Obiettivo Eversince, the study of discrete groups and their group rings has attracted researchers from variousmathematical branches and led to beautiful results with proofs involving fields such as number theory,combinatorics and analysis. The basic object of study is the structure of the group G itself, i.e. its subgroups, quotients, etc. and properties of the group ring kG with coefficients in a field k.Recently, techniques such as Randomization and Algebraic Approximation have lead to fruitful insights.This project is focused on new and groundbreaking applications of these two techniques in thestudy of groups and group rings. In order to illustrate this, I am explaining how useful these techniques are by focusing on three interacting topics: (i) new characterizations of amenability related to Dixmier’s Conjecture, (ii) the Atiyah conjecture for discrete groups, and (iii) algebraic approximation in the algebraic K-theory of algebras of functional analytic type. All three problems are presently wide open and progress in any of the three problems would mean a breakthrough in current research.Using Randomization techniques, I want to achieve important results in the understanding of groupsrings by contributing to a better understanding of conjectures of Dixmier’s and Atiyah’s. The field ofAlgebraic Approximation is new, and has already been successfully used by G. Cortinas and myself toresolve a longstanding conjecture in Algebraic K-theory due to Jonathan Rosenberg. Campo scientifico natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics 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-2011-StG_20101014 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante TECHNISCHE UNIVERSITAET DRESDEN Contributo UE € 460 847,92 Indirizzo HELMHOLTZSTRASSE 10 01069 Dresden Germania Mostra sulla mappa Regione Sachsen Dresden Dresden, Kreisfreie Stadt Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Andreas Thom (Prof.) Contatto amministrativo Friederieke Noack (Mrs.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto TECHNISCHE UNIVERSITAET DRESDEN Germania Contributo UE € 460 847,92 Indirizzo HELMHOLTZSTRASSE 10 01069 Dresden Mostra sulla mappa Regione Sachsen Dresden Dresden, Kreisfreie Stadt Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Andreas Thom (Prof.) Contatto amministrativo Friederieke Noack (Mrs.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato UNIVERSITAET LEIPZIG Partecipazione conclusa Germania Contributo UE € 439 152,08 Indirizzo RITTERSTRASSE 26 04109 Leipzig Mostra sulla mappa Regione Sachsen Leipzig Leipzig Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Gerhard Fuchs Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
