Objective The primary goal of the project is to obtain an understanding of geometric and dynamical properties of moduli spaces and mapping class groups. For a mapping class group of a surface of finite type, we are interested in subgroups, in particular in the trace fields of Veech groups beyond the case of genus 2. Convex cocompact surface subgroups are word hyperbolic surface-by-surface groups, and we aim at clarifying whether or not such groups exist.Fine asymptotics of the distribution of periodic orbits for the Teichmüller flow on strata of quadratic or abelian differentials can be related to dynamical zeta functions. A Borel conjugacy of the Teichmüller flow on the moduli space of quadratic differentials into the Weil-Petersson flow will be used to analyze dynamical properties of the Weil-Petersson flow.The handlebody is a finitely presented subgroup of the mapping class group which however is not quasi-isometrically embedded. A new geometric model for the group will be used towards obtaining a comprehensive understanding of the geometry of this group, in particular with respect to calculating the Dehn function and quasi-isometric rigidigy.A similar geometric model for the outer automorphism group of the free group may yield hyperbolicity of the electrified sphere graph on which this group acts by simplicial automorphisms.. Fields of science natural 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) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2011-ADG_20110209 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Coordinator RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Address Regina pacis weg 3 53113 Bonn Germany See on map Region Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Principal investigator Ursula Annemarie Hamenstädt (Prof.) Administrative Contact Daniela Sprinkmeier (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Germany EU contribution € 1 536 600,00 Address Regina pacis weg 3 53113 Bonn See on map Region Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Principal investigator Ursula Annemarie Hamenstädt (Prof.) Administrative Contact Daniela Sprinkmeier (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
