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Crossing probabilities for Voronoi percolationOct 24 2014Jul 30 2015We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, ... More

Homogenization via sprinklingMay 22 2015We show that a superposition of an $\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\mathbb Z^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli percolation. ... More

Locality of percolation for abelian Cayley graphsDec 06 2013We prove that the value of the critical probability for percolation on an abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pc defined on the set of Cayley graphs of abelian ... More

Renormalization of crossing probabilities in the planar random-cluster modelJan 24 2019The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on the model, including ... More

A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising modelFeb 10 2015Jan 21 2018We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we prove finiteness ... More

A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising modelFeb 10 2015Mar 21 2016We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we prove finiteness ... More

A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$Feb 10 2015We provide a new proof of the sharpness of the phase transition for nearest-neighbour Bernoulli percolation. More precisely, we show that - for $p<p_c$, the probability that the origin is connected by an open path to distance $n$ decays exponentially ... More

A note on Schramm's locality conjecture for random-cluster modelsJul 24 2017Aug 30 2017In this note, we discuss a generalization of Schramm's locality conjecture to the case of random-cluster models. We give some partial (modest) answers, and present several related open questions. Our main result is to show that the critical inverse temperature ... More

Confidence intervals for the critical value in the divide and color modelJul 10 2013We obtain confidence intervals for the location of the percolation phase transition in H\"aggstr\"om's divide and color model on the square lattice $\mathbb{Z}^2$ and the hexagonal lattice $\mathbb{H}$. The resulting probabilistic bounds are much tighter ... More

On the critical value function in the divide and color modelSep 15 2011Jul 10 2013The divide and color model on a graph $G$ arises by first deleting each edge of $G$ with probability $1-p$ independently of each other, then coloring the resulting connected components (\emph{i.e.}, every vertex in the component) black or white with respective ... More

Sharpness of the phase transition for continuum percolation in R^2May 19 2016We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii ... More

Critical Percolation and the Minimal Spanning Tree in SlabsDec 30 2015The minimal spanning forest on $\mathbb{Z}^{d}$ is known to consist of a single tree for $d \leq 2$ and is conjectured to consist of infinitely many trees for large $d$. In this paper, we prove that there is a single tree for quasi-planar graphs such ... More

Absence of infinite cluster for critical Bernoulli percolation on slabsJan 28 2014We prove that for Bernoulli percolation on a graph $\mathbb{Z}^2\times\{0,\dots,k\}$ ($k\ge 0$), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on $\mathbb{Z}^2$ which are invariant ... More

The box-crossing property for critical two-dimensional oriented percolationOct 31 2016We consider critical oriented Bernoulli percolation on the square lattice $\mathbb{Z}^2$. We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behavior: - We establish that the probability that ... More

Upper bounds on the percolation correlation lengthFeb 08 2019We study the size of the near-critical window for Bernoulli percolation on $\mathbb Z^d$. More precisely, we use a quantitative Grimmett-Marstrand theorem to prove that the correlation length, both below and above criticality, is bounded from above by ... More

A new computation of the critical point for the planar random-cluster model with $q\ge1$Apr 13 2016We present a new computation of the critical value of the random-cluster model with cluster weight $q\ge 1$ on $\mathbb{Z}^2$. This provides an alternative approach to the result of Beffara and Duminil-Copin. We believe that this approach has several ... More

Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le4$May 15 2015This article studies the planar Potts model and its random-cluster representation. We show that the phase transition of the nearest-neighbor ferromagnetic $q$-state Potts model on $\mathbb Z^2$ is continuous for $q\in\{2,3,4\}$, in the sense that there ... More

Sharp phase transition for the random-cluster and Potts models via decision treesMay 08 2017Dec 23 2018We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their random-cluster representations. ... More

Subcritical phase of $d$-dimensional Poisson-Boolean percolation and its vacant setMay 02 2018Nov 04 2018We prove that the Poisson-Boolean percolation on $\mathbb{R}^d$ undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a $5d-3$ finite moment (in particular we do not assume that the distribution is bounded). ... More

Exponential decay of connection probabilities for subcritical Voronoi percolation in $\mathbb{R}^d$May 22 2017We prove that for Voronoi percolation on $\mathbb{R}^d$, there exists $p_c\in[0,1]$ such that - for $p<p_c$, there exists $c_p>0$ such that $\mathbb{P}_p[0\text{ connected to distance }n]\leq \exp(-c_p n)$, - there exists $c>0$ such that for $p>p_c$, ... More

Long monotone trails in random edge-labelings of random graphsAug 22 2018Given a graph $G$ and a bijection $f : E(G)\rightarrow \{1, 2, \ldots,e(G)\}$, we say that a trail/path in $G$ is $f$-\emph{increasing} if the labels of consecutive edges of this trail/path form an increasing sequence. More than 40 years ago Chv\'atal ... More

Emergent Planarity in two-dimensional Ising Models with finite-range InteractionsJan 15 2018Mar 05 2018The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective ... More

Quenched Voronoi percolationJan 16 2015We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing ... More

The Bethe ansatz for the six-vertex and XXZ models: an expositionNov 29 2016In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector $\psi$ and energy $\Lambda$, which satisfy $V \psi = \Lambda \psi$, where $V$ is the the transfer matrix of the six-vertex ... More

Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$Nov 29 2016Sep 05 2017We prove that the $q$-state Potts model and the random-cluster model with cluster weight $q>4$ undergo a discontinuous phase transition on the square lattice. More precisely, we show - Existence of multiple infinite-volume measures for the critical Potts ... More

Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$Nov 29 2016We prove that the $q$-state Potts model and the random-cluster model with cluster weight $q>4$ undergo a discontinuous phase transition on the square lattice. More precisely, we show - Existence of multiple infinite-volume measures for the critical Potts ... More

Small permutation classesDec 24 2007Apr 05 2016We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number $\kappa$, approximately 2.20557, for which there are only countably many permutation classes of growth ... More

Maximal independent sets and separating coversNov 21 2009Aug 26 2010In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which ... More

Eliciting Single-Peaked Preferences Using Comparison QueriesJan 15 2014Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there ... More

Prediction Markets, Mechanism Design, and Cooperative Game TheoryMay 09 2012Prediction markets are designed to elicit information from multiple agents in order to predict (obtain probabilities for) future events. A good prediction market incentivizes agents to reveal their information truthfully; such incentive compatibility ... More

X- and Gamma-Ray Line Emission ProcessesAug 21 2002This chapter is intended to provide a general presentation of the atomic and nuclear processes responsible for X-ray line and gamma-ray line emission in various astrophysical environments. I consider line production from hot plasmas, from accelerated ... More

Can the coincidence problem be solved by a cosmological model of coupled dark energy and dark matter?Jul 23 2013Oct 12 2014Motivated by the cosmological constant and the coincidence problems, we consider a cosmological model where the dark sectors are interacting together through a phenomenological decay law $\dot{\rho}_{\Lambda}=Q\rho_{\Lambda}^n$ in a FRW spacetime with ... More

Baryon acoustic signature in the clustering of density maximaJun 02 2008Oct 22 2008We reexamine the two-point correlation of density maxima in Gaussian initial conditions. Spatial derivatives of the linear density correlation, which were ignored in the calculation of Bardeen, Bond, Kaiser & Szalay (1986), are included in our analysis. ... More

Environmental dependence in the ellipsoidal collapse modelJul 31 2007May 15 2008N-body simulations have demonstrated a correlation between the properties of haloes and their environment. In this paper, we assess whether the ellipsoidal collapse model can produce a similar dependence. First, we explore the statistical correlation ... More

Group analysis of an ideal plasticity modelJan 05 2012In this paper, we study the Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions of the system. The infinitesimal generators that span the Lie algebra for this system are obtained, ... More

Remplissage De L'Espace Euclidien Par Des Complexes PolyÉdriques D'Orientation ImposÉe Et De RotonditÉ UniformeDec 26 2008We build polyhedral complexes in Rn that coincide with dyadic grids with different orientations, while keeping uniform lower bounds (depending only on n) on the flatness of the added polyhedrons including their subfaces in all dimensions. After the definitions ... More

Diffusion of a particle quadratically coupled to a thermally fluctuating fieldFeb 09 2013Apr 19 2013We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak coupling limit, a path-integral formulation allows to compute the effective diffusion coefficient in the cases of an active particle, that ... More

On the trace and norm maps from $Γ_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$Jun 16 2014Let $f$ be a Drinfeld modular form for $\Gamma_0(\mathfrak{p})$. From such a form, one can obtain two forms for the full modular group $\operatorname{GL}_2(A)$: by taking the trace or the norm from $\Gamma_0(\mathfrak{p})$ to $\operatorname{GL}_2(A)$. ... More

Flatness, preorders and general metric spaces (revised)Feb 21 2006We use a generic notion of flatness in the enriched context to define various completions of metric spaces -- enrichments over [0,\infty] -- and preorders -- enrichments over 2. We characterize the weights of colimits commuting in [0,\infty] with the ... More

Flatness, preorders and general metric spacesSep 12 2003This paper studies a general notion of flatness in the enriched context: P-flatness where the parameter P stands for a class of presheaves. One obtains a completion of a category A by considering the category Flat_P(A) of P-flat presheaves over A. This ... More

Energy conservation and dissipation properties of time-integration methods for the nonsmooth elastodynamics with contactOct 09 2014This research report is devoted to the study of the conservation and the dissipation properties of the mechanical energy of several time--integration methods dedicated to the elasto--dynamics with unilateral contact. Given that the direct application ... More

Introduction to chtoucas for reductive groups and to the global Langlands parameterizationApr 25 2014Sep 17 2015This is a translation in English of version 3 of the article arXiv:1404.3998, which is itself an introduction to arXiv:1209.5352. We explain all the ideas of the proof of the following theorem. For any reductive group G over a global function field, we ... More

On some completions of the space of Hamiltonian mapsNov 16 2005Nov 23 2007We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, ... More

Hamiltonian pseudo-representationsMar 12 2007Jul 20 2007The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An unexpected consequence ... More

A Devastating Example for the Halfer RuleOct 17 2016How should we update de dicto beliefs in the face of de se evidence? The Sleeping Beauty problem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other ... More

Banach KK-theory and the Baum-Connes conjectureApr 22 2003The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion ... More

Cohomologie de de Rham entiere (Integral de Rham cohomology)Apr 06 2004Apr 06 2004The Cartier isomorphism allows a nice description of the Bockstein spectral sequence of the de Rham complex over the integers. It is used to compute the integral de Rham cohomology of affine spaces. ----- On decrit la suite spectrale de Bockstein issue ... More

Simultaneous double transformations of functions depending on space and timeNov 13 2013May 01 2014It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after the other ... More

On quasianalytic local ringsSep 13 2005Feb 07 2008This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classes are well-known in harmonic analysis since several decades, their study ... More

Limit groups and groups acting freely on R^n-treesJun 20 2003Nov 29 2004We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R^n-trees. We first prove that Sela's limit groups do have a free action on an R^n-tree. We then prove that a finitely generated group having a free action ... More

Invariants of Automorphic Lie AlgebrasApr 14 2015Automorphic Lie Algebras arise in the context of reduction groups introduced in the late 1970s in the field of integrable systems. They are subalgebras of Lie algebras over a ring of rational functions, defined by invariance under the action of a finite ... More

