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Orange emission in Pr3+-doped fluoroindate glassesOct 23 2012We synthesize and study the properties of praseodymium doped fluoroindate glasses. Glass compositions with praseodymium molar concentrations up to 5% were obtained with good optical quality. Thermal, optical, and luminescence properties are investigated. ... More

Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memoryJan 27 2014In quantum teleportation, the state of a single quantum system is disembodied into classical information and purely quantum correlations, to be later reconstructed onto a second system that has never directly interacted with the first one. This counterintuitive ... More

High Resolution Optical Spectroscopy and Magnetic Properties of Yb3+ in Y2SiO5Jun 22 2016Rare earth doped crystals are promising systems for quantum information processing. In particular paramagnetic rare earths could be used to build coherent interfaces with optical and microwave photons. In addition, isotopes with non zero nuclear spins ... More

Faithful Solid State Optical Memory with Dynamically Decoupled Spin Wave StorageFeb 14 2013We report an optical memory in a rare earth doped crystal with long storage times, up to 20 ms, together with an optical bandwidth of 1.5 MHz. This is obtained by transferring optical coherences to nuclear spin coherences, which were then protected against ... More

Tropical mirror symmetry in dimension oneSep 27 2018We prove a tropical mirror symmetry theorem for descendant Gromov-Witten invariants of the elliptic curve, generalizing a tropical mirror symmetry theorem for Hurwitz numbers of the elliptic curve. For the case of the elliptic curve, the tropical version ... More

Counts of (tropical) curves in $E\times \mathbb{P}^1$ and Feynman integralsDec 12 2018We study generating series of Gromov-Witten invariants of $E\times\mathbb{P}^1$ and their tropical counterparts. Using tropical degeneration and floor diagram techniques, we can express the generating series as sums of Feynman integrals, where each summand ... More

Towards highly multimode optical quantum memory for quantum repeatersDec 09 2015Long-distance quantum communication through optical fibers is currently limited to a few hundreds of kilometres due to fiber losses. Quantum repeaters could extend this limit to continental distances. Most approaches to quantum repeaters require highly ... More

Simultaneous coherence enhancement of optical and microwave transitions in solid-state electronic spinsDec 22 2017Solid-state electronic spins are extensively studied in quantum information science, both for quantum computation, sensing and communication. Electronic spins are highly interesting due to their large magnetic moments, which offer fast operations for ... More

Diode-pumped Pr:BaY2F8 cw orange laserNov 04 2010We report the realization of the continuous wave laser emission in the orange at 607 nm from a Pr:BaY2F8 (Pr:BYF) crystal pumped by a blue GaN laser diode. A maximal output power of 78 mW is obtained in a quasi single transverse mode beam. The effect ... More

Coherent spin control at the quantum level in an ensemble-based optical memoryJan 16 2015Jun 17 2015Long-lived quantum memories are essential components of a long-standing goal of remote distribution of entanglement in quantum networks. These can be realized by storing the quantum states of light as single-spin excitations in atomic ensembles. However, ... More

High precision measurement of the Dzyaloshinsky-Moriya interaction between two rare-earth ions in a solidMay 26 2016We report on a direct measurement of the pair-wise anti-symmetric exchange interaction, known as the Dzyaloshinsky-Moriya interaction (DMI), in a Nd3+-doped YVO4 crystal. To this end we introduce a broadband electron spin resonance technique coupled with ... More

Simultaneous coherence enhancement of optical and microwave transitions in solid-state electronic spinsDec 22 2017Jul 27 2018Solid-state electronic spins are extensively studied in quantum information science, as their large magnetic moments offer fast operations for computing and communication, and high sensitivity for sensing. However, electronic spins are more sensitive ... More

Hyperfine characterization and coherence lifetime extension in Pr3+:La2(WO4)3Jul 12 2011Rare-earth ions in dielectric crystals are interesting candidates for storing quantum states of photons. A limiting factor on the optical density and thus the conversion efficiency is the distortion introduced in the crystal by doping elements of one ... More

Coherent storage of microwave excitations in rare-earth nuclear spinsDec 23 2014Interfacing between various elements of a computer - from memory to processors to long range communication - will be as critical for quantum computers as it is for classical computers today. Paramagnetic rare earth doped crystals, such as Nd$^{3+}$:Y$_2$SiO$_5$ ... More

High resolution transient and permanent spectral hole burning in Ce$^{3+}$:Y$_2$SiO$_5$ at liquid helium temperaturesApr 08 2016We perform hole burning with a low drift stabilized laser within the zero phonon line of the 4f-5d transition in Ce$^{3+}$:Y$_2$SiO$_5$ at 2K. The narrowest spectral holes appear for small applied magnetic fields and are $6\pm4$ MHz wide (FWHM). This ... More

Electron Spin Coherences in Rare-Earth Optically Excited States for Microwave to Optical Quantum TransducersFeb 09 2018Efficient and reversible optical to microwave coherent transducers are required to enable entanglement transfer between superconducting qubits and light for quantum networks. Rare-earth-doped crystals that possess narrow optical and spin transitions are ... More

Experimental Tailoring of a Three-Level Lambda System in Tm3+:YAGSep 14 2005Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory ... More

Characterization of the hyperfine interaction of the excited $^5$D$_0$ state of Eu$^{3+}$:Y$_2$SiO$_5$Oct 20 2017We characterize the Europium (Eu$^{3+}$) hyperfine interaction of the excited state ($^5$D$_0$) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all ... More

Spectral hole lifetimes and spin population relaxation dynamics in neodymium-doped yttrium orthosilicateNov 16 2016We present a detailed study of the lifetime of optical spectral holes due to population storage in Zeeman sublevels of Nd$^{3+}$:Y$_2$SiO$_5$. The lifetime is measured as a function of magnetic field strength and orientation, temperature and Nd$^{3+}$ ... More

Characterization of the hyperfine interaction of the excited $^5$D$_0$ state of Eu$^{3+}$:Y$_2$SiO$_5$Oct 20 2017Mar 16 2018We characterize the Europium (Eu$^{3+}$) hyperfine interaction of the excited state ($^5$D$_0$) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all ... More

Measurement of line widths and permanent electric dipole moment change of the Ce 4f-5d transition in Y_2SiO_5 for a qubit readout scheme in rare-earth ion based quantum computingMar 04 2013In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce ... More

Optical Excitation of Nuclear Spin Coherence in Tm3+:YAGOct 17 2007A thulium-doped crystal is experimentally shown to be an excellent candidate for broadband quantum storage in a solid-state medium. For the first time, nuclear spin coherence is optically excited, detected and characterized in such a crystal. The lifetime ... More

Transferability of crystal-field parameters for rare-earth ions in Y$_2$SiO$_5$ tested by Zeeman spectroscopyOct 31 2018Zeeman spectroscopy is used to demonstrate that phenomenological crystal-field parameters determined for the two $C_1$ point-group sites in Er$^{3+}$:Y$_2$SiO$_5$ may be transferred to other ions. The two crystallographic six- and seven-coordinate substitutional ... More

A comprehensive understanding of ground and optically-excited hyperfine structure of $^{167}$Er$^{3+}$:Y$_2$SiO$_5$Sep 04 2018Using high-performance computing techniques and targeted experimental investigation we have developed a predictive crystal-field model of the complex hyperfine structure of $^{167}$Er$^{3+}$:Y$_2$SiO$_5$ We simultaneously match site-selective spectroscopic ... More

Branching ratio measurement of a "Lambda" system in Tm3+:YAG under magnetic fieldJun 06 2006Dec 21 2006A three-level Lambda system in Tm3+ doped YAG crystal is experimentally investigated in the prospect of quantum information processing. Zeeman effect is used to lift the nuclear spin degeneracy of this ion. In a previous paper [de Seze et al. Phys. Rev. ... More

Efficient optical pumping of Zeeman spin levels in Nd3+:YVO4Feb 15 2010We demonstrate that Zeeman ground-state spin levels in Nd3+:YVO4 provides the possibility to create an efficient lambda-system for optical pumping experiments. The branching ratio R in the lambda-system is measured experimentally via absorption spectroscopy ... More

High-cooperativity coupling of rare-earth spins using yttrium orthosilicate as a substrateJan 10 2019Yttrium orthosilicate (Y$_2$SiO$_5$, or YSO) has proved to be a convenient host for rare-earth ions used in demonstrations of microwave quantum memories and optical memories with microwave interfaces, and shows promise for coherent microwave-optical conversion ... More

A multiplicative property of quantum flag minorsDec 19 2001We study multiplicative properties of the (quantum) dual canonical basis B* associated to a semi-simple complex Lie group G. We provide a subset D of B* such that the following property holds : if two elements b, b' in B* q-commute and if one of these ... More

Gif Lectures on Cosmic AccelerationDec 18 2009Jan 06 2010These lecture notes cover some of the theoretical topics associated with cosmic acceleration. Plausible explanations to cosmic acceleration include dark energy, modified gravity and a violation of the Copernican principle. Each of these possibilities ... More

Harmonic functions on the real hyperbolic ball I : Boundary values and atomic decomposition of Hardy spacesFeb 08 1999We study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic ball. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution.In doing so, we put forward different ... More

Disambiguating with Controlled DisjunctionsOct 14 1997In this paper, we propose a disambiguating technique called controlled disjunctions. This extension of the so-called named disjunctions relies on the relations existing between feature values (covariation, control, etc.). We show that controlled disjunctions ... More

Weighted Paley-Wiener spaces and mountain chain axioms: a detailed expositionMay 01 2013The present work reviews the second half of Lyubarskii and Seip's paper, Weighted Paley--Wiener Spaces. Axioms defining a larger class of de Branges spaces are abstracted, allowing us to state and prove their results at a higher level of generality.

High temperature Sherrington-Kirkpatrick model for general spinsOct 09 2002Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a linear model. ... More

Zero-free regions of radar ambiguity functions and momentsJun 16 2006In this article, we give an estimate of the zero-free region around the origin of the ambiguity function of a signal $u$ in terms of the moments of $u$. This is done by proving an uncertainty relation between the first zero of the Fourier transform of ... More

Uncertainty principles for orthonormal basesJun 16 2006In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal ... More

Spin dynamics in Cuprates and its relation to superconductivitySep 25 2000The relevance of magnetism for the mechanism responsible for high-temperature superconductivity remains an open and still interesting issue. The observation by inelastic neutron scattering of strong antiferromagnetic dynamical correlations in superconducting ... More

T-homotopy and refinement of observation (IV) : Invariance of the underlying homotopy typeMay 16 2005Jun 06 2006This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this fourth part, it is proved ... More

T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologiesMay 16 2005Sep 20 2006This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part, it is proved ... More

T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalencesMay 16 2005Mar 26 2007This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts ... More

Concurrent Process up to Homotopy (II)Feb 24 2003One proves that the category of globular CW-complexes up to dihomotopy is equivalent to the category of flows up to weak dihomotopy. This theorem generalizes the classical theorem which states that the category of CW-complexes up to homotopy is equivalent ... More

A Convenient Category for The Homotopy Theory of ConcurrencyJan 25 2002May 03 2005Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.

SIMBOL-X, an X-ray telescope for the 0.5-70 keV rangeOct 10 2002SIMBOL-X is a high energy "mini" satellite class mission that is proposed by a European collaboration for a launch in 2009. SIMBOL-X is making use of a classical X-ray mirror, of ~600 cm2 maximum effective area, with a 30 m focal length in order to cover ... More

Spectroscopy of Gauge Theories Based on Exceptional Lie GroupsJul 18 2001Jul 25 2001We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E(6) and E(7), up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and revisit the ... More

Finite Number of States, de Sitter Space and Quantum Groups at Roots of UnityJun 26 2003Jul 20 2003This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why ... More

Raman Spectrometry, a Unique Tool to Analyze and Classify Ancient Ceramics and GlassesJan 15 2007Raman micro/macro-spectroscopy allows for a non-destructive remote analysis: body and glaze, crystalline and amorphous phases can be identified, including the nanosized pigments colouring the glaze. Last generation instruments are portable which allows ... More

Generalised Mertens and Brauer-Siegel TheoremsMar 20 2007In this article, we prove a generalisation of the Mertens theorem for prime numbers to number fields and algebraic varieties over finite fields, paying attention to the genus of the field (or the Betti numbers of the variety), in order to make it tend ... More

Computations of Nambu-Poisson cohomologiesJul 17 2000Mar 01 2001We try to generalize the Poisson cohomology of a 2-dimensional Poisson manifold to the n-vectors on a n-dimensional manifold. We define several cohomologies and we compute locally some of them, in the case of germs at 0 of n-vectors on a real or complex ... More

Free probability and combinatoricsApr 22 2003A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of cumulants in probability theory. We review this theory, and explain the ... More

Group actions, $k$-derivations and finite morphismsApr 06 2006Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which conditions on ... More

Isotypic Decomposition of the Cohomology and Factorization of the Zeta Functions of Dwork HypersurfacesDec 10 2009The aim of this article is to illustrate, on the example of Dwork hypersurfaces, how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.

