jan 07 2019A three-parameter integrable deformation of $\mathbb{Z}_4$ permutation supercosets is constructed. These supercosets are of the form $ {\widehat{F}} / {F_0}$ where $F_0$ is the bosonic diagonal subgroup of the product supergroup $\widehat{F}=\widehat{G} ... More
Assembling integrable sigma-models as affine Gaudin modelsMar 01 2019We explain how to obtain new classical integrable field theories by assembling two affine Gaudin models into a single one. We show that the resulting affine Gaudin model depends on a parameter $\gamma$ in such a way that the limit $\gamma \to 0$ corresponds ... More
Intermediate mass black holes and dark matter at the Galactic centerDec 01 2017Jan 30 2018Could there be a large population of intermediate-mass black holes (IMBHs) formed in the early universe? Whether primordial or formed in Population III, these are likely to be very subdominant compared to the dark matter density, but could seed early ... More
Breakdown of coherence in Kondo alloys: crucial role of concentration vs band fillingOct 12 2018We study the low energy states of the Kondo alloy model (KAM) as function of the magnetic impurity concentration per site, x, and the conduction electron average site occupation, nc. In previous works, two different Fermi liquid regimes had been identified ... More
Asymptotics for hitting timesMar 29 2005In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class {6pt} {-3mm}(A){6mm}F={F:R\to ... More
Three lectures on free probabilityMay 09 2012These are notes from a three-lecture mini-course on free probability given at MSRI in the Fall of 2010 and repeated a year later at Harvard. The lectures were aimed at mathematicians and mathematical physicists working in combinatorics, probability, and ... More
A minimal quasiparticle approach for the QGP and its large-$N_c$ limitsJun 03 2010Dec 13 2010We propose a quasiparticle approach allowing to compute the equation of state of a generic gauge theory with gauge group SU($N_c$) and quarks in an arbitrary representation. Our formalism relies on the thermal quasiparticle masses (quarks and gluons) ... More
Lifshitz transition in Kondo alloysOct 18 2012Jun 05 2013We study the low energy states of Kondo alloys as function of the magnetic impurity concentration per site, x, and the conduction electron average site occupation, nc. Using two complementary approaches, the mean-field coherent potential approximation ... More
A large-$N_c$ PNJL model with explicit Z$_{N_c}$ symmetryJul 23 2011Dec 29 2011A PNJL model is built, in which the Polyakov-loop potential is explicitly Z$_{N_c}$-symmetric in order to mimic a Yang-Mills theory with gauge group SU($N_c$). The physically expected large-$N_c$ and large-$T$ behaviours of the thermodynamic observables ... More
Champs algébriques et foncteur de PicardAug 24 2008This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint arXiv:0711.4545). ... More
Partial functional quantization and generalized bridgesJan 28 2011Sep 19 2012In this article, we develop a new approach to functional quantization, which consists in discretizing only a finite subset of the Karhunen-Lo\`eve coordinates of a continuous Gaussian semimartingale $X$. Using filtration enlargement techniques, we prove ... More
A fast nearest neighbor search algorithm based on vector quantizationMay 25 2011In this article, we propose a new fast nearest neighbor search algorithm, based on vector quantization. Like many other branch and bound search algorithms [1,10], a preprocessing recursively partitions the data set into disjointed subsets until the number ... More
Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz HamiltoniansJun 24 2008Jul 08 2008We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenvalues of the uncoupled system disappear and establish a limiting absorption ... More
Discrete D-branes in AdS3 and in the 2d black holeDec 19 2005Aug 11 2006I show how the AdS2 D-branes in the Euclidean AdS3 string theory are related to the continuous D-branes in Liouville theory. I then propose new discrete D-branes in the Euclidean AdS3 which correspond to the discrete D-branes in Liouville theory. These ... More
On sl3 Knizhnik-Zamolodchikov equations and W3 null-vector equationsNov 27 2008Aug 31 2009Starting from Sklyanin's separation of variables for the sl3 Yangian model, we derive the separation of variables for the quantum sl3 Gaudin model. We use the resulting new variables for rewriting the sl3 Knizhnik-Zamolodchikov equations, and comparing ... More
