Objectif "Our proposal has three components:1. Unitarizable representations.2. Spaces and groups of non-positive curvature.3. Bounds for characteristic classes.The three parts are independent and each one is justified by major well-known conjectures and/or ambitious goals. Nevertheless, there is a unifying theme: Group Theory and its relations to Geometry, Dynamics and Analysis.In the first part, we study the Dixmier Unitarizability Problem. Even though it has remained open for 60 years, it has witnessed deep results in the last 10 years. More recently, the PI and co-authors have obtained new progress. Related questions include the Kadison Conjecture. Our methods are as varied as ergodic theory, random graphs, L2-invariants.In the second part, we study CAT(0) spaces and groups. The first motivation is that this framework encompasses classical objects such as S-arithmetic groups and algebraic groups; indeed, the PI obtained new extensions of Margulis' superrigidity and arithmeticity theorems. We are undertaking an in-depth study of the subject, notably with Caprace, aiming at constructing the full ""semi-simple theory"" in the most general setting. This has many new consequences even for the most classical objects such as matrix groups, and we propose several conjectures as well as the likely methods to attack them.In the last part, we study bounded characteristic classes. One motivation is the outstanding Chern Conjecture, according to which closed affine manifolds have zero Euler characteristic. We propose a strategy using a range of techniques in order to either attack the problem or at least obtain new results on simplicial volumes." Champ scientifique natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Appel à propositions ERC-2010-AdG_20100224 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Contribution de l’UE € 1 332 710,40 Adresse BATIMENT CE 3316 STATION 1 1015 Lausanne Suisse Voir sur la carte Région Schweiz/Suisse/Svizzera Région lémanique Vaud Type d’activité Higher or Secondary Education Establishments Contact administratif Caroline Vandevyver (Ms.) Chercheur principal Nicolas Monod (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Suisse Contribution de l’UE € 1 332 710,40 Adresse BATIMENT CE 3316 STATION 1 1015 Lausanne Voir sur la carte Région Schweiz/Suisse/Svizzera Région lémanique Vaud Type d’activité Higher or Secondary Education Establishments Contact administratif Caroline Vandevyver (Ms.) Chercheur principal Nicolas Monod (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
