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Graded quivers and B-branes at Calabi-Yau singularitiesNov 16 2018A graded quiver with superpotential is a quiver whose arrows are assigned degrees $c\in \{0, 1, \cdots, m\}$, for some integer $m \geq 0$, with relations generated by a superpotential of degree $m-1$. Ordinary quivers ($m=1)$ often describe the open string ... More

Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)Jan 23 2009May 08 2009These lecture notes are an introduction to toric geometry. Particular focus is put on the description of toric local Calabi-Yau varieties, such as needed in applications to the AdS/CFT correspondence in string theory. The point of view taken in these ... More

Seiberg duality for Chern-Simons quivers and D-brane mutationsJan 11 2012Feb 06 2012Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons ... More

A Quiver of Many RunawaysJun 27 2007We study the quantum corrections to the moduli space of the quiver gauge theory corresponding to regular and fractional D3-branes at the dP_1 singularity. We find that besides the known runaway behavior at the lowest step of the duality cascade, there ... More

Comments on twisted indices in 3d supersymmetric gauge theoriesMay 20 2016Jun 21 2016We study three-dimensional ${\mathcal N}=2$ supersymmetric gauge theories on ${\Sigma_g \times S^1}$ with a topological twist along $\Sigma_g$, a genus-$g$ Riemann surface. The twisted supersymmetric index at genus $g$ and the correlation functions of ... More

The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric LocalizationNov 11 2013Mar 04 2014We compute the supersymmetric partition function of an $\mathcal{N}=1$ chiral multiplet coupled to an external Abelian gauge field on complex manifolds with $T^2 \times S^2$ topology. The result is locally holomorphic in the complex structure moduli of ... More

Toric Fano varieties and Chern-Simons quiversJan 11 2012Jul 17 2012In favourable cases the low energy dynamics of a stack of M2-branes at a toric Calabi-Yau fourfold singularity can be described by an N=2 supersymmetric Chern-Simons quiver theory, but there still does not exists an "inverse algorithm" going from the ... More

Comments on N=(2,2) Supersymmetry on Two-ManifoldsApr 09 2014Jul 01 2014We study curved-space rigid supersymmetry for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric fields theories with a vector-like $R$-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be viewed as holomorphic ... More

Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspectiveDec 26 2018Jan 22 2019We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing ... More

Comments on 3d Seiberg-like dualitiesAug 26 2011Aug 14 2012We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the duality map. ... More

Seifert fibering operators in 3d $\mathcal{N}=2$ theoriesJul 06 2018Oct 12 2018We study 3d $\mathcal{N}=2$ supersymmetric gauge theories on closed oriented Seifert manifold---circle bundles over an orbifold Riemann surface---, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result ... More

Supersymmetric partition functions and the three-dimensional A-twistJan 11 2017Jan 19 2017We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\Sigma_g$. We compute the $\mathcal{M}_{g,p}$ supersymmetric partition function and ... More

Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspectiveDec 26 2018Apr 17 2019We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing ... More

$\mathcal{N}{=}1$ supersymmetric indices and the four-dimensional A-modelJul 18 2017Aug 14 2017We compute the supersymmetric partition function of $\mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $\mathcal{M}_4 \cong \mathcal{M}_{g,p}\times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$ Riemann surface, ... More

Quantum moduli space of Chern-Simons quivers, wrapped D6-branes and AdS4/CFT3May 11 2011Jul 06 2011We study the quantum moduli space of N=2 Chern-Simons quivers with generic ranks and CS levels, proving along the way exact formulas for the charges of bare monopole operators. We then derive N=2 Chern-Simons quiver theories dual to AdS_4 x Y^{p,q}(CP2) ... More

't Hooft anomalies and the holomorphy of supersymmetric partition functionsMay 14 2019Jun 04 2019We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any diffeomorphism-invariant scheme ... More

B-branes and supersymmetric quivers in 2dNov 28 2017May 21 2018We study 2d $\mathcal{N}=(0,2)$ supersymmetric quiver gauge theories that describe the low-energy dynamics of D1-branes at Calabi-Yau fourfold (CY$_4$) singularities. On general grounds, the holomorphic sector of these theories---matter content and (classical) ... More

Supersymmetric gauged matrix models from dimensional reduction on a sphereDec 28 2017It was recently proposed that N=1 supersymmetric gauged matrix models have a duality of order four - that is, a quadrality - reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality ... More

Chiral flavors and M2-branes at toric CY4 singularitiesNov 23 2009Apr 28 2010We extend the stringy derivation of N=2 AdS4/CFT3 dualities to cases where the M-theory circle degenerates at complex codimension-two submanifolds of a toric conical CY4. The type IIA backgrounds include D6-branes, and the dual N=2 quiver gauge theories ... More

't Hooft anomalies and the holomorphy of supersymmetric partition functionsMay 14 2019We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any diffeomorphism-invariant scheme ... More

A-twisted correlators and Hori dualitiesMay 11 2017May 14 2017The Hori-Tong and Hori dualities are infrared dualities between two-dimensional gauge theories with $\mathcal{N}{=}(2,2)$ supersymmetry, which are reminiscent of four-dimensional Seiberg dualities. We provide additional evidence for those dualities with ... More

The equivariant A-twist and gauged linear sigma models on the two-sphereApr 23 2015Sep 22 2015We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $\Omega$-deformed sphere, $S^2_\Omega$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the $S^2_\Omega$ ... More

Localization of twisted $\mathcal{N}{=}(0,2)$ gauged linear sigma models in two dimensionsDec 26 2015Jan 18 2016We study two-dimensional $\mathcal{N}{=}(0,2)$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider $\mathcal{N}{=}(0,2)$ theories with an $R$-symmetry, which can always be defined on curved space by a pseudo-topological ... More

The Geometry of Supersymmetric Partition FunctionsSep 23 2013Oct 23 2013We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background gauge fields that ... More

From Rigid Supersymmetry to Twisted Holomorphic TheoriesJul 09 2014Oct 02 2014We study N=1 field theories with a U(1)_R symmetry on compact four-manifolds M. Supersymmetry requires M to be a complex manifold. The supersymmetric theory on M can be described in terms of conventional fields coupled to background supergravity, or in ... More

Supersymmetric Field Theories on Three-ManifoldsDec 14 2012Oct 22 2013We construct supersymmetric field theories on Riemannian three-manifolds M, focusing on N=2 theories with a U(1)_R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet ... More

The N=2 cascade revisited and the enhancon bearingsNov 13 2008Mar 31 2009Supergravity backgrounds with varying fluxes generated by fractional branes at non-isolated Calabi-Yau singularities had escaped a precise dual field theory interpretation so far. In the present work, considering the prototypical example of such models, ... More

Gauge/gravity duality and the interplay of various fractional branesApr 28 2008Nov 13 2008We consider different types of fractional branes on a Z_2 orbifold of the conifold and analyze in detail the corresponding gauge/gravity duality. The gauge theory possesses a rich and varied dynamics, both in the UV and in the IR. We find the dual supergravity ... More

On Stable Non-Supersymmetric Vacua at the Bottom of Cascading TheoriesJun 19 2006Jun 25 2006We consider a wide class of cascading gauge theories which usually lead to runaway behaviour in the IR, and discuss possible deformations of the superpotential at the bottom of the cascade which stabilize the runaway direction and provide stable non-supersymmetric ... More

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal TheoriesMay 18 2012Jun 25 2012We consider three-dimensional N=2 superconformal field theories on a three-sphere and analyze their free energy F as a function of background gauge and supergravity fields. A crucial role is played by certain local terms in these background fields, including ... More

Comments on Chern-Simons Contact Terms in Three DimensionsJun 22 2012Dec 29 2012We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their ... More

On the scaling limits of weakly asymmetric bridgesSep 19 2016We consider a discrete bridge from $(0,0)$ to $(2N,0)$ evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order $N^{-\alpha}$ with $\alpha \in (0,\infty)$. We provide a classification of the asymptotic ... More

Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve propertyMay 03 2012Jun 30 2014We encode the genealogy of a continuous-state branching process associated with a branching mechanism $\Psi$ - or $\Psi$-CSBP in short - using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable ... More

A bifurcation analysis for the Lugiato-Lefever equationJul 11 2016The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional ... More

Free Araki-Woods factors and Connes' bicentralizer problemSep 22 2008Aug 24 2009We show that for any free Araki-Woods factor $\mathcal{M} = \Gamma(H_\R, U_t)"$ of type ${\rm III_1}$, the bicentralizer of the free quasi-free state $\varphi_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal ... More

A new construction of factors of type ${\rm III_1}$Jan 09 2006Nov 20 2006We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, ... More

Exponential Mixing for Stochastic PDEs: The Non-Additive CaseMay 24 2005Jul 03 2006We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two representative examples: ... More

Discrete quantum Drinfeld-Sokolov correspondenceJun 14 2001We construct a discrete quantum version of the Drinfeld-Sokolov correspondence for the sine-Gordon system. The classical version of this correspondence is a birational Poisson morphism between the phase space of the discrete sine-Gordon system and a Poisson ... More

Weakly asymmetric bridges and the KPZ equationMar 11 2016Sep 13 2016We consider the corner growth dynamics on discrete bridges from $(0,0)$ to $(2N,0)$, or equivalently, the weakly asymmetric simple exclusion process with $N$ particles on $2N$ sites. We take an asymmetry of order $N^{-\alpha}$ with $\alpha \in (0,1)$ ... More

Thermodynamics of Quantum Open Systems: Applications in Quantum Optics and OptomechanicsSep 08 2017Thermodynamics was developed in the XIXth century to provide a physical description to engines and other macroscopic thermal machines. Since then, progress in nanotechnologies urged to extend these formalism, initially designed for classical systems, ... More

Gamma stability in free product von Neumann algebrasMar 17 2014Mar 19 2015Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer $M_1^{\varphi_1}$ is diffuse. We first show that any intermediate subalgebra ... More

From flows of Lambda Fleming-Viot processes to lookdown processes via flows of partitionsJul 18 2011Jun 26 2014The goal of this paper is to unify the lookdown representation and the stochastic flow of bridges, which are two approaches to construct the $\Lambda$-Fleming-Viot process along with its genealogy. First we introduce the stochastic flow of partitions ... More

Feynman Path Integral of a charged anisotropic HO in crossed electric and magnetic fields. Alternative calculational methodsAug 13 2019In the present paper the author evaluates the path integral of a charged anisotropic Harmonic Oscillator (HO) in crossed electric and magnetic fields by two alternative methods. Both methods enable a rather formal calculation and circumvent some mathematical ... More

Le défaut d'approximation forte dans les groupes linéaires connexesJun 18 2009Let G be a connected linear algebraic group over a number field k. We establish an exact sequence describing the closure of the group G(k) of rational points of G in the group of adelic points of G. This exact sequence describes the defect of strong approximation ... More

Four proofs of cocompacness for Sobolev embeddingsJan 19 2016Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the domain space) ... More

Brownian limits of planar maps with a prescribed degree sequenceMar 14 2019For non-negative integers $\varrho_n$ and $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a bipartite planar map with boundary-length $2\varrho_n$ and $n$ inner faces uniformly at random amongst those which have $d_n(k)$ inner faces ... More

On the growth of random planar maps with a prescribed degree sequenceFeb 12 2019Feb 18 2019For non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a bipartite planar map with $n$ faces uniformly at random amongst those which have $d_n(k)$ faces of degree $2k$ for every $k \ge 1$ and we study its asymptotic ... More

Théorèmes de dualité pour les complexes de toresJun 18 2009We consider a complex of tori of length 2 defined over a number field k. We establish here some local and global duality theorems for the (\'etale or Galois) hypercohomology of such a complex. We prove the existence of a Poitou-Tate exact sequence for ... More

Idéaux fermés de certaines algèbres de Beurling et application aux opérateurs à spectre dénombrableJan 25 2006We denote by $\bbt$ the unit circle and by $\bbd$ the unit disc of $\bbc$. Let $s$ be a non-negative real and $\omega$ a weight such that $\omega(n) = (1+n)^{s} \quad (n \geq 0)$ and such that the sequence $\dsp \Big(\frac{\omega(-n)}{(1+n)^{s}} \Big)_{n ... More

On some free products of von Neumann algebras which are free Araki-Woods factorsJun 12 2006May 11 2008We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and ... More

