Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebra Słowa kluczowe group theory functional analysis ergodic theory algebraic topology Program(-y) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Temat(-y) ERC-CoG-2015 - ERC Consolidator Grant Zaproszenie do składania wniosków ERC-2015-CoG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-COG - Consolidator Grant Instytucja przyjmująca TECHNISCHE UNIVERSITAET DRESDEN Wkład UE netto € 2 000 000,00 Adres HELMHOLTZSTRASSE 10 01069 Dresden Niemcy Zobacz na mapie Region Sachsen Dresden Dresden, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 2 000 000,00 Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko TECHNISCHE UNIVERSITAET DRESDEN Niemcy Wkład UE netto € 2 000 000,00 Adres HELMHOLTZSTRASSE 10 01069 Dresden Zobacz na mapie Region Sachsen Dresden Dresden, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 2 000 000,00