Objetivo Eversince, the study of symmetry in mathematics and mathematical physics has been fundamentalto a thourough understanding of most of the fundamental notions. Group theory in all its formsis the theory of symmetry and thus an indispensible tool in many of the basic theoretical sciences.The study of infinite symmetry groups is especially challenging, since most of the tools from thesophisticated theory of finite groups break down and new global methods of study have to be found.In that respect, the interaction of group theory and the study of group rings with methods from ringtheory, probability, Riemannian geometry, functional analyis, and the theory of dynamical systemshas been extremely fruitful in a variety of situations. In this proposal, I want to extend this line ofapproach and introduce novel approaches to longstanding and fundamental problems.There are four main interacting themes that I want to pursue:(i) Groups and their study using ergodic theory of group actions(ii) Approximation theorems for totally disconnected groups(iii) Kaplansky’s Direct Finiteness Conjecture and p-adic analysis(iv) Kervaire-Laudenbach Conjecture and topological methods in combinatorial group theoryThe theory of `2-homology and `2-torsion of groups has provided a fruitful context to study globalproperties of infinite groups. The relationship of these homological invariants with ergodic theoryof group actions will be part of the content of Part (i). In Part (ii) we seek for generalizations of`2-methods to a context of locally compact groups and study the asymptotic invariants of sequencesof lattices (or more generally invariant random subgroups). Part (iii) tries to lay the foundation of a padicanalogue of the `2-theory, where we study novel aspects of p-adic functional analysis which helpto clarify the approximation properties of (Z/pZ)-Betti numbers. Finally, in Part (iv), we try to attackvarious longstanding combinatorial problems in group theory with tools from algebraic topology andp-local homotopy theory. Ámbito científico natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebra Palabras clave group theory functional analysis ergodic theory algebraic topology Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-CoG-2015 - ERC Consolidator Grant Convocatoria de propuestas ERC-2015-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-COG - Consolidator Grant Institución de acogida TECHNISCHE UNIVERSITAET DRESDEN Aportación neta de la UEn € 2 000 000,00 Dirección HELMHOLTZSTRASSE 10 01069 Dresden Alemania Ver en el mapa Región Sachsen Dresden Dresden, 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 € 2 000 000,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo TECHNISCHE UNIVERSITAET DRESDEN Alemania Aportación neta de la UEn € 2 000 000,00 Dirección HELMHOLTZSTRASSE 10 01069 Dresden Ver en el mapa Región Sachsen Dresden Dresden, 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 € 2 000 000,00