Proof of the Tadic conjecture U0 on the unitary dual of GL(m,D)Feb 01 2007Let F be a non-Archimedean local field of characteristic 0, and let D be a finite dimensional central division algebra over F. We prove that any unitary irreducible representation of a Levi subgroup of GL(m,D), with m a positive integer, induces irreducibly ... More

Inexact cuts in Stochastic Dual Dynamic ProgrammingSep 04 2018Sep 10 2018We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of ... More

Rigorous justification of the Favrie-Gavrilyuk approximation to the Serre-Green-Naghdi modelJul 18 2018The (Serre-)Green-Naghdi system is a non-hydrostatic model for the propagation of surface gravity waves in the shallow-water regime. Recently , Favrie and Gavrilyuk proposed in [Nonlinearity, 30(7) (2017)] an efficient way of numerically computing approximate ... More

The Hierarchical Adaptive Forgetting Variational FilterMay 15 2018A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We present a ... More

Structured Variational Inference for Coupled Gaussian ProcessesNov 03 2017Nov 29 2017Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such as regression ... More

Traceability of Deep Neural NetworksDec 17 2018[Context.] The success of deep learning makes its usage more and more tempting in safety-critical applications. However such applications have historical standards (e.g., DO178, ISO26262) which typically do not envision the usage of machine learning. ... More

Adaptive Shivers Sort: An Alternative Sorting AlgorithmSep 22 2018Jan 08 2019We present one stable mergesort algorithm, called \Adaptive Shivers Sort, that exploits the existence of monotonic runs for sorting efficiently partially sorted data. We also prove that, although this algorithm is simple to implement, its computational ... More

Cosmological-scale coherent orientations of quasar optical polarization vectors in the $Planck$ era Investigating the Galactic dust contamination scenarioSep 29 2017Jan 17 2019Gigaparsec scale alignments of the quasar optical polarization vectors have been proven to be robust against a scenario of contamination by the Galactic interstellar medium (ISM). This claim has been established by means of optical polarization measurements ... More

A mass for ALF manifoldsMar 19 2008Mar 20 2008We prove positive mass theorems on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.

Which nestohedra are removahedra?Jul 09 2014Oct 13 2014A removahedron is a polytope obtained by deleting inequalities from the facet description of the classical permutahedron. Relevant examples range from the associahedra to the permutahedron itself, which raises the natural question to characterize which ... More

On a model for the storage of files on a hardware I : Statistics at a fixed time and asymptoticsNov 14 2006Jan 24 2008We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line. We specify the distribution of the space of unoccupied locations ... More

Hausdorff dimensions for SLE_6Apr 16 2002Mar 30 2005We prove that the Hausdorff dimension of the trace of SLE_6 is almost surely 7/4 and give a more direct derivation of the result (due to Lawler-Schramm-Werner) that the dimension of its boundary is 4/3. We also prove that, for all \kappa<8, the SLE_{\kappa} ... More

Is a Finite Intersection of Balls Covered by a Finite Union of Balls in Euclidean Spaces ?Apr 18 2018Sep 24 2018Considering a finite intersection of balls and a finite union of other balls in an Euclidean space, we propose an exact method to test whether the intersection is covered by the union. We reformulate this problem into quadratic programming problems. For ... More

On Hessian limit directions along non-oscillating gradient trajectoriesMar 03 2011Given a non-oscillating gradient trajectory G of a real analytic function f, we show that the limit v of the secants at the limit point O of G along the trajectory G is an eigen-vector of the limit of the direction of the Hessian matrix Hess (f) at O ... More

DASC: a Decomposition Algorithm for multistage stochastic programs with Strongly Convex cost functionsNov 09 2017Nov 18 2017We introduce DASC, a decomposition method akin to Stochastic Dual Dynamic Programming (SDDP) which solves some multistage stochastic optimization problems having strongly convex cost functions. Similarly to SDDP, DASC approximates cost-to-go functions ... More

Exact computation of the CDF of the Euclidean distance between a point and a random variable uniformly distributed in disks, balls, or polyhedrons and application to PSHAMay 30 2014Aug 19 2014We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this set: a union ... More

