Results for "Raquel García-Bertrand"

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Robust Transmission Network Expansion Planning under Correlated UncertaintyJan 26 2015Apr 02 2019This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given ... More
Robust Dynamic Transmission and Renewable Generation Expansion Planning: Walking Towards Sustainable SystemsJan 30 2017Nowadays, the transition from a conventional generation system to a renewable generation system is one of the most difficult challenges for system operators and companies. There are several reasons: the long-standing impact of investment decisions, the ... More
Robust Transmission Network Expansion Planning Problem Considering Storage UnitsJul 10 2019This paper addresses the transmission network expansion planning problem considering storage units under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby short- and long-term uncertainties ... More
Multifractality of open quantum systemsJun 12 2019We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify ... More
Adaptive Robust Transmission Network Expansion Planning using Structural Reliability and Decomposition TechniquesJan 26 2015Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem ... More
On the Solution of Large-Scale Robust Transmission Network Expansion Planning under Uncertain Demand and Generation CapacitySep 26 2016Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, available solution methodologies for the resulting trilevel robust ... More
Electric and magnetic dipolar response of Germanium spheres: Interference effects, scattering anisotropy and optical forcesApr 18 2011We address the scattering cross sections, and their consequences, for submicrometer Germanium spheres. It is shown that there is a wide window in the near infrared where light scattering by these particles is fully described by their induced electric ... More
Scaling theory of the Anderson transition in random graphs: ergodicity and universalitySep 09 2016Nov 09 2016We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase ... More
Modular classes of Poisson-Nijenhuis Lie algebroidsJan 17 2007May 18 2007The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the ... More
Phase-Space Noncommutativity and the Dirac EquationMay 13 2011Oct 06 2011We consider full phase-space noncommutativity in the Dirac equation, and find that in order to preserve gauge invariance, configuration space noncommutativity must be dropped. The resulting space structure gives rise to a constant magnetic field background ... More
Sequences of Open Riemannian Manifolds with BoundaryJan 17 2013Jun 19 2013We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we examine "$\delta$ inner regions" which avoid the boundary by a distance ... More
Robust Transmission Network Expansion Planning in Energy Systems: Improving Computational PerformanceJan 22 2015Jul 01 2015In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem tractable in realistic ... More
Selection rules for quasiparticle interference with internal nonsymmorphic symmetriesDec 26 2017Dec 10 2018We study how nonsymmorphic symmetries that commute with lattice translations are reflected in the quasiparticle interference (QPI) maps measured by scanning tunneling microscopy (STM). QPI maps, which result from scattering of Bloch states off impurities, ... More
Fatou-Bieberbach domains as basins of attraction of automorphisms tangent to the identityJul 12 2009We prove that there exists an automorphism of C^2 tangent to the identity with a domain of attraction to the origin, biholomorphic to the origin, along a degenerate characteristic direction.
Osculating properties of decomposable scrollsNov 23 2007Osculating spaces of decomposable scrolls (of any genus and not necessarily normal)are studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in the setting ... More
Análisis de distancias temporales y espaciales entre el Lugar de La Mancha y cuatro puntos de referenciaJul 22 2008Oct 20 2008The identity of the famous place of La Mancha appearing at the Quijote is an unknown with a history almost as long as that of the famous book by Miguel de Cervantes. This work analyzes data obtained from a Geographic Information System and compares the ... More
Mutations of simple-minded systems in Calabi-Yau categories generated by a spherical objectDec 31 2015In this article, we give a definition and a classification of 'higher' simple-minded systems in triangulated categories generated by spherical objects with negative Calabi-Yau dimension. We also study mutations of this class of objects and that of 'higher' ... More
On the importance of light scattering for high performances nanostructured antireflective surfacesJun 14 2019An antireflective coating presenting a continuous refractive index gradient is theoretically better than its discrete counterpart because it can give rise to a perfect broadband transparency. This kind of surface treatment can be obtained with nanostructures ... More
Sharp estimates of the Kobayashi metric and Gromov hyperbolicityJan 03 2008Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain ... More
The energy-momentum tensor as a second fundamental formFeb 18 2003We show that it is natural to consider the energy-momentum tensor associated with a spinor field as the second fundamental form of an isommetric immersion. In particular we give a generalization of the warped product construction over a Riemannian manifold ... More
Caractères tordus des représentations admissiblesJul 21 2010Jan 12 2016Let $F$ be a non--Archimedean locally compact field (${\rm car}(F)\geq 0$), ${\bf G}$ be a connected reductive group defined over $F$, $\theta$ be an $F$--automorphism of ${\bf G}$, and $\omega$ be a character of ${\bf G}(F)$. We fix a Haar measure $dg$ ... More
Galois descent in Galois theoriesJul 19 2010Inspired by Kummer theory on abelian varieties, we give similar looking descriptions of the Galois groups occuring in the differential Galois theories of Picard-Vessiot, Kolchin and Pillay, and mention some arithmetic applications.
Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifoldsOct 08 2007Let D be a J-pseudoconvex region in a smooth almost complex manifold (M,J) of real dimension four. We construct a local peak J-plurisubharmonic function at every boundary point p of finite D'Angelo type. As applications we give local estimates of the ... More
Conformal Fractal Geometry and Boundary Quantum GravityMar 13 2003Mar 14 2003This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by exploiting an underlying ... More
Surface properties at the Kosterlitz-Thouless transitionAug 27 2002Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order parameter correlation ... More
Surfaces in S^3 and H^3 via SpinorsApr 08 2002Feb 18 2003We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main argument is the ... More
Potentials and Jacobian algebras for tensor algebras of bimodulesApr 13 2010Jan 24 2012We introduce and study potentials, mutations and Jacobian algebras in the framework of tensor algebras associated with symmetrizable dualizing pairs of bimodules on a symmetric algebra over any commutative ground ring. The graded context is also considered ... More
Laminations dans les espaces projectifs complexesOct 17 2004Nov 26 2004In this work, we extend K. Kodaira's embedding theorem to non compact hermitian complex manifolds and laminations by complex manifolds.
Torsion pairs in a triangulated category generated by a spherical objectApr 17 2014Nov 06 2015We extend Ng's characterisation of torsion pairs in the 2-Calabi-Yau triangulated category generated by a 2-spherical object to the characterisation of torsion pairs in the w-Calabi-Yau triangulated category, $T_w$, generated by a w-spherical object for ... More
Simple-minded systems and reduction for negative Calabi-Yau triangulated categoriesAug 07 2018We develop the basic properties of $w$-simple-minded systems in $(-w)$-Calabi-Yau triangulated categories for $w \geq 1$. The main result is a reduction technique for negative Calabi-Yau triangulated categories. We show that the theory of simple-minded ... More
A Sheet of Maple to Compute Second-Order Edgeworth Expansions and Related Quantities of any Function of the Mean of an iid Sample of an Absolutely Continuous DistributionSep 30 2018We designed a completely automated Maple ($\geqslant 15$) worksheet for deriving Edgeworth and Cornish-Fisher expansions as well as the acceleration constant of the bootstrap bias-corrected and accelerated technique. It is valid for non-parametric or ... More
A geometric model for the module category of a gentle algebraMar 15 2018In this article, gentle algebras are realised as tiling algebras, which are associated to partial triangulations of unpunctured surfaces with marked points on the boundary. This notion of tiling algebras generalise the notion of Jacobian algebras of triangulations ... More
Statistical Mechanics of Self-Avoiding Manifolds (Part II)Aug 18 2004We consider a model of a D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. Use of intrinsic distance geometry provides a rigorous definition of the analytic continuation of the perturbative expansion for arbitrary ... More
Eigenvalue estimates for the Dirac-Schrödinger operatorsJan 12 2001We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the limiting cases of the estimates ... More
Kac-Moody groups: split and relative theories. LatticesNov 17 2002In this survey article, we recall some facts about split Kac-Moody groups as defined by J. Tits, describe their main properties and then propose an analogue of Borel-Tits theory for a non-split version of them. The main result is a Galois descent theorem, ... More
Special points and Poincaré bi-extensions, with an Appendix by Bas EdixhovenApr 27 2011The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.
Real Zeuthen numbers for two linesOct 04 2007Given three natural numbers $k,l,d$ such that $k+l=d(d+3)/2$, the Zeuthen number $N_{d}(l)$ is the number of nonsingular complex algebraic curves of degree $d$ passing through $k$ points and tangent to $l$ lines in $\PP^2$. It does not depend on the generic ... More
Pseudodifferential calculus on manifolds with corners and groupoidsJul 22 1997Jul 25 1997We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also define an algebra ... More
Large N expansion of the 2-matrix model, multicut caseJul 25 2003We present a method, based on loop equations, to compute recursively, all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model, in the case where the support of the density of eigenvalues is not connected. ... More
Line Complexity Asymptotics of Polynomial Cellular AutomataApr 10 2016Apr 12 2016Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial transition rules, ... More
Almost complex structures on the cotangent bundleJul 04 2005Jan 04 2006We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric ... More
Nondegenerate Monge-Ampere structures in dimension 6Nov 12 2002We define a nondegenerate Monge-Amp\`ere structure on a 6-dimensional manifold as a pair $(\Omega,\omega)$, such that $\Omega$ is a symplectic form and $\omega$ is a 3-differential form which satisfies $\omega\wedge\Omega=0$ and which is nondegenerate ... More
Non rigidity of hyperbolic laminationsSep 14 2004In this note we prove infinite dimensionality of the Teichm\"uller space of a hyperbolic Riemann surface lamination of a compact space having a simply connected leaf.
Extensions panachées autodualesNov 21 2010We study self-duality of Grothendieck's blended extensions (extensions panach\'ees) in the context of a tannakian category. The set of equivalence classes of symmetric, resp. antisymmetric, blended extensions is naturally endowed with a torsor structure, ... More
A non-simply laced version for cluster structures on 2-Calabi-Yau categoriesOct 27 2009Dec 06 2013This paper investigates a non simply-laced version of cluster structures for 2-Calabi-Yau or stably 2-Calabi-Yau categories over arbitrary fields. It results that 2-Calabi-Yau or stably 2-Calabi-Yau categories having a cluster tilting subcategory with ... More
Stability of flat-band edge states in topological superconductors without inversion centerNov 27 2013Feb 06 2014Nodal superconductors without inversion symmetry exhibit nontrivial topological properties, manifested by topologically protected flat-band edge states. Here we study the effects of breaking translational symmetry, crucial to the definition of the topological ... More
Jacobi-Nijenhuis algebroids and their modular classesJun 11 2007Sep 26 2007Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi-Nijenhuis ... More
Graph HyperNetworks for Neural Architecture SearchOct 12 2018Jan 12 2019Neural architecture search (NAS) automatically finds the best task-specific neural network topology, outperforming many manual architecture designs. However, it can be prohibitively expensive as the search requires training thousands of different networks, ... More
Why does the effective field theory of inflation work?Nov 04 2013May 16 2014The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, $\zeta$. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary ... More
On fractional p-Laplacian problems with weightApr 22 2014We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional p-Laplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.
Non-adiabatic entropy production for non-Markov dynamicsMay 16 2012Sep 06 2012We extend the definition of non-adiabatic entropy production given for Markovian systems in [M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104 090601, (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing ... More
Inversion of a mapping associated with the Aomoto-Forrester systemFeb 06 2013Dec 05 2013This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. The interest for such a class comes from a previous article of Aomoto and ... More
A family of 8-dimensional generalized complex nilmanifolds with infinitely many real homotopy typesMay 27 2019We prove that there are infinitely many real homotopy types of $8$-dimensional nilmanifolds admitting generalized complex structures of type $k$ for every $0 \leq k \leq 4$. This is in deep contrast to the $6$-dimensional case.
Inflectional loci of scrollsDec 14 2006Mar 28 2007Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let $\L=\mathcal O_{\mathbb P^N}(1)|_X$ denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of $\L$ are locally free. ... More
Dynamic Robust Transmission Expansion PlanningOct 11 2015Jan 30 2017Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem considering uncertainties computationally ... More
Thouless energy and critical statistics on the metallic side of the many-body localization transitionJun 27 2016Jul 01 2016We study a one-dimensional (1d) XXZ spin-chain in a random field on the metallic side of the many-body localization transition by level statistics. For a fixed interaction, and intermediate disorder below the many-body localization transition, we find ... More
Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transitionJun 27 2016Nov 24 2016We study a one-dimensional (1d) XXZ spin-chain in a random field on the metallic side of the many-body localization transition by level statistics. For a fixed interaction, and intermediate disorder below the many-body localization transition, we find ... More
Endomorphism algebras for a class of negative Calabi-Yau categoriesFeb 06 2016Feb 16 2016We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose endomorphism algebras ... More
Analyzing Tag Distributions in Folksonomies for Resource ClassificationFeb 23 2012Recent research has shown the usefulness of social tags as a data source to feed resource classification. Little is known about the effect of settings on folksonomies created on social tagging systems. In this work, we consider the settings of social ... More
Asymptotically linear fractional Schrodinger equationsJan 09 2014By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically linear nonlinearity. ... More
PIXOR: Real-time 3D Object Detection from Point CloudsFeb 17 2019Mar 02 2019We address the problem of real-time 3D object detection from point clouds in the context of autonomous driving. Computation speed is critical as detection is a necessary component for safety. Existing approaches are, however, expensive in computation ... More
A bridge between liquids and socio-economic systems: the key role of interaction strengthsMay 14 2004One distinctive and pervasive aspect of social systems is the fact that they comprise several kinds of agents. Thus, in order to draw parallels with physical systems one is lead to consider binary (or multi-component) compounds. Recent views about the ... More
Reconstructing WKB from topological recursionJun 14 2016Aug 08 2017We prove that the topological recursion reconstructs the WKB expansion of a quantum curve for all spectral curves whose Newton polygons have no interior point (and that are smooth as affine curves). This includes nearly all previously known cases in the ... More
Eros 2 proper motion survey for halo white dwarfsAug 24 2000Since 1996 EROS 2 has surveyed 440 square degrees at high Galactic latitude in order to search for high proper motion stars in the Solar neighbourhood. We present here the analysis of 250 square degrees for which we have three years of data. No object ... More
Invariant holomorphic discs in some non-convex domainsApr 10 2017We give a description of complex geodesics and we study the structure of stationary discs in some non-convex domains for which complex geodesics are not unique.
Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjectureApr 28 2003May 12 2003We show that if $(M,\tensor,I)$ is a monoidal model category then $\REnd_M(I)$ is a (weak) 2-monoid in $\sSet$. This applies in particular when $M$ is the category of $A$-bimodules over a simplicial monoid $A$: the derived endomorphisms of $A$ then form ... More
A Lindemann-Weierstrass theorem for semiabelian varieties over function fieldsOct 02 2008Nov 01 2008We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of Q-linearly independent algebraic numbers are algebraically independent) for commutative algebraic groups G without unipotent quotients, over function fields. We concentrate ... More
Existence of self-similar profile for a kinetic annihilation modelSep 15 2012Oct 10 2014We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard-spheres such that, whenever two particles meet, they either annihilate with probability ... More
Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphismsNov 03 2017Mar 12 2018Let $F$ be a non-Archimedan local field, $G$ a connected reductive group defined and split over $F$, and $T$ a maximal $F$-split torus in $G$. Let $\chi_0$ be a depth zero character of the maximal compact subgroup $\mathcal{T}$ of $T(F)$. It gives by ... More
Topology and dynamics of Levi-flats in surfaces of general typeMar 28 2012We focus on the topology and dynamics of minimal sets and Levi-flats in surfaces of general type. Our method relies on the ergodic theory of Riemann surfaces laminations: we use harmonic measures and Lyapunov exponents. Our first result establishes that ... More
Geometry of Spectral Curves and All Order Dispersive Integrable SystemOct 22 2011Dec 18 2012We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal asymptotic series ... More
Spectral analysis of transport equations with bounce-back boundary conditionsJun 05 2008We investigate the spectral properties of the time-dependent linear transport equation with bounce-back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly continuous streaming ... More
Composite Fermions and the Fermion-Chern-Simons TheoryOct 01 2003The concept of composite fermions, and the related Fermion-Chern-Simons theory, have been powerful tools for understanding quantum Hall systems with a partially full lowest Landau level. We shall review some of the successes of the Fermion-Chern-Simons ... More
Lyapunov exponents of the Brownian motion on a Kähler manifoldFeb 08 2017If E is a flat bundle of rank r over a K\"ahler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using harmonic measures ... More
"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectraSep 08 2003Jun 29 2004We develop homotopical algebraic geometry (see math.AG/0207028) in the special context where the base symmetric monoidal model category is the category S of spectra, i.e. what might be called, after Waldhausen, ``brave new algebraic geometry''. We discuss ... More
Classification of load forecasting studies by forecasting problem to select load forecasting techniques and methodologiesDec 21 2018This article proposes a two-dimensional classification methodology to select the relevant forecasting tools developed by the scientific community based on a classification of load forecasting studies. The inputs of the classifier are the articles of the ... More
The asymptotic expansion of Tracy-Widom GUE law and symplectic invariantsDec 13 2010We establish the relation between two objects: an integrable system related to Painlev\'e II equation, and the symplectic invariants of a certain plane curve S(TW). This curve describes the average eigenvalue density of a random hermitian matrix spectrum ... More
A discrete contact model for crowd motionJan 08 2009The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to ... More
A topological index theorem for manifolds with cornersJul 29 2005We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator if an only ... More
Sparsity vs. Statistical Independence in Adaptive Signal Representations: A Case Study of the Spike ProcessApr 06 2001Finding a basis/coordinate system that can efficiently represent an input data stream by viewing them as realizations of a stochastic process is of tremendous importance in many fields including data compression and computational neuroscience. Two popular ... More
Non-stationary Robust Transmission Expansion PlanningOct 11 2015May 15 2016Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem computationally tractable for real systems. ... More
Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gasesOct 05 2004We analyze the asymptotic behavior of linear Fokker-Planck equations with time-dependent coefficients. Relaxation towards a Maxwellian distribution with time-dependent temperature is shown under explicitly computable conditions. We apply this result to ... More
