Objectif The purpose of this project is to study the interactions between Riemannian Geometry and the topology of open manifolds. A general question is to find the best Riemannian metric on a given manifold; a related question is to understand the topological consequences of the existence of a metric with given properties. This programme has already been highly successful in the compact case whereas basic questions are not answered in the open case. The key tool which ought to be used in the three items is the Ricci flow with bubbling off, in dimension 3, described by myself and my collaborators. This opened the way to applying Ricci flow to non-compact manifolds and it is a breakthrough which gives a very optimistic approach to some deep conjectures. The study of Whitehead manifolds will open a wide realm of research since results are scarce. This will provide work for quite a few graduate students and for several years. My goal is to make such a significant progress that the subject will become proeminent in Riemannian Geometry. Again, for this the Ricci flow will be an unavoidable tool. Constructing explicit Riemannian metrics with various properties is another goal, which pertains to the same circle of ideas, and will lead to a systematic study of these spaces. This is a new and groundbreaking direction of research. I have already obtained some results in these direction and I intend to go much further and to enhance my national and international collaborations using the grant if accepted. Champ scientifique natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry 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-2012-ADG_20120216 Voir d’autres projets de cet appel Régime de financement ERC-AG - ERC Advanced Grant Institution d’accueil UGA-Université Grenoble Alpes Contribution de l’UE € 998 276,80 Adresse 621, AVENUE CENTRALE 38401 SAINT MARTIN D'HERES France Voir sur la carte Région RUP FR — Régions Ultrapériphériques Françaises Guadeloupe Guadeloupe Type d’activité Higher or Secondary Education Establishments Contact administratif Aurélie Diringer-Dagorne (Ms.) Chercheur principal Gérard Robert Besson (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (2) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire UGA-Université Grenoble Alpes France Contribution de l’UE € 998 276,80 Adresse 621, AVENUE CENTRALE 38401 SAINT MARTIN D'HERES Voir sur la carte Région RUP FR — Régions Ultrapériphériques Françaises Guadeloupe Guadeloupe Type d’activité Higher or Secondary Education Establishments Contact administratif Aurélie Diringer-Dagorne (Ms.) Chercheur principal Gérard Robert Besson (Dr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée UNIVERSITE JOSEPH FOURIER GRENOBLE 1 Participation terminée France Contribution de l’UE Aucune donnée Adresse Avenue Centrale, Domaine Universitaire 621 38041 GRENOBLE Voir sur la carte Type d’activité Higher or Secondary Education Establishments Contact administratif Yann Leroux (Mr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
