Publications

2022

• Nonsmooth mean field games with state constraints
  
  • Sadeghi Arjmand Saeed
  • Mazanti Guilherme
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2022, 28, pp.Paper No. 74, 42 pp.. In this paper, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time. Congestion phenomena are modeled through a constraint on the velocity of an agent that depends on the average density of agents around their position. The model is considered in the presence of state constraints: roughly speaking, these constraints may model walls, columns, fences, hedges, or other kinds of obstacles at the boundary of the domain which agents cannot cross. After providing a more detailed description of the model, the paper recalls some previous results on the existence of equilibria for such games and presents the main difficulties that arise due to the presence of state constraints. Our main contribution is to show that equilibria of the game satisfy a system of coupled partial differential equations, known mean field game system, thanks to recent techniques to characterize optimal controls in the presence of state constraints. These techniques not only allow to deal with state constraints but also require very few regularity assumptions on the dynamics of the agents. (10.1051/cocv/2022069)
  DOI : 10.1051/cocv/2022069
• Non-archimedean aspects of the SYZ conjecture
  
  • Pille-Schneider Léonard
  , 2022. We define a class of plurisubharmonic metrics on the hybrid space X^hyb associatedto a polarized degeneration (X,L) of complex manifolds over the punctured disk.Such a psh metric induces by restriction a psh metric on L in the usual sense, aswell as a psh metric on the non-archimedean analytification X^an of X with respectto the t-adic absolute value on C((t)). We prove that any complex psh metric on(X, L) admits a canonical plurisubharmonic extension to the hybrid space X^hyb. Wealso focus on the case of a complex polarized toric variety (Z, L), where we providea combinatorial description of continuous plurisubharmonic hybrid toric metrics onL.We then study maximal degenerations X/D∗ of Calabi-Yau manifolds, with the goalof constructing a non-archimedean avatar rho : X^an → Sk(X) of the conjectural SYZfibration on the complex fibers. To that extend, we study the integral affine structures induced on the skeleton Sk(X) by the Berkovich retraction rho_X associatedto a good dlt R-model of X. This allows us to construct, in the case of degenerations of hypersurfaces, a non-archimedean SYZ fibration inducing on Sk(X) theintegral affine structure predicted by the Gross-Siebert program. When the familyof hypersurfaces is the Fermat one, we furthermore prove that the non-archimedeanCalabi-Yau metric is invariant under this retraction.Finally, we consider degenerations of canonically polarized manifolds and computethe non-archimedean limit of the family of Kähler-Einstein metrics inside the asso-ciated hybrid space.
• Duality for Landau-Ginzburg models
  
  • Sabbah Claude
  , 2022. This article surveys various duality statements attached to a pair consisting of a smooth complex quasi-projective variety and a regular function on it. It is dedicated to the memory of Bumsig Kim.
• Mean field games with free final time
  
  • Sadeghi Arjmand Saeed
  , 2022. Motivated by economical and engineering topics, around 2006, mean field games were introduced by Jean-Michel Lasry and Pierre-Louis Lions, and Peter E.~Caines, Minyi Huang and Roland P.~Malhamé, independently. This thesis addresses some mean field games models with free final time.In the first chapter, we consider several interacting populations evolving in R aiming at reaching given target sets in minimal time. The control system satisfied by each agent depends on an agent's position, the distribution of other agents in the same population, and the distribution of agents on other populations. Thus, interactions between agents occur through their dynamics. We consider in this chapter the existence of Lagrangian equilibria to this mean field game, their asymptotic behavior, and their characterization as solutions of a mean field game system, under few regularity assumptions on agents' dynamics. In particular, the mean field game system is established without relying on semiconcavity properties of the value function.Similarly to the first chapter, in the second chapter, we consider a mean field game model inspired by crowd motion where agents aim to reach a closed set, called target set, in minimal time, however in addition to congestion phenomena, which affects the velocity of an agent, the model is considered in the presence of state constraints: roughly speaking, these constraints may model walls, columns, fences, hedges, or other kinds of obstacles at the boundary of the domain which agents cannot cross. We first recall some previous results on the existence of equilibria for such games and presents the main difficulties that arise due to the presence of state constraints. Our main contribution is to show that equilibria of the game satisfy a mean field game system, thanks to recent techniques to characterize optimal controls in the presence of state constraints. These techniques not only allow to deal with state constraints but also require very few regularity assumptions on the dynamics of the agents.In our last chapter, we consider a mean field game model for crowd motion in which pedestrians interact not only through their position, but also through their velocity. More precisely, each pedestrian is assumed to minimize a cost involving their time to reach a certain target set, an individual integral cost, and an interaction integral cost modelling the fact that agents want to avoid congestion and prefer to move together with agents going in the same direction, in which can be seen as a Cucker--Smale type interaction. The main result we obtain in this chapter is the existence of equilibria for such a game, which is based on a variational approach.
• Correspondance de Langlands locale $p$-adique et anneaux de Kisin
  
  • Colmez Pierre
  • Dospinescu Gabriel
  • Nizioł Wiesława
  , 2022. We use a ${\mathcal B}$-adic completion and the $p$-adic local Langlands correspondence for ${\mathrm {GL}}_2({\mathbf Q}_p )$ to give a construction of Kisin's rings and the attached universal Galois representations (in dimension 2 and for ${\mathbf Q}_p$) directly from the classical Langlands correspondence. This gives, in particular, a uniform proof of the geometric Breuil-M\'ezard conjecture in the supercuspidal case.
• Arithmetic subgroups of Chevalley group schemes over function fields I: quotients of the Bruhat-Tits building by $\{P\}$-arithmetic subgroups
  
  • Loisel Benoit
  • Bravo Claudio
  , 2022. Let $\mathbf{G}$ be a reductive Chevalley group scheme (defined over $\mathbb{Z}$). Let $\mathcal{C}$ be a smooth, projective, geometrically integral curve over a field $\mathbb{F}$. Let $\p$ be a closed point on $\mathcal{C}$. Let $A$ be the ring of functions that are regular outside $\lbrace P \rbrace$. The fraction field $k$ of $A$ has a discrete valuation $\nu=\nu_{P}: k^{\times} \rightarrow \mathbb{Z}$ associated to $P$. In this work, we study the action of the group $ \mathbf{G}(A)$ of $A$-points of $\mathbf{G}$ on the Bruhat-Tits building $\mathcal{X}=\mathcal{X}(\mathbf{G},k,\nu_P)$ in order to describe the structure of the orbit space $ \mathbf{G}(A)\backslash \mathcal{X}$. We obtain that this orbit space is the ``gluing'' of a closed connected CW-complex with some sector chambers. The latter are parametrized by a set depending on the Picard group of $\mathcal{C} \smallsetminus \{P\}$ and on the rank of $\mathbf{G}$. Moreover, we observe that any rational sector face whose tip is a special vertex contains a subsector face that embeds into this orbit space.
• Analyse de quelques inégalités fonctionnelles et équations aux dérivées partielles liées à de grands systèmes quantiques
  
  • Sabin Julien
  , 2022. We study several topics in analysis which come from many-body quantum mechanics. More specifically, we consider nonlinear partial differential equations and functional inequalities that describe a large number of fermions in a mean-field approximation. This leads to the mathematical analysis of one-body density matrices with large or infinite trace, with a special emphasis on the associated spatial distribution of particles. We adapt tools from dispersive PDEs, Fourier and semiclassical analysis to this setting. In a first part, we relate several evolution equations describing large quantum systems (relativistic and nonrelativistic) in various asymptotic regimes, employing both compactness methods or strong estimates. In a second part, we develop methods in harmonic analysis that imply functional inequalities on density matrices that we call fermionic. In a third and last part (unrelated to many-body quantum mechanics), we study the existence of optimizers for Fourier extension inequalities by compactness methods.
• Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces
  