Boundary three-point function on AdS2 D-branesAug 22 2007Jan 10 2008Using the H3+-Liouville relation, I explicitly compute the boundary three-point function on AdS2 D-branes in H3+, and check that it exhibits the expected symmetry properties and has the correct geometrical limit. I then find a simple relation between ... More
A Type System For Call-By-Name ExceptionsJul 12 2009Nov 02 2009We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type for programs whose execution may raise an exception at top level, and a corruption type for programs that may raise ... More
Substitutional Al solute interaction with edge and screw dislocation in Ni: a comparison between atomistic computation and continuum elastic theoryMar 03 2009Molecular static simulations have been performed to study the interaction between a single dislocation and a substitutional Al solute atom in a pure crystal of Ni. When the Al solute is situated at intermediate distance from the slip plane, we find that ... More
Microquasars and JetsJun 01 2005I present an overview of past, present and future research on microquasars and jets, showing that microquasars, i.e. galactic jet sources, are among the best laboratories for high energy phenomena. After remindind the analogy with quasars, I focus on ... More
Multi-wavelength observations of the microquasar XTE J1720-318: a transition from high-soft to low-hard stateNov 17 2006To gain a better understanding of high-energy Galactic sources, we observed the Galactic X-ray binary and black hole candidate XTE J1720-318 in the optical and near-infrared, just after the onset of its X-ray outburst in January, 2003. These observations ... More
The role of microquasars in astroparticle physicsJul 31 2006I present an overview of past, present and future research on microquasars and jets, showing that microquasars, i.e. galactic jet sources, are among the best laboratories for high energy phenomena and astroparticle physics. After reminding the analogy ... More
Tensor hierarchies and Lie $n$-extensions of Leibniz algebrasAug 23 2017Aug 16 2018A Lie $n$-extension of a Leibniz algebra is a particular Lie $n$-algebra that lifts the skew-symmetric part of the Leibniz product in a natural way. In the present paper, we use the relationship between Leibniz algebras and tensor hierarchies to provide ... More
Some open 3-manifolds and 3-orbifolds without locally finite canonical decompositionsFeb 11 2008Feb 15 2008We give examples of open 3-manifolds and 3-orbifolds that exhibit pathological behavior with respect to splitting along surfaces (2-suborbifolds) with nonnegative Euler characteristic.
Contact manifolds and Weinstein h-cobordismsOct 09 2014Dec 01 2014We prove that closed connected contact manifolds of dimension $\geq 5$ related by an h-cobordism with a flexible Weinstein structure become contactomorphic after some kind of stabilization. We also provide examples of non-conjugate contact structures ... More
Proof of de Smit's conjecture: a freeness criterionJul 07 2016Jun 16 2017Let $A\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper "The ... More
Théorie des déformations équivariantes des morphismes localement d'intersection complèteOct 09 2003This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
Reconstruction du squelette des courbes analytiquesApr 05 2019In this work we bring to light some anabelian behaviours of analytic curves in the setting of Berkovich geometry. We show more precisely that the knowledge of the tempered fundamental group of some curves that we call anabelian determines their analytic ... More
Galactic Winds: Near and FarSep 03 2003Sep 15 2003Multiwavelength data on star-forming galaxies provide strong evidence for large-scale galactic winds in both nearby and distant objects. The results from recent ground-based and space-borne programs are reviewed. The impact of these winds on the host ... More
Spectroscopic Diagnostics for AGNsJan 08 2002A review of the spectroscopic tools needed to characterize AGNs is presented. This review focusses on ultraviolet, optical and infrared emission-line diagnostics specifically designed to help differentiate AGNs from starburst-dominated galaxies. The strengths ... More
Multiwavelength Observations of Galactic Winds: Near and FarOct 20 2003This paper provides a critical discussion of the observational evidence for winds in our own Galaxy, in nearby star-forming and active galaxies, and in the high-redshift universe. The implications of galactic winds on the formation and evolution of galaxies ... More