Geometry of the Casimir EffectAug 19 2004When the vacuum is partitioned by material boundaries with arbitrary shape, one can define the zero-point energy and the free energy of the electromagnetic waves in it: this can be done, independently of the nature of the boundaries, in the limit that ... More
Algebraic Geometry over model categories (a general approach to derived algebraic geometry)Oct 10 2001For a (semi-)model category M, we define a notion of a ''homotopy'' Grothendieck topology on M, as well as its associated model category of stacks. We use this to define a notion of geometric stack over a symmetric monoidal base model category; geometric ... More
Homotopical Algebraic Geometry II: geometric stacks and applicationsApr 21 2004Mar 14 2006This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category, such as derivations, ... More
Dirichlet and Neumann problems for planar domains with parameterOct 31 2011Let $\Gamma(\cdot,\lambda)$ be smooth, i.e.\, $\mathcal C^\infty$, embeddings from $\bar{\Omega}$ onto $\bar{\Omega^{\lambda}}$, where $\Omega$ and $\Omega^\lambda$ are bounded domains with smooth boundary in the complex plane and $\lambda$ varies in ... More
Uniqueness of the self-similar profile for a kinetic annihilation modelJun 27 2014We show the existence of a self-similar solution for a We prove the uniqueness of the self-similar profile solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard spheres such ... More
Commensurators of some non-uniform tree lattices and Moufang twin treesFeb 18 2004Sh. Mozes showed that the commensurator of the lattice ${\rm PSL}_2 \bigl({\bf F}_p[t{}^{-1}] \bigr)$ is dense in the full automorphism group of the Bruhat-Tits tree of valency $p+1$, the latter group being much bigger than ${\rm PSL}_2 \bigl({\bf F}_p((t)) ... More
Fluctuations of the Empirical Measure of Freezing Markov ChainsMay 05 2017In this work, we consider a finite-state inhomogeneous-time Markov chain whose probabilities of transition from one state to another tend to decrease over time. This can be seen as a cooling of the dynamics of an underlying Markov chain. We are interested ... More
Integrability of $\mathcal W({\mathfrak{sl}_d})$-symmetric Toda conformal field theories I : Quantum geometryJan 10 2018Jan 23 2019In this article which is the first of a series of three, we consider $\mathcal W({\mathfrak{sl}_d})$-symmetric conformal field theory in topological regimes for a generic value of the background charge, where $\mathcal W({\mathfrak{sl}_d})$ is the W-algebra ... More
Homotopical Algebraic Geometry I: Topos theoryJul 02 2002Jun 20 2004This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts (for part II, see math.AG/0404373). In this first part we investigate a notion of higher topos. For this, we use ... More
Galois theory, functional Lindemann-Weierstrass, and Manin mapsFeb 06 2015We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations. Using related techniques, we also give a generalization of the ... More
Pink's conjecture on unlikely intersections and families of semi-abelian varietiesApr 03 2019The Poincar\'e torsor of a Shimura family of abelian varieties can be viewed both as a family of semi-abelian varieties and as a mixed Shimura variety. We show that the special subvarieties of the latter cannot all be described in terms of the group subschemes ... More
A Bayes interpretation of stacking for M-complete and M-open settingsFeb 16 2016In M-open problems where no true model can be conceptualized, it is common to back off from modeling and merely seek good prediction. Even in M-complete problems, taking a predictive approach can be very useful. Stacking is a model averaging procedure ... More
A Non-Algebraic PatchworkJan 09 2007Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first ... More
Trace and Kunneth formulas for singularity categories and applicationsOct 16 2017Jan 31 2019We present an $\ell$-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove K\"unneth formulas for dg-category of singularities, and for inertia-invariant vanishing cycles. As an application, ... More
Planar maps, circle patterns and 2d gravityJul 11 2013Dec 20 2013Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point process. We show ... More
Random conformal dynamical systemsJun 10 2005We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that ... More
Mass Generation in Abelian U(1) Gauge Theories: A Rich Network of DualitiesJul 20 2018Following a novel approach, all known basic mass generation mechanisms consistent with an exact abelian U(1) gauge symmetry are shown to be related through an intricate network of dualities whatever the spacetime dimension. This equivalence which applies ... More
Quantum Computation of a Complex System : the Kicked Harper ModelSep 06 2004The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as ... More