  • Pille-Schneider Léonard
  , 2022. Using a construction by Yamamoto of tropical contractions, we construct a non-archimedean SYZ fibration on the Berkovich analytification of a class of maximally degenerate hypersurfaces in projective space. We furthermore prove that under a discrete symmetry assumption, the potential for the non-archimedean Calabi-Yau metric is constant along the fibers of the retraction. The proof uses the work of Li on the Fermat degeneration of hypersurfaces, and an explicit description of toric plurisubharmonic metrics on the hybrid space associated to a complex toric variety. (10.48550/arXiv.2210.05578)
  DOI : 10.48550/arXiv.2210.05578
• Construction of high-frequency spacetimes
  
  • Touati Arthur
  , 2022. This thesis is interested in high-frequency solutions to the equations of general relativity. These solutions describe the propagation of gravitational waves in a non-linear context. They also display the backreaction phenomenon and thus contribute to the study of Burnett's conjecture.Chapters 2 and 3 are devoted to the construction of high-frequency local in time solutions (gλ)λ to the Einstein vacuum equations in generalised wave coordinates, approaching in a weak sense a background null-dust solution. The initial data for the Einstein vacuum must satisfy the constraint equations and we construct high-frequency solutions of these equations on R³ in Chapter 2 by adapting the conformal method, where the parameters are defined by high-frequency ansatz. In Chapter 3, we construct the family (gλ)λ, defined by a high-frequency ansatz. For the oscillating part of the ansatz, we identify a hierarchy of transport equations as well as polarization conditions. The later are propagated through the Bianchi identities, and allow us to control the creation of harmonics thanks to the weak polarized null structure of the semi-linear terms. The coupling with the quasi-linear wave equation for the remainder induces a loss of derivatives which we regain using the background double null foliation and a Fourier cut-off. Thus, we avoid constructing the double null foliation for the metrics gλ .Chapter 4 is devoted to the long time study of high-frequency solutions to a semi-linear wave equation with a null structure. We show global existence using the vector field method.
• When do two rational functions have locally biholomorphic Julia sets?
  
  • Dujardin Romain
  • Favre Charles
  • Gauthier Thomas
  Transactions of the American Mathematical Society, American Mathematical Society, 2022. In this note we address the following question, whose interest was recently renewed by problems arising in arithmetic dynamics: under which conditions does there exist a local biholomorphism between the Julia sets of two given one-dimensional rational maps? In particular we find criteria ensuring that such a local isomorphism is induced by an algebraic correspondence. This extends and unifies classical results due to Baker, Beardon, Eremenko, Levin, Przytycki and others. The proof involves entire curves and positive currents. (10.1090/tran/8775)
  DOI : 10.1090/tran/8775
• L-functions of Kloosterman sheaves
  
  • Qin Yichen
  , 2022. The classical Kloosterman sheaves are l-adic local systems over GmFv whose traces of Frobenius are Kloosterman sums. They are special cases of Kloosterman sheaves for reductive groups introduced by Heinloth, Ngô, and Yun. This thesis aims to generalize the work of Fresán, Sabbah, and Yu on the L-functions of Kloosterman sheaves for SL2. We show that the L-functions of several Kloosterman sheaves for SLn+1 can be extended meromorphically to the complex plane and satisfy functional equations. In particular, some L-functions arise from modular forms, as predicted by conjectures of Evans type.We first construct motives over Q such that their l-adic realizations have the same L-functions as Kloosterman sheaves for SLn+1. Then we compute the Hodge numbers of the de Rham realizations of these motives by computing the irregular Hodge filtration. As long as we find a motive such that the Hodge numbers of its de Rham realization are either zero or one, we can apply a theorem of Patrikis and Taylor to show the potential automorphy of Galois representations. Contrary to the case of Kloosterman sheaves for SL2, the Hodge numbers can be bigger than one.When the corresponding motives of Kloosterman sheaves have dimension 2, we can use Serre's modularity conjecture to show that the L-functions of Kloosterman sheaves coincide with the L-functions of modular forms.
• Density of automorphic points in deformation rings of polarized global Galois representations
  
  • Hellmann Eugen
  • Margerin Christophe
  • Schraen Benjamin
  Duke Mathematical Journal, Duke University Press, 2022, 171 (13), pp.2699--2752. Conjecturally, the Galois representations that are attached to essentially self-dual regular algebraic cuspidal automorphic representations are Zariski-dense in a polarized Galois deformation ring. We prove new results in this direction in the context of automorphic forms on definite unitary groups over totally real fields. This generalizes the infinite fern argument of Gouvêa–Mazur and Chenevier and relies on the construction of nonclassical p-adic automorphic forms and the computation of the tangent space of the space of trianguline Galois representations. This boils down to a surprising statement about the linear envelope of intersections of Borel subalgebras. (10.1215/00127094-2021-0080)
  DOI : 10.1215/00127094-2021-0080
• Global pluripotential theory on hybrid spaces
  
  • Pille-Schneider Léonard
  , 2022. Let A be a Banach ring, and X/A be a projective scheme of finite type, endowed with a semi-ample line bundle L. Assuming that A is a geometric base ring, we define a class PSH(X,L) of plurisubharmonic metrics on L on the Berkovich analytification X^an and prove various basic properties thereof. We focus in particular on the case where A is a hybrid ring of complex power series and X/A is a smooth variety, so that X^an is the hybrid space associated to a degeneration X of complex varieties over the punctured disk. We then prove that when L is ample, any plurisubharmonic metric on L with logarithmic growth at zero admits a canonical plurisubharmonic extension to the hybrid space X^hyb . We also discuss the continuity of the family of Monge-Amp\`ere measures associated to a continuous plurisubharmonic hybrid metric. In the case where X is a degeneration of canonically polarized manifolds, we prove that the canonical psh extension is continuous on Xhyb and describe it explicitly in terms of the canonical model (in the sense of MMP) of the degeneration. (10.48550/arXiv.2209.04879)
  DOI : 10.48550/arXiv.2209.04879
• Degenerating complex variations of Hodge structure in dimension one
  
  • Sabbah Claude
  • Schnell Christian
  , 2022. We analyze the behavior of polarized complex variations of Hodge structure on the punctured unit disk. For integral variations of Hodge structure, this analysis was first carried out by Wilfried Schmid. We get rid of the assumption that the eigenvalues of the monodromy transformation are roots of unity. In this generality, we give new (and, we think, more conceptual) proofs for all the major results in Schmid's paper, such as the estimates for the rate of growth of the Hodge norm; the existence of a limiting mixed Hodge structure; the nilpotent orbit theorem; and a simplified (but still sufficiently powerful) version of the SL(2)-orbit theorem.
• The relative hermitian duality functor
  
  • Fernandes Teresa Monteiro
  • Sabbah Claude
  , 2022. We extend to the category of relative regular holonomic modules on a manifold $X$, parametrized by a curve $S$, the Hermitian duality functor (or conjugation functor) of Kashiwara. We prove that this functor is an equivalence with the similar category on the conjugate manifold $\overline X$, parametrized by the same curve. As a byproduct we introduce the notion of regular holonomic relative distribution.
• HUSIMI, WIGNER, TÖPLITZ, QUANTUM STATISTICS AND ANTICANONICAL TRANSFORMATIONS
  
  • Paul Thierry
  , 2022. We study the behaviour of Husimi, Wigner and Töplitz symbols of quantum density matrices when quantum statistics are tested on them, that is when on exchange two coordinates in one of the two variables of their integral kernel. We show that to each of these actions is associated a canonical transform on the cotangent bundle of the underlying classical phase space. Equivalently can one associate a complex canonical transform on the complexification of the phase-space. In the off-diagonal Töplitz representation introduced in [P], the action considered is associated to a complex aanticanonical relation.
• ON QUANTUM COMPLEX FLOWS
  
  • Paul Thierry
  , 2022. We study the propagation of quantum Töplitz observables through quantized complex linear canonical transformation of one degree of freedom systems. We associate to such a propagated observable a non local "Töplitz" expression involving off diagonal terms. We study the link of this constrauction with the usual Weyl symbolic paradigm.
• Birational automorphisms of varieties
  
  • Kusnetsova Alexandra
  , 2022. The thesis covers various problems on groups of regular and birational automorphisms of algebraic and complex varieties, and roughly explores the differences and similarities between these two groups.First, we focus on the description of finite subgroups of the group of birational automorphisms Bir(X) of a rationally connected complex threefold X. We prove that any 3-subgroup in Bir(X) can be generated by at most 5 elements and in all but two concrete cases it can be generated by at most 4 elements. Also we describe the group of regular automorphisms Aut(S) of a quasi-projective surface S defined over a field k such that char(k) > 0. We show that this group satisfies the p-Jordan property. One of the main ingredients here is the MMP, which allows us to reduce questions about finite subgroups of birational transformations to classifying groups of regular automorphisms of very special algebraic varieties that arise as the end result of MMP.Then we consider birational automorphisms of infinite order, and try to understand when it is possible to construct a birational model where the induced automorphism is regular. We are mainly interested in a family of examples of birational automorphisms of P^3 introduced by J. Blanc. These birational automorphisms induce pseudo-automorphisms on a special birational model of P^3 i.e. it has a small extremal locus, and is therefore close to being regular. However, the main result of the second part of the thesis is that it is not conjugate to a regular automorphism. The approach we take is dynamical in nature, and the action of birational maps on the Néron-Severi space plays an important role.The last part of the thesis is concerned with the description of the automorphism group of a class of non-Kähler manifolds introduced by D. Guan and further studied by F. Bogomolov. These manifolds are non-Kähler analogues of hyperkähler manifolds; thus, we expect that their properties are similar. By Bogomolov’s construction these manifolds fiber over the projective space with abelian varieties as generic fibers; thus, algebraic tools can be used to study their geometry. More precisely, we prove that an algebraic reduction of Bogomolov-Guan manifold of dimension 2n is the projective space of dimension n. Then we study the locus of singular fibers of an algebraic reduction and conclude that the group of regular automorphisms of Bogomolov-Guan manifolds is Jordan. In the four-dimensional case the same is true for the group of bimeromorphic automorphisms.
• Cohomology of hyperplane sections of (co)adjoint varieties
  
  • Benedetti Vladimiro
  • Perrin Nicolas
  , 2023. In this paper we study general hyperplane sections of adjoint and coadjoint varieties. We show that these are the only sections of homogeneous varieties such that a maximal torus of the automorphism group of the ambient variety stabilizes them. We then study their geometry, provide formulas for their classical cohomology rings in terms of Schubert classes and compute the quantum Chevalley formula. This allows us to obtain results about the semi-simplicity of the (small) quantum cohomology, analogous to those holding for (co)adjoint varieties.
• Compactness methods in Lieb’s work
  
  • Sabin Julien
  , 2022, 2 (1), pp.219-251. (10.4171/90-2/38)
  DOI : 10.4171/90-2/38
• General remarks on the propagation of chaos in wave turbulence and application to the incompressible Euler dynamics
  
  • de Suzzoni Anne-Sophie
  , 2022. In this paper, we prove propagation of chaos in the context of wave turbulence for a generic quasisolution. We then apply the result to full solutions to the incompressible Euler equation.
• SOLIS. XVI. Mass ejection and time variability in protostellar outflows: Cep E
  