Spatial smoothness of the stationary solutions of the 3D Navier--Stokes equationsDec 02 2005Jul 06 2006We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part. The random part of the force is white in time ... More

Level set approach for fractional mean curvature flowsJul 16 2008Mar 12 2009This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the associated flow appears in two important applications: dislocation ... More

Une formule pour le groupe de Brauer algébrique d'un torseurNov 23 2010For a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a canonical complex of Galois modules of length 3 and a canonical isomorphism between an hypercohomology group ... More

Structure of ${\rm II_1}$ factors arising from free Bogoljubov actions of arbitrary groupsSep 24 2012May 22 2014In this paper, we investigate several structural properties for crossed product ${\rm II_1}$ factors $M$ arising from free Bogoljubov actions associated with orthogonal representations $\pi : G \to \mathcal O(H_\mathbf R)$ of arbitrary countable discrete ... More

Twinning is not shearing: Case of the extension twins in magnesiumAug 25 2016Aug 29 2016A crystallographic model is proposed for the extension twins in magnesium. It is based on a hard-sphere assumption previously used for martensitic transformations, and it reverses the approach of the classical theory of mechanical twinning. First, the ... More

One-dimensional reduction of viscous jetsNov 07 2015We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion ... More

Infinite-time observability of the wave equation with time-varying observation domains under a geodesic recurrence conditionApr 24 2019Our goal is to relate the observation (or control) of the wave equation on observation domains which evolve in time with some dynamical properties of the geodesic flow. In comparison to the case of static domains of observation, we show that the observability ... More

Structures immobilières pour un groupe de Kac-Moody sur un corps localDec 02 2009May 27 2010In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the incidence properties ... More

An extension of the Masur domainJan 11 2019The Masur domain is a subset of the space of projective measured geodesic laminations on the boundary of a 3-manifold M. This domain plays an important role in the study of the hyperbolic structures on the interior of M. In this paper, we define an extension ... More

Radiative transport of relativistic species in cosmologyFeb 25 2019We review the general construction of distribution functions for gases of fermions and bosons (photons), emphasizing the similarities and differences between both cases. The central object which describes polarization for photons is a tensor-valued distribution ... More

Structural results for free Araki-Woods factors and their continuous coresDec 07 2008Sep 01 2010We show that for any type ${\rm III_1}$ free Araki-Woods factor $\mathcal{M} = \Gamma(H_\R, U_t)"$ associated with an orthogonal representation $(U_t)$ of $\R$ on a separable real Hilbert space $H_\R$, the continuous core $M = \mathcal{M} \rtimes_\sigma ... More

On the growth of powers of operators with spectrum contained in Cantor setsJan 25 2006For $\xi \in \big(0, {1/2} \big)$, we denote by $E_{\xi}$ the perfect symmetric set associated to $\xi$, that is $$ E_{\xi} = \Big\{\exp \big(2i \pi (1-\xi) \dsp \sum_{n = 1}^{+\infty} \epsilon_{n} \xi^{n-1} \big) : \epsilon_{n} = 0 \textrm{or} 1 \quad ... More

Exponential mixing for the 3D stochastic Navier--Stokes equationsDec 02 2005Jul 06 2006We study the Navier-Stokes equations in dimension 3 (NS3D) driven by a noise which is white in time. We establish that if the noise is at same time sufficiently smooth and non degenerate in space, then the weak solutions converge exponentially fast to ... More

Trudinger-Moser inequality with remainder termsApr 24 2012May 20 2013The paper gives an improvement of the Trudinger-Moser inequality, in which the constraint set is defined not by the squared gradient norm, but with the squared gradient norm minus a remainder term of the weighted L^p-type. This is a two-dimensional counterpart ... More

Quantizations of the Witt algebra and of simple Lie algebras in characteristic pNov 12 2003We first quantize the Witt algebra in characteristic 0. Then, we consider the reduction modulo p of our formulas. This gives polynomial deformations of the restricted envelopping algebra of the Witt algebra. By this way, we get new families of noncommutative ... More

Continuity of the bending mapNov 18 2004The bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space of geometrically ... More

