Objectif In this project, we propose to study mixing and rigidity properties of a large class offlows in geometry and dynamical systems using novel microlocal and spectral methods. Such methods, recently developed for flows with hyperbolicity, are based on the construction of new functional spaces, adapted to the considered flow, on which the generating vector field is Fredholm withdiscrete spectrum, known as the resonance spectrum. We want to apply these tools to the following categories of long-standing problems:1) Geometric inverse problems: boundary and lens rigidity problems, analysis of the X-ray transforms for geodesic flows and its applications to Calderon and Gelfand inverse problems.2) Rigidity for Anosov flows: determination of the minimal regularity of the stable/unstable foliations providing rigidity, rigidity questions for regular conjugacies of flows. 3) Rate of mixing for flows of hyperbolic type: decay of correlations of Axiom A flows, Anosov flows, and their compact Lie groups extensions, frame flows of negatively curved manifolds.4) Resonances for locally symmetric spaces: relation between resonances of the flow and the spectrum of Laplacians on bundles.To address these problems, we will develop a thorough analysis for the regularity and the long time properties of solutions to transport equations. We are convinced that the proposed approach will provide solutions to these problems, which have been out of reach for a long time. Champ scientifique natural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Mots‑clés Inverse problems geodesic flows hyperbolic dynamic Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-COG - ERC Consolidator Grant Appel à propositions ERC-2016-COG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 1 133 236,00 Adresse RUE MICHEL ANGE 3 75794 Paris France Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 133 236,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France Contribution nette de l'UE € 1 133 236,00 Adresse RUE MICHEL ANGE 3 75794 Paris Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 133 236,00
