Obiettivo The scientific goal of the proposal is to answer central questions related to diffeomorphism groups of manifolds of dimension 2 and 3, and to their deformation invariant analogs, the mapping class groups. While the classification of surfaces has been known for more than a century, their automorphism groups have yet to be fully understood. Even less is known about diffeomorphisms of 3-manifolds despite much interest, and the objects here have only been classified recently, by the breakthrough work of Perelman on the Poincar\'e and geometrization conjectures. In dimension 2, I will focus on the relationship between mapping class groups and topological conformal field theories, with applications to Hochschild homology. In dimension 3, I propose to compute the stable homology of classifying spaces of diffeomorphism groups and mapping class groups, as well as study the homotopy type of the space of diffeomorphisms. I propose moreover to establish homological stability theorems in the wider context of automorphism groups and more general families of groups. The project combines breakthrough methods from homotopy theory with methods from differential and geometric topology. The research team will consist of 3 PhD students, and 4 postdocs, which I will lead. Campo scientifico natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field theory Programma(i) 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) Argomento(i) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Invito a presentare proposte ERC-2009-StG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante KOBENHAVNS UNIVERSITET Contributo UE € 724 992,00 Indirizzo NORREGADE 10 1165 Kobenhavn Danimarca Mostra sulla mappa Regione Danmark Hovedstaden Byen København Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Nathalie Wahl (Dr.) Contatto amministrativo Ivan Kristoffersen (Mr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto KOBENHAVNS UNIVERSITET Danimarca Contributo UE € 724 992,00 Indirizzo NORREGADE 10 1165 Kobenhavn Mostra sulla mappa Regione Danmark Hovedstaden Byen København Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Nathalie Wahl (Dr.) Contatto amministrativo Ivan Kristoffersen (Mr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato