Je présenterai des résultats d'existence et d'unicité de traces dans l'espace des fonctions de type positif des réseaux de rang supérieur. Je mentionnerai quelques applications à la théorie des représentations unitaires et à la structure de leurs C﹡-algèbres. Ces résultats fournissent des généralisations noncommutatives de théorèmes dus à Margulis, Stuck—Zimmer et Nevo—Zimmer.
La propagation des ondes est un des phénomènes physiques les plus communs dans le monde qui nous entoure : le son, les vibrations, les ondes à la surface de l’eau, les télécommunications, les radars,… L’étude des équations qui découlent de la modélisation de ces phénomènes et leur simulation est un champ de recherche très large et actif. Dans beaucoup d’applications, il est question de propagation d’ondes en régime harmonique, c’est à dire qu’elles ont une dépendance harmonique en temps, dans des milieux qui sont très grands devant la longueur d’onde […]
21 Mars 2024, Antoine Georges (Collège de France, Paris and Flatiron Institute, New York) Title: Applications of Machine Learning and Neural Networks to Quantum Systems Abstract: Applications of learning algorithms using deep neural networks have developed considerably recently, often with spectacular results. The physics of complex quantum systems is no exception, with multiple applications that constitute a new field of research. Examples include the representation and optimization of wave functions of quantum systems with large numbers of degrees of freedom (neural quantum states), the determination of wave functions from measurements (quantum tomography), and applications […]
This talk is about a simple but rich model problem at the cross section of stochastic homogenization and singular stochastic PDE: We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. As already realized in the physics literature, the critical case of two space dimensions is most interesting: The elliptic generator requires a small-scale cut-off for well- posedness, and one expects marginally super-diffusive behavior on large scales. I will explain the criticality of the two-dimensional case in the introductory course by scaling arguments. […]
Le modèle de dimères représente la répartition de molécules di-atomiques sur la surface d'un cristal. Il appartient à la grande famille des modèles de mécanique statistique définis sur les graphes, dont d'autres représentant célèbres sont le modèle d'Ising et la percolation. Après une introduction générale, nous nous intéresserons aux résultats fondateurs du modèle de dimères lorsque le graphe sous-jacent est fini, en particulier au théorème de Kasteleyn qui prouve une formule close pour le nombre de configurations de dimères.
04 Avril 2024, Lénaïc Chizat (EPFL) Title: A Formula for Feature Learning in Large Neural Networks Abstract: Deep learning succeeds by doing hierarchical feature learning, but tuning hyperparameters such as initialization scales, learning rates, etc., only give indirect control over this behavior. This calls for theoretical tools to predict, measure and control feature learning. In this talk, we will first review various theoretical advances (signal propagation, infinite width dynamics, etc) that have led to a better understanding of the subtle impact of hyperparameters and architectural choices on the training dynamics. We will then introduce […]
April 16 (Tuesday) For this seminar we will have the pleasure of listening to three talks: 14.00 - 14.45 Andrei Jaikin-Zapirain (UAM), "Compressed subgroups in free groups are inert" 15.00 - 15.45 Timothée Marquis (UCL), "Amalgams of rational unipotent groups and residual nilpotence". 16.15 - 17.00 Olga Kharlampovich (CUNY), "Quantification of separability of cubically convex-cocompact subgroups of RAAGs via representations". Andrei Jaikin-Zapirain "Compressed subgroups in free groups are inert". Let F be a free group. A finitely generated subgroup H is called compressed in F if it is not contained […]
Mini-course: Flows of nonsmooth vector fields Consider a vector field v on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindelöf) Theorem states that, if the vector field is Lipschitz in space, for every initial datum x there is a unique trajectory γ starting at x at time 0 and solving the ODE γ'(t) = v(t, γ(t)). The theorem looses its validity as soon as v is slightly less regular. However, if we bundle all trajectories into a global map allowing x to vary, a celebrated theory started by DiPerna […]
Michael Jordan (UC Berkeley and INRIA Paris) Collaborative Learning, Information Asymmetries, and Incentives This colloquium is organized around data sciences in a broad sense, with the goal of bringing together researchers with diverse backgrounds (including mathematics, computer science, physics, chemistry and neuroscience) but a common interest in dealing with complex, large scale, or high dimensional data. More information can be found on the web page of the seminar: https://data-ens.github.io/seminar/
