Obiettivo The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?My motivation is two-fold:- Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious.- In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior. Campo scientifico natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisoperator algebra Programma(i) 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) Argomento(i) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Invito a presentare proposte ERC-2010-StG_20091028 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante UNIVERSITAT WIEN Contributo UE € 1 065 500,00 Indirizzo UNIVERSITATSRING 1 1010 Wien Austria Mostra sulla mappa Regione Ostösterreich Wien Wien Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Gulnara Arzhantseva (Prof.) Contatto amministrativo Helmut Schaschl (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto UNIVERSITAT WIEN Austria Contributo UE € 1 065 500,00 Indirizzo UNIVERSITATSRING 1 1010 Wien Mostra sulla mappa Regione Ostösterreich Wien Wien Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Gulnara Arzhantseva (Prof.) Contatto amministrativo Helmut Schaschl (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato