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Séminaire Analyse

organisé par l'équipe Analyse

  • Joffrey Mathien

    Cutoff for geodesic path and Brownian motion on hyperbolic manifolds

    22 janvier 2026 - 11:00Salle de conférences IRMA

    For an ergodic dynamical system, the cutoff describes an abrupt transition to equilibrium. Historically introduced in seminal work by Diaconis, Shahshahani and Aldous for card shuffling and other random walks on finite groups, there are now numerous examples of Markov chains and Markov processes where the cutoff has been established. Most of the current examples are on finite spaces. In this talk, we study cutoff for classical processes -- namely Brownian motion and geodesic paths -- on compact hyperbolic manifolds, and we develop a spectral strategy introduced by Lubetzky and Peres in 2016 for Ramanujan graphs and further developed in different geometric contexts. In particular, we extend results obtained by Golubev and Kamber in 2019 to any dimension and still are able to obtain cutoff under weaker hypothesis. Based on a joint work with C. Bordenave

  • Annalaura Stingo

    Trivial resonances for a system of Klein-Gordon equations and statistical applications

    29 janvier 2026 - 11:00Salle de conférences IRMA

    In the derivation of the kinetic equation from the cubic NLS, a key feature is the invariance of the Schrödinger equation under the action of U(1), which allows the quasi-resonances of the equation to drive the effective dynamics of the correlations. In this talk, I will give an example of equation that does not enjoy such type of invariance and show that the exact resonances always take precedence over quasi-resonances. As a result, the effective dynamics is not of kinetic type but still nonlinear. I will present the problem, the ideas behind the derivation of the effective dynamics and some elements of the proof. This is based on a recent work in collaboration with de Suzzoni (Université Evry Paris-Saclay) and Touati (CNRS and Université de Bordeaux).

  • Théo Fradin

    Continuous density variations in the ocean

    5 février 2026 - 11:00Salle de conférences IRMA

    The aim of this talk is to study the well-posedness of the incompressible Euler equations in an oceanic setting, including continuous density variations. Because of specific features of our setting (presence of a free-surface, small scale ratios, i.e. the shallow water parameter), a first approach will consist in studying the case of small density variations, which will lead to the justification of the well-known non-linear shallow water equations. We then move to a case where large density variations can be studied, which is when the density is strictly decreasing with height. This setting of so-called stable stratification is widely used in the study of geophysical flows, and is one of the main ingredients that contribute to the global oceanic circulation, regulating the Earth' climate.

  • Baptiste Louf

    Bivariate asymptotics for high genus geometry, random matrices, biological modelling etc.

    12 février 2026 - 11:00Salle de conférences IRMA

    Given a sequence a_n, one can ask about its behaviour as n grows, i.e., its asymptotics. This question has been very well studied in a wide context, with general results developped, for instance, within analytic combinatorics. What happens when our sequence has two parameters that both go to infinity ? Now we're in the realm of bivariate asymptotics, for which there exists some results from analytic combinatorics, but the current knowledge is still much more limited than in the univariate case. Together with Andrew Elvey Price, Wenjie Fang and Michael Wallner, we developped new methods to study bivariate recurrences and obtain asymptotics from it, which we apply to several contexts as advertised in the title. I will explain the historical background as well as our new results, without going too much into the technicalities.

  • Yingtong Hou

    BPHZ renormalisation of invariant measures via multi-indices

    5 mars 2026 - 11:00Salle de conférences IRMA

    In this talk, we provide a method to obtain the renormalised measures in quantum field theory by renormalising the cumulant expansion of the original measures. After reviewing the main ingredients of renormalisation: cumulant expansion, Wick renormalisation, Feynman diagrams, we introduce our approach based on BPHZ renormalisation via multi-indices which are combinatorial objects originating from describing scalar-valued singular SPDEs. To automate the renormalisation procedure, we propose a multi-index counterpart of the Hopf-algebraic program initiated by Connes and Kreimer for the renormalisation of Feynman diagrams. This is a joint work with Yvain Bruned.

  • Jacques-Arthur Weil

    Détermination des groupoïdes de Malgrange des équations de Painlevé admettant une solution algébrique

    12 mars 2026 - 11:00Salle de conférences IRMA

    Le groupoïde de Malgrange est une des généralisations aux équations différentielles non-linéaires du groupe de Galois. Introduite il y a une vingtaine d’années, sa théorie a bien été développée mais son calcul reste hors de portée en général. Dans ce projet, commun avec Guy Casale et Primitivo Acosta-Humanez, nous utilisons un résultat majeur de Casale, dans la suite des travaux de Morales et Ramis : lorsque l’on linéarise une équation différentielle le long d’une solution algébrique, les groupes de Galois des équations linéarisées peuvent se voir comme sous-objets du groupe de Malgrange. Celà nous a permis de donner un critère effectif sur la dimension de ces groupes de Galois différentiels pour déterminer les groupoïdes de Malgrange des équations de Painlevé admettant une solution algébrique. L’exposé s’appuiera sur des exemples où l’on peut dérouler toute la démarche et voir la plupart des calculs “à la main”.