Objetivo Many milestone results in mathematics emerge from interactions and transfer of techniques and methods between different areas. I want to attack outstanding problems concerning K-theory, L^2-invariants, manifolds and group theory. The time is ripe to use the exciting and profound progress that has been made during the last years in the individual areas to build new bridges, gain new insights, open the door to new applications, and to trigger new innovative activities worldwidelasting beyond the proposed funding period.The starting point are the prominent conjectures of Farrell-Jones on the algebraic K- and L-theory of group rings, of Baum-Connes on the topological K-theory of reduced group C^*-algebras, and of Atiyah on the integrality of L^-Betti numbers.I intend to analyze and establish the Farrell-Jones Conjecture in other settings such as topological cyclic homology of ``group rings'' over the sphere spectrum, algebraic K-theory of Hecke algebras of totally disconnected groups, the topological K-theory of Fr'echet group algebras, and Waldhausen's A-theory of classifying spaces of groups. This has new and far-reaching consequences for automorphism groups of closed aspherical manifolds, the structure of group rings, and representation theory. Recent proofs by the PI of the Farrell-Jones Conjecture for certain classes of groups require input from homotopy theory, geometric group theory, controlled topology and flows on metric spaces, and will be transferred to the new situations. There is also a program towards a proof of the Atiyah Conjecture based on the Farrell-Jones Conjecture and ring theory. Furthermore, I want to attack open problems such as the approximation of L^2-torsion for towers of finite coverings, and the relation of the first L^2-Betti number, the cost and the rank gradient of a finitely generated group. I see a high potential for new striking applications of the Farrell-Jones Conjecture and L^2-techniques to manifolds and groups. Ámbito científico natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometry Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-ADG-2014 - ERC Advanced Grant Convocatoria de propuestas ERC-2014-ADG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-ADG - Advanced Grant Institución de acogida RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Aportación neta de la UEn € 1 719 583,00 Dirección REGINA PACIS WEG 3 53113 Bonn Alemania Ver en el mapa Región Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 719 583,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Alemania Aportación neta de la UEn € 1 719 583,00 Dirección REGINA PACIS WEG 3 53113 Bonn Ver en el mapa Región Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 719 583,00