Reconstructing compositionsOct 16 2006We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutations). We show that every composition w of n\ge 3k+1 can be reconstructed ... More

Constraints on $Λ(t)$-cosmology with power law interacting dark sectorsMay 30 2012May 31 2012Motivated by the cosmological constant and the coincidence problems, we consider a cosmological model where the cosmological constant $\Lambda_0$ is replaced by a cosmological term $\Lambda(t)$ which is allowed to vary in time. More specifically, we are ... More

The large-scale clustering of massive dark matter haloesMay 06 2010The statistics of peaks of the initial, Gaussian density field can be used to interpret the abundance and clustering of massive dark matter haloes. I discuss some recent theoretical results related to their clustering and its redshift evolution. Predictions ... More

Simple physics of the partly pinned fluid systemsMay 12 2014Sep 08 2014In this paper, we consider some aspects of the physics of the partly pinned (PP) systems obtained by freezing in place particles in equilibrium bulk fluid configurations in the normal (nonglassy) state. We first discuss the configurational overlap and ... More

Statistical mechanics of homogeneous partly pinned fluid systemsJun 24 2010Dec 05 2010The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, ... More

Semantic Vector MachinesMay 14 2011We first present our work in machine translation, during which we used aligned sentences to train a neural network to embed n-grams of different languages into an $d$-dimensional space, such that n-grams that are the translation of each other are close ... More

Gluon Mass, Glueballs and Gluonic MesonsFeb 18 2011We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar ... More

Philosophy in the Face of Artificial IntelligenceMay 19 2016In this article, I discuss how the AI community views concerns about the emergence of superintelligent AI and related philosophical issues.

Cosmic anisotropies from quasars: from polarization to structural-axis alignmentsApr 18 2016The comparison of the orientations of the optical-polarization vectors of quasars that are separated by billions of light-years has led to the discovery that they are aligned instead of pointing in random directions as expected. This discovery has been ... More

Approximation of stochastic processes by non-expansive flows and coming down from infinityNov 23 2015May 25 2016We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property of the flow, ... More

Growth rates of permutation classes: from countable to uncountableMay 13 2016Sep 05 2016We establish that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi$, there are only countably many less than $\xi$. Central to the proof are various ... More

Mean-field microrheology of a very soft colloidal suspension: inertia induces shear-thickeningMar 03 2015Apr 27 2015Colloidal suspensions have a rich rheology and can exhibit shear-thinning as well as shear-thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions ... More

A new test of uniformity for object orientations in astronomyJul 20 2015We briefly present a new coordinate-invariant statistical test dedicated to the study of the orientations of transverse quantities of non-uniformly distributed sources on the celestial sphere. These quantities can be projected spin-axes or polarization ... More

Why are tensor field theories asymptotically free?Jul 15 2015In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate ... More

A Contribution to the Theory Behind the M0 Capture-Recapture Model: An Improved EstimatorDec 10 2012Nov 28 2018We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator ... More

Gradient trajectories for plane singular metrics I: oscillating trajectoriesMay 30 2012We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries ... More

A very short proof of Forester's rigidity resultJan 24 2003May 22 2003The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester ... More

Numerical Simulations of the Ising Model on the Union Jack LatticeJan 26 2011The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by Lars Onsager ... More

On the non-extendability of quasianalytic germsJun 21 2010Sep 07 2010Let $\mathcal{E}_1(M)^+$ be the local ring of germs at 0 of functions belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0 in $[0,+\infty[$. We show that the ring $\mathcal{E}_1(M)^+$ contains elements that cannot be extended ... More

The Joint Physics Analysis Center WebsiteJan 08 2016The Joint Physics Analysis Center is a collaboration between theorists and experimentalists working in hadronic physics. In order to facilitate the exchange of information between the different actors in hadron spectroscopy, we created an interactive ... More