How to reveal the mysteries of the most obscured high-energy sources of our Galaxy, discovered by INTEGRAL?Oct 01 2007A new type of high-energy binary systems has been revealed by the INTEGRAL satellite. These sources are in the course of being unveiled by means of multi-wavelength optical, near- and mid-infrared observations. Among these sources, two distinct classes ... More
Numerical Contractor Renormalization applied to strongly correlated systemsOct 28 2005We demonstrate the utility of effective Hamilonians for studying strongly correlated systems, such as quantum spin systems. After defining local relevant degrees of freedom, the numerical Contractor Renormalization (CORE) method is applied in two steps: ... More
Tree structures for the current fluctuations in the exclusion processNov 18 2009Feb 22 2010We consider the asymmetric simple exclusion process on a ring, with an arbitrary asymmetry between the hopping rates of the particles. Using a functional formulation of the Bethe equations of the model, we derive exact expressions for all the cumulants ... More
Ground state energy of the $δ$-Bose gas at weak coupling from double extrapolationOct 12 2016Nov 04 2016We consider the ground state energy $e(\gamma)$ of the $\delta$-Bose gas with repulsive interaction in the weak coupling regime $\gamma\to0$, where previous studies gave the expansion $e(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$. ... More
A family of solvable non-rational conformal field theoriesMar 14 2008May 23 2008We find non-rational conformal field theories in two dimensions, which are solvable due to their correlators being related to correlators of Liouville theory. Their symmetry algebra consists of the dimension-two stress-energy tensor, and two dimension-one ... More
Minimal lectures on two-dimensional conformal field theorySep 29 2016We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define Liouville theory and minimal ... More
Cordes et D-branes dans les espaces-temps courbesSep 30 2003Oct 10 2003This thesis is devoted to the construction and study of D-branes in some curved space-times in string theory. On the one hand, those D-branes are described geometrically as submanifolds subject to Born-Infeld effective dynamics. On the other hand, they ... More
On the instability of eigenvaluesJan 05 2011This is the proceeding of a talk given in Workshop on Differential Geometry and its applications at Alexandru Ioan Cuza University Ia\c{s}i, Romania, September 2--4, 2009. I explain how positive commutator estimates help in the analysis of embedded eigenvalues ... More
The Nyström method for functional quantization with an application to the fractional Brownian motionSep 07 2010In this article, the so-called "Nystr\"om method" is tested to compute optimal quantizers of Gaussian processes. In particular, we derive the optimal quantization of the fractional Brownian motion by approximating the first terms of its Karhunen-Lo\`eve ... More
A Simplicial Approach to Stratified Homotopy TheoryJan 15 2018In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial combinatorial model category. ... More
Topologies de Grothendieck, descente, quotientsOct 01 2012In this note, we present a few existence theorems for the quotient of a scheme by the action of a group. The first two sections are devoted to Grothendieck topologies and descent theory. The third one is dealing with quotients: we first give direct and ... More
Duality for commutative group stacksApr 01 2014Jun 21 2019We study in this article the dual of a (strictly) commutative group stack $G$ and give some applications. Using the Picard functor and the Picard stack of $G$, we first give some sufficient conditions for $G$ to be dualizable. Then, for an algebraic stack ... More
Stratified Whitehead's theorem and knot invariantsApr 03 2019By considering homotopies that preserve the stratification, one obtains a natural notion of homotopy for stratified spaces. In this short note, we introduce invariants of stratified homotopy, the stratified homotopy groups. We show that they satisify ... More
Espace de modules des courbes hyperelliptiques stables et une inégalité de Cornalba-Harris-XiaoJul 03 2001Mar 21 2002In this paper, we show an inequality between the degrees of the conductor and the Hodge fiber of a hyperelliptic curve above a discrete valuation ring. For that we have to show theorems about the lifting of $p$-cyclic covers in order to obtain informations ... More
Aller-retour vers l'inseparableSep 14 2009We construct inseparable morphisms between curves of genus $\ge 2$ that are degenerations of separable morphisms.
