Objective 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. Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicsapplied mathematicsmathematical physicsconformal field 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2009-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution KOBENHAVNS UNIVERSITET EU contribution € 724 992,00 Address NORREGADE 10 1165 Kobenhavn Denmark See on map Region Danmark Hovedstaden Byen København Activity type Higher or Secondary Education Establishments Principal investigator Nathalie Wahl (Dr.) Administrative Contact Ivan Kristoffersen (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all KOBENHAVNS UNIVERSITET Denmark EU contribution € 724 992,00 Address NORREGADE 10 1165 Kobenhavn See on map Region Danmark Hovedstaden Byen København Activity type Higher or Secondary Education Establishments Principal investigator Nathalie Wahl (Dr.) Administrative Contact Ivan Kristoffersen (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