The quantum Poincare group from quantum group contractionSep 18 1994We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$ is sent to ... More

The Herschel View of Star FormationSep 30 2013Recent studies of the nearest star-forming clouds of the Galaxy at submillimeter wavelengths with the Herschel Space Observatory have provided us with unprecedented images of the initial conditions and early phases of the star formation process. The Herschel ... More

Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard modelAug 17 2015May 10 2016An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the doped Hubbard ... More

Cuspidal RobotsOct 13 2016This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then been fascinating ... More

Estimation of the shift parameter in regression models with unknown distribution of the observationsDec 20 2013This paper is devoted to the estimation of the shift parameter in a semiparametric regression model when the distribution of the observation times is unknown. Hence, we propose to use a stochastic algorithm which takes into account the estimation of the ... More

Against all odds? Forming the planet of the HD196885 binaryMar 20 2011HD196885Ab is the most "extreme" planet-in-a-binary discovered to date, whose orbit places it at the limit for orbital stability. The presence of a planet in such a highly perturbed region poses a clear challenge to planet-formation scenarios. We investigate ... More

Logarithmic conformal invariance in the Abelian sandpile modelMar 18 2013We review the status of the two-dimensional Abelian sandpile model as a strong candidate to provide a lattice realization of logarithmic conformal invariance with central charge c=-2. Evidence supporting this view is collected from various aspects of ... More

Wind on the boundary for the Abelian sandpile modelJul 25 2007Jul 25 2007We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic ... More

Symmetric boundary conditions in boundary critical phenomenaApr 14 1999Jun 30 1999Conformally invariant boundary conditions for minimal models on a cylinder are classified by pairs of Lie algebras $(A,G)$ of ADE type. For each model, we consider the action of its (discrete) symmetry group on the boundary conditions. We find that the ... More

Automorphisms of the affine SU(3) fusion rulesJan 29 1993We classify the automorphisms of the (chiral) level-k affine SU(3) fusion rules, for any value of k, by looking for all permutations that commute with the modular matrices S and T. This can be done by using the arithmetic of the cyclotomic extensions ... More

Idéal de Bernstein d'un arrangement central générique d'hyperplansOct 06 2016Let $ V $ a vector space of dimension $n$. A $V$ family $ \{H_1, \ldots, H_p \} $ of vectorial hyperplanes being distinct two by two defines an arrangement $ {\cal A}_p = {\cal A} ( H_1, \ldots ,H_p ) $ of $ V $. For $ i \in \{ 1, \ldots, p \} $, let ... More

L'idéal de Bernstein d'un arrangement libre d'hyperplans linéairesOct 06 2016Let $ V $ a vector space of dimension $n$. A family $ \{H_1, \ldots, H_p \} $ of vectorial hyperplans $V$ defines an arrangement $ {\cal A} $ of $ V $. For $ i \in \{ 1, \ldots, p \} $, let $ l_i $ be a linear form on $V$ with $H_i$ as kernel. We denote ... More

A note on rational surfaces in projective four-spaceMay 24 1999It is proved that a smooth rational surface in projective four-space, which is ruled by cubics or quartics has degree at most 12. It is also proved that a smooth rational surface in projective four-space which is the image of Fn by a linear system with ... More

Spin-1/2 frustrated antiferromagnet on a spatially anisotopic square lattice: contribution of exact diagonalizationsJul 04 2003Apr 07 2004The phase diagram of a spin-1/2 $J-J'-J_2$ model is investigated by means of exact diagonalizations on finite samples. This model is a generalization of the $J_1-J_2$ model on the square lattice with two different nearest-neighbor couplings $J,J'$ and ... More

Comment on the article arXiv 0710.0349 by Chapoton et al. titled ``An operational calculus for the Mould operad''Oct 11 2007Apr 16 2008This paper has been withdrawn.