The radiative transfer at second order: a full treatment of the Boltzmann equation with polarizationSep 18 2008Dec 18 2009This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the distribution ... More

Graph representation of balance sheets: from exogenous to endogenous moneyApr 15 2015Sep 10 2015The nature of monetary arrangements is often discussed without any reference to its detailed construction. We present a graph representation which allows for a clear understanding of modern monetary systems. First, we show that systems based on commodity ... More

On the growth of random planar trees and maps with a prescribed degree sequenceFeb 12 2019For non-negative integers $(d_n(k))_{k \ge 1}$ such that $\sum_{k \ge 1} d_n(k) = n$, we sample a planar tree with $n$ inner vertices uniformly at random amongst those which have $d_n(k)$ vertices with out-degree $k$ for every $k \ge 1$ and we study its ... More

Backreaction of particle production on false vacuum decayNov 17 2015Apr 28 2016As originally described by Rubakov, particles are produced during the tunneling of a metastable quantum field. We propose to extend his formalism to compute the backreaction of these particles on the semiclassical decay probability of the field. The idea ... More

Expressive recommender systems through normalized nonnegative modelsNov 15 2015We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems ... More

Not all entangled states violate Leggett's crypto-nonlocalityMay 20 2013Oct 18 2013This note is a reply to M. Navascu\'es' claim that "all entangled states violate Leggett's crypto-nonlocality" [arXiv:1303.5124v2]. I argue that such a conclusion can only be reached if one introduces additional assumptions that further restrict Leggett's ... More

Generalized Compactification in Heterotic String TheoryApr 15 2012In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. ... More

Scaling limits of random bipartite planar maps with a prescribed degree sequenceDec 27 2016Aug 25 2017We study the asymptotic behaviour of uniform random maps with a prescribed face-degree sequence, in the bipartite case, as the number of faces tends to infinity. Under mild assumptions, we show that, properly rescaled, such maps converge in distribution ... More

Gauge invariant Boltzmann equation and the fluid limitJun 29 2007May 01 2008This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution function and brightness, ... More

The radiative transfer at second order: a full treatment of the Boltzmann equation with polarizationSep 18 2008Jun 26 2018This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the distribution ... More

XX Heisenberg Spin Chain and an Example of Path Integral with "Automorphic" Boundary ConditionsApr 01 2002New representation for the generating function of correlators of third components of spins in the XX Heisenberg spin chain is considered in the form given by the fermionic Gaussian path integrals. A part of the discrete anti-commuting integration variables ... More

Ergodicity for the stochastic Complex Ginzburg-Landau equationsMay 27 2004Jul 06 2006We study a stochastic complex Ginzburg--Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markovian transition semi-group toward a unique invariant probability measure. Since Doob Theorem does not ... More

Quasi-stationary distributions associated with explosive CSBPDec 14 2012Oct 16 2013We characterise all the quasi-stationary distributions and the Q-process associated with a continuous state branching process that explodes in finite time. We also provide a rescaling for the continuous state branching process conditioned on non-explosion ... More

Strongly solid group factors which are not interpolated free group factorsJan 25 2009Feb 15 2010We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant $\Lambda_{\cb}(\Gamma) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(\Gamma)$ are strongly solid, i.e. the normalizer ... More

Compactifications polygonales d'un immeuble affineMar 03 2009We define a compactification of an affine building $\I$ indexed by a family of partitions of the director space $\vec A$ of one of its appartments $A$. This compactification is similar to Satake's compatification of a symetric space, and it generalizes ... More

Obstructions de Brauer-Manin entières sur les espaces homogènes à stabilisateurs finis nilpotentsFeb 27 2014Let $k$ be a number field. We construct homogeneous spaces of $SL_{n,k}$ with finite nilpotent non-abelian stabilizers for which the Brauer-Manin obstruction does not explain the failure of strong approximation (resp. the failure of the integral Hasse ... More

Pseudodifferential operators on manifolds with linearizationNov 11 2008Sep 07 2009We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard pseudodifferential calculus ... More

A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebraMar 30 2012Apr 16 2014We show that for every mixing orthogonal representation $\pi : \Z \to \mathcal O(H_\R)$, the abelian subalgebra $\LL(\Z)$ is maximal amenable in the crossed product ${\rm II}_1$ factor $\Gamma(H_\R)\dpr \rtimes_\pi \Z$ associated with the free Bogoljubov ... More