Déformations équivariantes des courbes stables I : Étude cohomologiqueOct 09 2003Let $k$ be a field, $C\to \Spec k$ be a stable curve and let $G$ be a finite group acting faithfully on the curve $C\to \Spec k$. In this article, we compute the vector space $\Ext^1_G(\Omega_{C/k}, \O_C)$, the sheaf $\Omega_{C/k}$ being the sheaf of ... More
Ground state energy of the $δ$-Bose gas at weak coupling from double extrapolationOct 12 2016We consider the ground state energy $e(\gamma)$ of the $\delta$-Bose gas with repulsive interaction in the weak coupling regime $\gamma\to0$, where previous analytical studies gave the expansion $e(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$. ... More
Fabry-Perot Survey of Emission-Line GalaxiesJan 29 2002The recent results from a deep Fabry-Perot survey of nearby active and star-forming galaxies are presented. Line-emitting material is detected over two orders of magnitude in galactocentric radius, from the 100-pc scale of the active or starbursting nucleus ... More
The Starburst-AGN ConnectionDec 06 2000The issue of a starburst-AGN connection in local and distant galaxies is relevant for understanding galaxy formation and evolution, the star formation and metal enrichment history of the universe, the origin of the extragalactic background at low and ... More
Local Ultraluminous Infrared Galaxies and QuasarsMar 01 2006This paper reviews the recent results from a comprehensive investigation of the most luminous mergers in the local universe, the ultraluminous infrared galaxies (ULIRGs) and the quasars. First, the frequency of occurrence and importance of black hole ... More
Perturbations of C1-diffeomorphisms and dynamics of generic conservative diffeomorphisms of surfaceNov 21 2010In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generic conservative diffeomorphism of a connected compact ... More
Fermi-LAT results on Galactic Plane gamma-ray Transient SourcesMay 01 2010The Large Area Telescope on the Fermi gamma-ray Space Telescope provides unprecedented sensitivity for all-sky monitoring of gamma-ray activity. It has detected a few Galactic sources, including 2 gamma-ray binaries and a microquasar. In addition, it ... More
Perturbation de la dynamique de difféomorphismes en topologie C^1 / Perturbation of the dynamics of diffeomorphisms in the C^1-topologyDec 15 2009Les travaux pr\'esent\'es dans ce m\'emoire portent sur la dynamique de diff\'eomorphismes de vari\'et\'es compactes. Pour l'\'etude des propri\'et\'es g\'en\'eriques ou pour la construction d'exemples, il est souvent utile de savoir perturber un syst\`eme. ... More
A combinatorial solution for the current fluctuations in the exclusion processApr 15 2009Jul 31 2009We conjecture an exact expression for the large deviation function of the stationary state current in the partially asymmetric exclusion process with periodic boundary conditions. This expression is checked for small systems using functional Bethe Ansatz. ... More
Choosing a penalty for model selection in heteroscedastic regressionDec 16 2008Jun 04 2010We consider the problem of choosing between several models in least-squares regression with heteroscedastic data. We prove that any penalization procedure is suboptimal when the penalty is a function of the dimension of the model, at least for some typical ... More
D3-branes in NS5-brane backgroundsJan 14 2003May 07 2003We study D3-branes in an NS5-branes background defined by an arbitrary 4d harmonic function. Using a gauge-invariant formulation of Born-Infeld dynamics as well as the supersymmetry condition, we find the general solution for the $\omega$-field. We propose ... More
A JSJ splitting for triangulated open 3-manifoldsFeb 11 2008We give a sufficient condition for an open 3-manifold to admit a decomposition along properly embedded open annuli and tori, generalizing the toric splitting of Jaco-Shalen and Johannson.
Computation of the Central Charge for the Leading Order of the N=2 Super-Yang-Mills Effective ActionMay 26 1999The central charge in the N=2 Super-Yang-Mills theory plays an essential role in the work of Seiberg and Witten as it gives the mass spectrum of the BPS states of the quantum theory. Our aim in this note is to present a direct computation of this central ... More
Model selection by resampling penalizationJun 17 2009In this paper, a new family of resampling-based penalization procedures for model selection is defined in a general framework. It generalizes several methods, including Efron's bootstrap penalization and the leave-one-out penalization recently proposed ... More
Conformal field theory on the planeJun 17 2014Feb 25 2016We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. ... More
Minisuperspace limit of the AdS3 WZNW modelDec 22 2009May 28 2010We derive the three-point function of the AdS3 WZNW model in the minisuperspace limit by Wick rotation from the H3+ model. The result is expressed in terms of Clebsch-Gordan coefficients of the Lie algebra sl(2,R). We also introduce a covariant basis ... More
Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theoryJul 12 2005Aug 28 2005I generalize the Knizhnik-Zamolodchikov equations to correlators of spectral flowed fields in AdS3 string theory. If spectral flow is preserved or violated by one unit, the resulting equations are equivalent to the KZ equations. If spectral flow is violated ... More
Expansion of the propagation of chaos for Bird and Nanbu systemsJan 22 2009Oct 18 2016The Bird and Nanbu systems are particle systems used to approximate the solution of the mollied Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94, GM97, GM99], we use coupling techniques and results on branching ... More
Fluctuations and skewness of the current in the partially asymmetric exclusion processMay 27 2008Jul 17 2008We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant) and obtain ... More
Obscured sources and Supergiant Fast X-ray Transients: new classes of high mass X-ray binariesOct 01 2007A new type of high-energy binary systems has been revealed by the INTEGRAL satellite. These sources are in the course of being unveiled by means of multi-wavelength optical, near- and mid-infrared observations. Among these sources, two distinct classes ... More
Phase diagram of interacting spinless fermions on the honeycomb latticeSep 05 2016Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical ... More
Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard latticeNov 15 2016We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible ... More
Proof of de Smit's conjecture: a freeness criterionJul 07 2016Let $A\to B$ be a morphism of Artin local rings with the same embedding dimension. We prove that any $A$-flat $B$-module is $B$-flat. This freeness criterion was conjectured by de Smit in 1997 and improves Diamond's Theorem 2.1 from his 1997 paper "The ... More
Foncteur de Picard d'un champ algébriqueNov 28 2007In this article we study the Picard functor and the Picard stack of an algebraic stack. We give a new and direct proof of the representability of the Picard stack. We prove that it is quasi-separated, and that the connected component of the identity is ... More
Conformal field theory on the planeJun 17 2014May 09 2017We provide an introduction to conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry. ... More
A spherical decomposition for Riemannian open 3-manifoldsMay 12 2006We show that open 3-manifolds that have a locally finite decomposition along 2-spheres are characterized by the existence of a Riemannian metric with respect to which the second homotopy group of the manifold is generated by small elements.