From entangled codipterous coalgebras to coassociative manifoldsJan 09 2003We construct from coassociative coalgebras, bialgebras, Hopf algebras, new objects such as Poisson algebras, Leibniz algebras defined by J-L Loday and M. Ronco and explore the notion of coassociative manifolds.

Maximal eigenvalue and norm of the product of Toeplitz matrices. Study of a particular caseOct 29 2012In this paper we describe the asymptotic behaviour of the spectral norm of the product of two finite Toeplitz matrices as the matrix dimension goes to the infinity. These Toeplitz matrices are generated by positive functions with Fisher-Hartwig singularities ... More

On the Zeta Function of a Family of QuinticsJul 21 2009In this article, we give a proof of the link between the zeta function of two families of hypergeometric curves and the zeta function of a family of quintics that was observed numerically by Candelas, de la Ossa, and Rodriguez Villegas. The method we ... More

Laplace copulas of multifactor gamma distributions are new generalized Farlie-Gumbel-Morgenstern copulasNov 22 2016This paper provides bifactor gamma distribution, trivariate gamma distribution and two copula families on [0, 1] n obtained from the Laplace transforms of the multivariate gamma distribution and the multi-factor gamma distribution given by [P ($\theta$)] ... More

Fedosov Star-Products and 1-Differentiable DeformationsSep 07 1998We show that every star product on a symplectic manifold defines uniquely a 1-differentiable deformation of the Poisson bracket. Explicit formulas are given. As a corollary we can identify the characteristic class of any star product as a part of its ... More

Invariant hypersurfaces for derivations in positive characteristicFeb 15 2006Let $A$ be an integral $k$-algebra of finite type over an algebraically closed field $k$ of characteristic $p>0$. Given a collection ${\cal{D}}$ of $k$-derivations on $A$, that we interpret as algebraic vector fields on $X=Spec(A)$, we study the group ... More

Asymptotics of the solitary waves for the generalised Kadomtsev-Petviashvili equationsFeb 21 2009We investigate the asymptotic behaviour of the localised solitary waves for the generalised Kadomtsev-Petviashvili equations. In particular, we compute their first order asymptotics in any dimension $N \geq 2$.

L-algebras, triplicial-algebras, within an equivalence of categories motivated by graphsSep 21 2007Apr 16 2008In a previous work, we gave a coalgebraic framework of directed graphs equipped with weights (or probability vectors) in terms of (Markov) L-coalgebras. They are K-vector spaces equipped with two co-operations, \Delta_M, \tilde{\Delta}_M verifying, (\tilde{\Delta}_M ... More

Sur le spectre des longueurs des groupes de trianglesJan 29 2009Feb 25 2009We describe in this report the beginning of the length spectra of fuchsian triangular groups

Directed algebraic topology and higher dimensional transition systemMar 25 2009Jun 18 2010Cattani-Sassone's notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional ... More

Homotopical equivalence of combinatorial and categorical semantics of process algebraNov 08 2007Nov 12 2007It is possible to translate a modified version of K. Worytkiewicz's combinatorial semantics of CCS (Milner's Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a ... More

Towards a homotopy theory of process algebraJan 19 2007May 15 2008This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every ... More

The geometry of cubical and regular transition systemsMay 20 2014Sep 29 2015There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and homotopical results of ... More

Towards a homotopy theory of higher dimensional transition systemsNov 03 2010Jan 30 2014We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition systems. In this paper, ... More

A characterization of Fourier transformsDec 16 2009The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups $\Z/nZ$, the integers $\Z$, the Torus $\T$ ... More

Embedding Dark Energy in SupergravityNov 15 2007We give a brief overview of some of the constraints on the embedding of dark energy in supergravity.

Relative exactness modulo a polynomial map and algebraic $(\mathbb{C}^p,+)$-actionsFeb 10 2006Let $F=(f_1,...,f_q)$ be a polynomial dominating map from $\mathbb{C}^n$ to $\mathbb{C}^q$. We study the quotient ${\cal{T}}^1(F)$ of polynomial 1-forms that are exact along the fibres of $F$, by 1-forms of type $dR+\sum a_idf_i$, where $R,a_1,...,a_q$ ... More