  • de A. Schutzer A.
  • Rivera-Ortiz P R
  • Lefloch B.
  • Gusdorf A.
  • Favre C.
  • Segura-Cox D.
  • López-Sepulcre A.
  • Neri R.
  • Ospina-Zamudio J.
  • de Simone M.
  • Codella C.
  • Viti S.
  • Podio L.
  • Pineda J.
  • O’donoghue R.
  • Ceccarelli C.
  • Caselli P.
  • Alves F.
  • Bachiller R.
  • Balucani N.
  • Bianchi E.
  • Bizzocchi L.
  • Bottinelli S.
  • Caux E.
  • Chacón-Tanarro A.
  • Dulieu F.
  • Enrique-Romero J.
  • Fontani F.
  • Feng S.
  • Holdship J.
  • Jiménez-Serra I.
  • Jaber Al-Edhari A.
  • Kahane C.
  • Lattanzi V.
  • Oya Y.
  • Punanova A.
  • Rimola A.
  • Sakai N.
  • Spezzano S.
  • Sims Ian R
  • Taquet V.
  • Testi L.
  • Theulé P.
  • Ugliengo P.
  • Vastel C.
  • Vasyunin A I
  • Vazart F.
  • Yamamoto S.
  • Witzel A.
  Astronomy & Astrophysics - A&A, EDP Sciences, 2022, 662, pp.A104. Context. Protostellar jets are an important agent of star formation feedback, tightly connected with the mass-accretion process. The history of jet formation and mass ejection provides constraints on the mass accretion history and on the nature of the driving source. Aims. We characterize the time-variability of the mass-ejection phenomena at work in the class 0 protostellar phase in order to better understand the dynamics of the outflowing gas and bring more constraints on the origin of the jet chemical composition and the mass-accretion history. Methods. Using the NOrthern Extended Millimeter Array (NOEMA) interferometer, we have observed the emission of the CO 2–1 and SO N J = 5 4 –4 3 rotational transitions at an angular resolution of 1.0″ (820 au) and 0.4″ (330 au), respectively, toward the intermediate-mass class 0 protostellar system Cep E. Results. The CO high-velocity jet emission reveals a central component of ≤400 au diameter associated with high-velocity molecular knots that is also detected in SO, surrounded by a collimated layer of entrained gas. The gas layer appears to be accelerated along the main axis over a length scale δ 0 ~ 700 au, while its diameter gradually increases up to several 1000 au at 2000 au from the protostar. The jet is fragmented into 18 knots of mass ~10 −3 M ⊙ , unevenly distributed between the northern and southern lobes, with velocity variations up to 15 km s −1 close to the protostar. This is well below the jet terminal velocities in the northern (+ 65 km s −1 ) and southern (−125 km s −1 ) lobes. The knot interval distribution is approximately bimodal on a timescale of ~50–80 yr, which is close to the jet-driving protostar Cep E-A and ~150–20 yr at larger distances >12″. The mass-loss rates derived from knot masses are steady overall, with values of 2.7 × 10 −5 M ⊙ yr −1 and 8.9 × 10 −6 M ⊙ yr −1 in the northern and southern lobe, respectively. Conclusions. The interaction of the ambient protostellar material with high-velocity knots drives the formation of a molecular layer around the jet. This accounts for the higher mass-loss rate in the northern lobe. The jet dynamics are well accounted for by a simple precession model with a period of 2000 yr and a mass-ejection period of 55 yr. (10.1051/0004-6361/202142931)
  DOI : 10.1051/0004-6361/202142931
• Geodesic distance and Monge-Amp\`ere measures on contact sets
  
  • Di Nezza Eleonora
  • Lu Chinh H.
  Analysis Mathematica, Springer Verlag, 2022, 48 (2), pp.451-488. We prove a geodesic distance formula for quasi-psh functions with finite entropy, extending results by Chen and Darvas. We work with big and nef cohomology classes: a key result we establish is the convexity of the $K$-energy in this general setting. We then study Monge-Amp\`ere measures on contact sets, generalizing a recent result by the first author and Trapani. (10.1007/s10476-022-0159-1)
  DOI : 10.1007/s10476-022-0159-1
• Hodge theory of Kloosterman connections
  
  • Fresán Javier
  • Sabbah Claude
  • Yu Jeng-Daw
  Duke Mathematical Journal, Duke University Press, 2022, 171 (8). (10.1215/00127094-2021-0036)
  DOI : 10.1215/00127094-2021-0036
• BBB une réponse à l'explosion des besoins en visioconférence?
  