Construction of type ${\rm II_1}$ factors with prescribed countable fundamental groupApr 26 2007Aug 31 2009In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type ${\rm II_1}$ with prescribed fundamental group. First we investigate state-preserving group actions on the almost periodic free ... More

Horospheres in degenerate 3-manifoldsJun 23 2016We study horospheres in hyperbolic 3-manifolds M all whose ends are degenerate. Deciding which horospheres in M are properly embedded and which are dense reduces to a) studying the horospherical limit set; b) deciding which almost minimizing geodesics ... More

Rigidity of free product von Neumann algebrasJul 08 2015Let $I$ be any nonempty set and $(M_i, \varphi_i)_{i \in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $\mathcal C_{\rm anti-free}$ of (possibly type III) von Neumann algebras including ... More

Amenable absorption in amalgamated free product von Neumann algebrasJun 02 2016We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \ast_B M_2$. Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection ... More

A quantum system strongly coupled to a finite size reservoir: the case of a hybrid opto-mechanical deviceOct 02 2015Apr 22 2016We study the dynamics of a mechanical resonator parametrically coupled to a driven dissipative quantum emitter in the ultra-strong coupling regime. We show that this regime is fully compatible with a semi-classical treatment, and we derive master equations ... More

Weak Harnack inequality for the Boltzmann equation without cut-offAug 26 2016In this paper, we obtain the weak Harnack inequality and H\"older estimates for a large class of kinetic integro-differential equations. We prove that the Boltzmann equation without cut-off can be written in this form and satisfies our assumptions provided ... More

Generalized junction conditions for degenerate parabolic equationsJan 08 2016Oct 07 2016We are interested in the study of parabolic equations on a multi-dimensional junction (Imbert, Monneau (2014)), i.e. the union of a finite number of copies of a half-hyperplane of R d+1 whose boundaries are identified. The common boundary is referred ... More

Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networksJun 11 2013Feb 10 2016We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex ... More

Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional caseOct 12 2014Jul 06 2016A \emph{multi-dimensional junction} is the singular $(d+1)$-manifold obtained by gluying through their boundaries a finite number of copies of the half-space $\R^{d+1}\_+$. We show that the general theory developed by the authors (2013) for the network ... More

Ergodicity for the weakly damped stochastic non-linear Schrödinger equationsOct 20 2004Jul 06 2006We study a damped stochastic non-linear Schr\"{o}dinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish convergence of the Markovian transition semi-group toward a unique invariant ... More

Robust guarantees for learning an autoregressive filterMay 23 2019The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control theory is to make ... More

The Schauder estimate for kinetic integral equationsDec 31 2018Mar 08 2019We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form $f_t + v \cdot \nabla_x f = \mathcal L_v f + c$, where $\mathcal L_v$ is an integro-differential diffusion operator of order ... More

Stochastic Dynamics of Discrete Curves and Exclusion Processes. Part 1: Hydrodynamic Limit of the ASEP SystemMar 09 2006This report is the foreword of a series dedicated to stochastic deformations of curves. Problems are set in terms of exclusion processes, the ultimate goal being to derive hydrodynamic limits for these systems after proper scalings. In this study, solely ... More

The higgsino-singlino sector of the NMSSM: Combined constraints from dark matter and the LHCJun 25 2018Jul 06 2018A light singlino is a promising candidate for dark matter, and a light higgsino is natural in the parameter space of the NMSSM. We study the combined constraints on this scenario resulting from the dark matter relic density, the most recent results from ... More

Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groupsNov 21 2006We study coercive inequalities in Orlicz spaces associated to the probability measures on finite and infinite dimensional spaces which tails decay slower than the Gaussian ones. We provide necessary and sufficient criteria for such inequalities to hold ... More

Free independence in ultraproduct von Neumann algebras and applicationsAug 25 2014Apr 29 2015The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct ${\rm II_1}$ factors [Po95] to the framework of ultraproduct von Neumann algebras $(M^\omega, \varphi^\omega)$ where $(M, \varphi)$ is ... More