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La maîtrise des eaux autour des abbayes cisterciennes d’Auvergne et du Velay : réflexion méthodologique
No full textLe propos, en guise d’introduction au séminaire « Ville et eaux en milieu alpin » s’inscrit en contrepoint des contributions constitutives de cette rencontre scientifique. En effet, l’aire et les objets d’étude ne concernent ni les Alpes, ni la ville. Sont abordés les équipements hydrauliques sur les sites occupés par les cisterciens et les cisterciennes des anciens diocèses de Clermont et du Puy, données issues d’une thèse de doctorat soutenue en 2016. Le sujet est traité d’un point de vue méthodologique ; il questionne les données de terrain, des modes de collecte à l’interprétation fonctionnelle et chronologique. Il est ponctuellement illustré par quelques exemples mettant en lumière la notion de systèmes hydrauliques dont la portée dépasse largement le seul usage vital et économique des communautés, puisqu’elle tend à nourrir l’histoire de la fabrique des paysages sur le temps long
Finite -representation type for homogeneous coordinate rings of non-Fano varieties
No full textFinite -representation type is an important notion in characteristic-commutative algebra, but explicit examples of varieties with or without thisproperty are few. We prove that a large class of homogeneous coordinate ringsin positive characteristic will fail to have finite -representation type. Todo so, we prove a connection between differential operators on the homogeneouscoordinate ring of and the existence of global sections of a twist of. By results of Takagi and Takahashi, thisallows us to rule out FFRT for coordinate rings of varieties with not ``positive''. By using results positivityand semistability conditions for the (co)tangent sheaves, we show that severalclasses of varieties fail to have finite -representation type, includingabelian varieties, most Calabi--Yau varieties, and complete intersections ofgeneral type. Our work also provides examples of the structure of the ring ofdifferential operators for non--pure varieties, which to this point havelargely been unexplored.Comment: v5: final published versio
Invariant bilinear differential operators
No full textI classified bilinear differential operators acting in the spaces of tensorfields on any real or complex manifold and invariant with respect to thediffeomorphisms in 1980. Here I give the details of the proof.Comment: 49 pages, LaTe
Matrix formulas for multiplicities in the spin module
No full textWe obtain inductive and enumerative formulas for the multiplicities of theweights of the spin module for the Clifford algebra of a Levi subalgebra in acomplex semisimple Lie algebra. Our formulas involve only matrices andtableaux, and our techniques combine linear algebra, Lie theory, andcombinatorics. Moreover, this suggests a relationship with complex nilpotentorbits. The case of the special linear Lie algebra \mathfrak{sl}(n,{\mathbbC}) is emphasized.Comment: Revised version, to appear in Communications in Mathematic
Arboreal Categories: An Axiomatic Theory of Resources
No full textGame comonads provide a categorical syntax-free approach to finite modeltheory, and their Eilenberg-Moore coalgebras typically encode importantcombinatorial parameters of structures. In this paper, we develop a frameworkwhereby the essential properties of these categories of coalgebras are capturedin a purely axiomatic fashion. To this end, we introduce arboreal categories,which have an intrinsic process structure, allowing dynamic notions such asbisimulation and back-and-forth games, and resource notions such as number ofrounds of a game, to be defined. These are related to extensional or "static"structures via arboreal covers, which are resource-indexed comonadicadjunctions. These ideas are developed in a general, axiomatic setting, andapplied to relational structures, where the comonadic constructions forpebbling, Ehrenfeucht-Fra\"iss\'e and modal bisimulation games recentlyintroduced by Abramsky et al. are recovered, showing that many of thefundamental notions of finite model theory and descriptive complexity arisefrom instances of arboreal covers
Les projets olympiques au service des politiques sportives partenariales. Le cas de la Fédération française de cyclisme et de la communauté d'agglomération de Saint-Quentin-en-Yvelines
No full textThis article questions the leveraging effect of Olympic bids in kind of collaborative governance, by articulating federal-local interests. It is based on a case study of the collaborative relation between the Saint-Quentin-en-Yvelines Agglomeration Community and the French cycling federation from 2000 to 2020. The contribution retraces the local collaboration process in a specific context: first showing the role the 2012 Olympic bid played in the implementation of a federal-local partnership, 2nd explaining in which extent the 2024 Olympic bid has been used to foster the structuration of this partnership. This work uses Kingdon’ streams theory to put in light the capacity of Olympic bids to open up ‘policy windows’ for the implementation of collaborative sport policies.Le présent article interroge la capacité des candidatures olympiques à créer les conditions de l'articulation entre les politiques sportives fédérales et locales. Il s'appuie sur un cas d'étude portant sur la relation entre Saint-Quentin-en-Yvelines (un territoire intercommunal situé à 20 kilomètres de Paris) et la Fédération française de cyclisme entre 2000 et 2020. La contribution retrace le processus de collaboration entre ces deux organisations dans les contextes de candidature parisienne aux Jeux Olympiques et Paralympiques de 2012 et de 2024. En s'appuyant sur la force explicative des dynamiques locales, les auteurs mobilisent la théorie des flux de Kingdon (1984) pour souligner le rôle déterminant des candidatures olympiques dans la convergence des flux des problèmes, de la politique et des politiques publiques. Celles-ci favorisent donc l'ouverture de fenêtres d'opportunité vers la mise en place de politiques sportives partenariales
L'utilisation de la musique en thérapie au cours des âges
No full textIf we define music therapy as the use of music to promote, maintain or restore health on a physical, mental, emotional or even spiritual level, we are highlighting the multiplicity of music's effects on the organism and the variety of its uses over the centuries and in different civilizations. Let's not forget that many physicians, from Hippocrates, considered the "father" of medicine, and Empedocles to Rabelais, were also musicians. Let's take a look at the history of the relationship between music and medicine, and how it has evolved from its original curative purpose to its modern preventive use to ensure a form of well-being.Si on définit la musicothérapie comme l’usage de la musique afin de promouvoir, maintenir, restaurer la santé sur le plan physique, mental, émotionnel voire spirituel, on souligne ainsi la multiplicité des effets de la musique sur l’organisme et la variété de son utilisation au cours des siècles et dans les différentes civilisations. N’oublions pas que bon nombre de médecins, depuis Hippocrate, considéré comme le « père » de la médecine, et Empédocle jusqu’à Rabelais, étaient aussi des musiciens. Dressons donc un panorama historique des rapports qui ont existé entre musique et médecine et leur évolution d’un objectif originellement curatif à un usage moderne également préventif afin d’assurer une forme de bien-être
Transitions between root subsets associated with Carter diagrams
No full textFor any two root subsets associated with two Carter diagrams that have thesame type and the same size, we construct the transition matrix that mapsone subset to the other. The transition between these two subsets is carriedout in some canonical way affecting exactly one root, so that this root ismapped to the minimal element in some root subsystem. The constructedtransitions are involutions. It is shown that all root subsets associated withthe given Carter diagram are conjugate under the action of the Weyl group. Anumerical relationship is observed between enhanced Dynkin diagrams, and (introduced by Dynkin-Minchenko)and Carter diagrams. This relationship echoes the assertions obtainedby Ringel, Rosenfeld and Baez in completely different contexts regarding theDynkin diagrams , , .Comment: 43 pages, 48 figures, 7 table
Lacon-, Shrub- and Parity-Decompositions: Characterizing Transductions of Bounded Expansion Classes
No full textThe concept of bounded expansion provides a robust way to capture sparsegraph classes with interesting algorithmic properties. Most notably, everyproblem definable in first-order logic can be solved in linear time on boundedexpansion graph classes. First-order interpretations and transductions ofsparse graph classes lead to more general, dense graph classes that seem toinherit many of the nice algorithmic properties of their sparse counterparts.In this paper, we show that one can encode graphs from a class withstructurally bounded expansion via lacon-, shrub- and parity-decompositionsfrom a class with bounded expansion. These decompositions are useful forlifting properties from sparse to structurally sparse graph classes
Bounds on the Twin-Width of Product Graphs
No full textTwin-width is a graph width parameter recently introduced by Bonnet, Kim,Thomass\'{e} & Watrigant. Given two graphs and and a graph product, we address the question: is the twin-width of bounded by afunction of the twin-widths of and and their maximum degrees? It isknown that a bound of this type holds for strong products (Bonnet, Geniet, Kim,Thomass\'{e} & Watrigant; SODA 2021). We show that bounds of the same form holdfor Cartesian, tensor/direct, corona, rooted, replacement, and zig-zagproducts. For the lexicographical product it is known that the twin-width ofthe product of two graphs is exactly the maximum of the twin-widths of theindividual graphs (Bonnet, Kim, Reinald, Thomass\'{e} & Watrigant; IPEC 2021).In contrast, for the modular product we show that no bound can hold. Inaddition, we provide examples showing many of our bounds are tight, and giveimproved bounds for certain classes of graphs.Comment: 24 pages, 1 table, 1 figur