Some applications of Ricci flow to 3-manifoldsJan 31 2008We decribe and announce some results (joint with G. Besson, L. Bessieres, M. Boileau and J.Porti) about the geometry and topology of 3-manifolds. Most of the article is primarily intended as an introduction for nonexperts to geometrization of 3-manifolds, ... More
A finite presentation of the mapping class group of an oriented surfaceNov 27 1998We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.
Partial hyperbolicity far from homoclinic bifurcationsSep 29 2008We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its chain-recurrent ... More
Large-scale conformal rigidity in dimension threeOct 28 2002We define a complete Riemannian manifold X to be large-scale conformally rigid if all groups that are quasi-isometric to some complete Riemannian manifold of bounded geometry conformal to X are quasi-isometric to X. We prove that many 3-manifolds, including ... More
The general setting for Shape AnalysisApr 07 2015In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion encompasses every ... More
Hardy inequality and asymptotic eigenvalue distribution for discrete LaplaciansJun 03 2011Oct 25 2013In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.
Unboundedness of adjacency matrices of locally finite graphsOct 19 2009Mar 16 2010Given a locally finite simple graph so that its degree is not bounded, every self-adjoint realization of the adjacency matrix is unbounded from above. In this note we give an optimal condition to ensure it is also unbounded from below. We also consider ... More
AdS2 D-branes in AdS3 spacetimeJul 10 2002I review some recent progress in understanding the properties of AdS2 branes in AdS3. Different methods - classical string motion, Born-Infeld dynamics, boundary states - are evocated and compared.
The AGN Paradigm: Radio-Quiet ObjectsNov 11 2002The current paradigm for radio-quiet AGNs is reviewed, taking into account new results from recent large-scale surveys carried out from the ground and from space. Topics include structure of the central engine, AGN demography, fueling/triggering processes, ... More
Singular topologies in the Boulatov modelDec 13 2011Jun 28 2012Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.
On 2d CFTs that interpolate between minimal modelsSep 11 2018Dec 04 2018We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions ... More
Quelques calculs d'espaces $\R^i f_* G$ sur des courbesMar 31 2008Mar 17 2009We give some properties (cancellation, representability, stratification) of the sheaf R^i f_* G for an affine relative curve f:U -> S admitting a smooth compactification and G a solvable group.
A short guide through integration theorems of generalized distributionsOct 04 2017Aug 27 2018The generalization of Frobenius' theorem to foliations with singularities is usually attributed to Stefan and Sussmann, for their simultaneous discovery around 1973. However, their result is often referred to without caring much on the precise statement, ... More
On a compactification of a Hurwitz space in the wild caseSep 06 2005Let $g$ and $g'$ be two integers and $p$ a prime number. Denote by $\mathscr H_{g, g', p}^c$ the moduli space of morphisms of degree $p$ between smooth curves of genus $g$ and $g'$ and with constant ramification. The purpose of this article is to construct ... More
V-fold cross-validation improved: V-fold penalizationFeb 05 2008Feb 07 2008We study the efficiency of V-fold cross-validation (VFCV) for model selection from the non-asymptotic viewpoint, and suggest an improvement on it, which we call ``V-fold penalization''. Considering a particular (though simple) regression problem, we prove ... More