
Activités scientifiques du département
Le DMA est à la fois un département d'enseignement et un département de recherche. Cette structuration originale vise notamment à mettre très tôt les élèves au plus près de la recherche en train de se faire.
Publications
L'essentielle de publications des membres du département, des thèses et des HDR qui y sont soutenues sont disponibles sur le serveur HAL.
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18 March 2025 hal-04996372 publication
Tony Jin, João Ferreira, Michel Bauer, Michele Filippone, Thierry Giamarchi
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1 April 2025 hal-05015621 pré-publication
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure, according to certain weights assigned to each cycle length. The proof is based on uniform control of the characteristic polynomial using results from the singularity analysis of generating functions, together with the convergence of traces to explicit random variables expressed via a Poisson family. The limit function is the exponential of a Poisson series which has already appeared in the case of uniform permutation matrices. It is the Poisson analog of the Gaussian Holomorphic Chaos, related to the limit of characteristic polynomials for other matrix models such as Circular Ensembles, i.i.d. matrices, and Gaussian elliptic matrices.
Quentin François
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19 March 2025 tel-03905418 thèse
This thesis studies the persistent homology of real-valued continuous functions f on compact topological spaces X. The introduction of homological indices and homological dimensions allows us to link persistence theory to metric quantities of the compact space X, such as its upper-box dimension. These quantities give a precise framework to the Wasserstein p-stability results known in the literature, but also extend them to Hölder functions on more general spaces (including all compact Riemannian manifolds) with explicit constants and whose regime for p is optimal. In degree zero of homology, a more in-depth study can be made using trees associated to f, which generalize the merge trees which are definable when f is Morse. It is possible to link the dimension of these trees to the persistence index of f and to its barcode. We apply these deterministic results to the stochastic setting to draw consequences about the barcodes of random functions of prescribed regularity. These consequences also allow us to develop distributional discrimination tests for the processes, of which we present a particular example. Finally, we define the zeta-functions associated with a stochastic process and compute these functions and other related quantities for several processes in dimension one, including the Brownian motion and the alpha-stable Lévy processes.
Daniel Perez
Les actualités de la recherche
Annonce de conférences, congrès et autres événements scientifiques.
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Mathematical Fluid Dynamics advanced summer school
Co-organisée par Emmaunel Dormy avec le soutien financier du DMA, cette 3e édition se déroule
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Développer son propre style en mathématiques : rencontre avec Cyril Houdayer
Le professeur est porteur du projet NET, lauréat de l'ERC Advanced Grant
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Gabriel Peyré et les mathématiques de l’intelligence artificielle
Entretien dans le cadre du Sommet pour l'Action sur l'intelligence artificielle (IA) des 10 et

Annales de l’ENS
Les Annales scientifiques de l’École normale supérieure publient 6 fascicules par an. Elles sont éditées par la Société mathématique de France depuis 2008.