Dessins d'enfants for analystsApr 01 2015We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus 0 or 1, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with subsequent lattice ... More

The metric completion of the Riemannian space of Kähler metricsJan 30 2014Apr 09 2014Let $X$ be a compact K\"ahler manifold and $\a \in H^{1,1}(X,\R)$ a K\"ahler class. We study the metric completion of the space $\HH_\a$ of K\"ahler metrics in $\a$, when endowed with the Mabuchi $L^2$-metric $d$. Using recent ideas of Darvas, we show ... More

Conic intersections, Maximal Cohen-Macaulay modules and the Four Subspace problemFeb 21 2017Mar 10 2017Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by reducing the classification to the Four Subspace problem solved by Nazarova and Gel$'$fand-Ponomarev, ... More

Shtukas for reductive groups and Langlands correspondence for function fieldsMar 10 2018We discuss recent developments in the Langlands program for function fields, and in the geometric Langlands program. In particular we explain a canonical decomposition of the space of cuspidal automorphic forms for any reductive group G over a function ... More

Definability of types over finite partial order indiscerniblesAug 11 2011In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by giving a decomposition ... More

Estimates for Weierstrass division in ultradifferentiable classesNov 26 2015Mar 23 2016We study the Weierstrass division theorem for function germs in strongly non-quasianalytic Denjoy-Carleman classes $\mathcal{C}_M$. For suitable divisors $P(x,t)=x^d+a_1(t)x^{d-1}+\cdots+a_d(t)$ with real-analytic coefficients $a_j$, we show that the ... More

Fonctorial Construction of Frobenius CategoriesMar 16 2009Let $\Ascr,\Bscr$ be exact categories with $\Ascr$ karoubian and $M$ be an exact functor. Under suitable adjonction hypotheses for $M$, we are able to show that the direct factors of the objects of $\Ascr$ of the form $MY$ with $Y \in \Bscr$ make up a ... More

Brick polytopes, lattice quotients, and Hopf algebrasMay 28 2015Nov 30 2017This paper is motivated by the interplay between the Tamari lattice, J.-L. Loday's realization of the associahedron, and J.-L. Loday and M. Ronco's Hopf algebra on binary trees. We show that these constructions extend in the world of acyclic $k$-triangulations, ... More

Cardinality of Rauzy classesJun 04 2011Rauzy classes define a partition of the set of irreducible (or indecomposable) permutations. They were defined by G. Rauzy as part of an induction algorithm for interval exchange transformations. In this article we prove an explicit formula for the cardinality ... More

Abelianization of Subgroups of Reflection Group and their Braid Group; an Application to CohomologyMar 03 2010Aug 31 2010The final result of this article gives the order of the extension $$\xymatrix{1\ar[r] & P/[P,P] \ar^{j}[r] & B/[P,P] \ar^-{p}[r] & W \ar[r] & 1}$$ as an element of the cohomology group $H^2(W,P/[P,P])$ (where $B$ and $P$ stands for the braid group and ... More

Lecture notes on Liouville theory and the DOZZ formulaDec 03 2017The purpose of these notes, based on a series of 4 lectures given by the author at IHES, is to explain the recent proof of the DOZZ formula for the three point correlation functions of Liouville conformal field theory (LCFT). We first review the probabilistic ... More

Hofer's distance on diameters and the Maslov indexMar 09 2011Jul 11 2011We prove that Hofer's distance between two diameters of the open 2-disk admits an upper bound in terms of the Maslov index of their intersection points.

Fast Computation of Shifted Popov Forms of Polynomial Matrices via Systems of Modular Polynomial EquationsFeb 01 2016May 12 2016We give a Las Vegas algorithm which computes the shifted Popov form of an $m \times m$ nonsingular polynomial matrix of degree $d$ in expected $\widetilde{\mathcal{O}}(m^\omega d)$ field operations, where $\omega$ is the exponent of matrix multiplication ... More