Toric degenerations of Schubert varietiesDec 18 2000Let $G$ be a simply connected semi-simple complex algebraic group. Fix a maximal torus $T$ and a Borel subgroup $B$ such that $T\subset B\subset G$. Let $W$ the Weyl group of $G$ relative to $T$. For any $w$ in $W$, let $X_w=\bar {BwB/B}$ denote the Schubert ... More

On harmonic elements for semi-simple Lie algebraDec 12 2000Let ${\goth g}$ be a semi-simple complex Lie algebra, ${\goth g}={\goth n^-}\oplus{\goth h}\oplus{\goth n}$ its triangular decomposition. Let $U({\goth g})$, resp. $U_q({\goth g})$, be its enveloping algebra, resp. its quantized enveloping algebra. This ... More

Directed polymer in random environment and last passage percolationAug 28 2008The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the Legendre transform ... More

T-homotopy and refinement of observation (I) : IntroductionMay 09 2005Jan 19 2006This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other construction in dihomotopy ... More

A model category for the homotopy theory of concurrencyAug 06 2003Dec 18 2003We construct a cofibrantly generated model structure on the category of flows such that any flow is fibrant and such that two cofibrant flows are homotopy equivalent for this model structure if and only if they are S-homotopy equivalent. This result provides ... More

The homotopy branching space of a flowJul 24 2003In this talk, I will explain the importance of the homotopy branching space functor (and of the homotopy merging space functor) in dihomotopy theory. The paper is a detailed abstract of math.AT/0304112 and math.AT/0305169.

T-homotopy and refinement of observation (V) : Strom model structure for branching and merging homologiesJan 05 2004May 16 2005We check that there exists a model structure on the category of flows whose weak equivalences are the S-homotopy equivalences. As an application, we prove that the generalized T-homotopy equivalences preserve the branching and merging homology theories ... More

On algebraic automorphisms and their rational invariantsApr 12 2007Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F) be the transcendence ... More

Coassociativity breaking and oriented graphsApr 29 2002This paper is an attempt to unify coassociative coalgebra theory and random walks on oriented graphs.

Kadath: a spectral solver for theoretical physicsSep 07 2009Jan 16 2010Kadath is a library that implements spectral methods in a very modular manner. It is designed to solve a wide class of problems that arise in the context of theoretical physics. Several types of coordinates are implemented and additional geometries can ... More

Fully Packed Loop configurations in a Triangle and Littlewood-Richardson coefficientsDec 01 2011In this work we continue our study of Fully Packed Loop (FPL) configurations in a triangle. These are certain subgraphs on a triangular subset of the square lattice, which first arose in the study of the usual FPL configurations on a square grid. We show ... More

Fully Packed Loop configurations in a triangleNov 25 2011Fully Packed Loop configurations (FPLs) are certain configurations on the square grid, naturally refined according to certain link patterns. If $A_X$ is the number of FPLs with link pattern $X$, the Razumov--Stroganov correspondence provides relations ... More

Nanomechanics of Advanced Polymer FibresOct 23 2006The micro/nano-structural evolution before and after tensile/compressive loading, fatigue and ultimately, failure has been studied by Raman (and IR) microspectroscopy for PBO, PET, PA66, PP, silk and hair using three probes: low wavenumber collective ... More

On Tsfasman--Vlăduţ Invariants of Infinite Global FieldsJan 07 2008In this article we study certain asymptotic properties of global fields. We consider the set of Tsfasman-Vladuts invariants of infinite global fields and answer some natural questions arising from their work. In particular, we prove the existence of infinite ... More

Rectangular Young tableaux and the Jacobi ensembleOct 22 2015It has been shown by Pittel and Romik that the random surface associated with a large rectangular Young tableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle. We show that in the corner, ... More

A Pleijel-type theorem for the quantum harmonic oscillatorDec 24 2015We prove a Pleijel-type theorem for the asymptotic behaviour of the number of nodal domains of eigenfunctions of the quantum harmonic oscillator in any dimension.

An Environmental Variation of ConstantsOct 09 2013Jun 24 2014Models of modified gravity, whereby local tests of gravity are evaded thanks to a screening mechanism of the chameleon or Damour-Polyakov types, lead to a spatial variation of the particle masses and the fine structure constant. This is triggered by the ... More

Isoparametric functions and harmonic unit vector fields in K-contact geometrySep 16 2013We provide some examples of harmonic unit vector fields as normalized gradients of isoparametric functions from a K-contact geometry setting.