  • Massias Henri
  • Layrisse Sandrine
  • Khabzaoui Mohammed
  • Delavennat David
  • Shih Albert
  , 2022. <div><p>Nous présentons l'expérience humaine, technique et organisationnelle qui a permis à la PLM (Plateforme en Ligne pour les Mathématiques) de remplacer en très peu de temps une plateforme de webconférences, vieillissante et limitée. L'objectif était de répondre à une augmentation massive du nombre d'utilisateurs, en restant sur une solution de type « logiciel libre ».</p><p>Alors que le premier confinement se profile, une instance du couple Greenlight/BigBlueButton est installée. Rapidement la demande explose et la « recette » se transmet entre les ASR des laboratoires de mathématiques. Des installations sont mises en production sur des petites infrastructures de laboratoires et testées sur le cloud VirtualData à Paris-Saclay. Dans un second temps, une frontale Greenlight, un système de répartition de charge Scalelite, et quatorze workers BigBlueButton y sont déployés. Des solutions sont trouvées pour résoudre les problèmes de filtrage rencontrés par certains utilisateurs, pour l'authentification SSO sur la fédération RENATER et pour pallier la défaillance éventuelle d'un site.</p><p>Les différentes installations sont documentées et publiées.</p></div> <div>Au travers de cette présentation, nous partagerons notre vision des avantages et inconvénients de cette solution ainsi que nos choix de configuration. Ils se sont révélés utiles lors des sollicitations pour héberger des événements tels que JDEV, conférences internationales, ou réunions à plus de 200 personnes. JRES 2021 -Marseille 1/12<p>Avec l'acquisition massive de licences propriétaires (telles que Zoom, Teams, etc.) au sein de l'ESR et le retour en présentiel, se pose désormais la question de l'avenir et le maintien de tout ou partie de ces solutions de visioconférences.</p></div> <div>Mots-clefs<p>Webconférence, visioconférence, BBB</p></div> <div>Contexte<p>La PLM est la Plate-forme en Ligne pour les Mathématiques, développée par la PLM-team, une équipe d'une douzaine de membres du réseau thématique Mathrice du CNRS.</p><p>Mathrice 1 rassemble les acteurs informatiques des laboratoires de mathématiques français, principalement des administrateurs système et réseau (ASR), mais aussi quelques développeurs et enseignants-chercheurs 2 qui contribuent au fonctionnement des moyens informatiques de leur laboratoire. Sa finalité est double :</p><p>animer et faire évoluer une communauté d'informaticiens, dans l'esprit d'un réseau métier ;</p><p>proposer des outils numériques à la communauté mathématique.</p><p>C'est une initiative prise en 1999 par les responsables de la discipline mathématiques du CNRS (institutionnalisée aujourd'hui par l'INSMI 3 , l'Institut National des Sciences Mathématiques et de leurs Interactions). Elle s'explique par le fait que la communauté mathématique est disséminée et mobile 4 :</p><p>disséminée, car on trouve des mathématiciens partout : un laboratoire dans quasiment chaque université, des mathématiciens affectés dans des laboratoires de physique théorique, d'informatique, de biologie, etc. ;</p><p>mobile par obligation, parce qu'il n'y a pas de recrutement local (donc la carrière du chercheur progresse en changeant de laboratoire), ce qui le conduit à collaborer avec des personnes n'appartenant pas à son laboratoire.</p></div>