Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry Program(-y) 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) Temat(-y) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Zaproszenie do składania wniosków ERC-2012-ADG_20120216 Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-AG - ERC Advanced Grant Instytucja przyjmująca UGA-Université Grenoble Alpes Wkład UE € 998 276,80 Adres 621, AVENUE CENTRALE 38401 SAINT MARTIN D'HERES Francja Zobacz na mapie Region RUP FR — Régions Ultrapériphériques Françaises Guadeloupe Guadeloupe Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Aurélie Diringer-Dagorne (Ms.) Kierownik naukowy Gérard Robert Besson (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (2) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko UGA-Université Grenoble Alpes Francja Wkład UE € 998 276,80 Adres 621, AVENUE CENTRALE 38401 SAINT MARTIN D'HERES Zobacz na mapie Region RUP FR — Régions Ultrapériphériques Françaises Guadeloupe Guadeloupe Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Aurélie Diringer-Dagorne (Ms.) Kierownik naukowy Gérard Robert Besson (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych UNIVERSITE JOSEPH FOURIER GRENOBLE 1 Zakończenie uczestnictwa Francja Wkład UE Brak danych Adres Avenue Centrale, Domaine Universitaire 621 38041 GRENOBLE Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Yann Leroux (Mr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych