Objective 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. Fields of science natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2011-StG_20101014 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution TECHNISCHE UNIVERSITAET DRESDEN EU contribution € 460 847,92 Address HELMHOLTZSTRASSE 10 01069 Dresden Germany See on map Region Sachsen Dresden Dresden, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Principal investigator Andreas Thom (Prof.) Administrative Contact Friederieke Noack (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all TECHNISCHE UNIVERSITAET DRESDEN Germany EU contribution € 460 847,92 Address HELMHOLTZSTRASSE 10 01069 Dresden See on map Region Sachsen Dresden Dresden, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Principal investigator Andreas Thom (Prof.) Administrative Contact Friederieke Noack (Mrs.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data UNIVERSITAET LEIPZIG Participation ended Germany EU contribution € 439 152,08 Address RITTERSTRASSE 26 04109 Leipzig See on map Region Sachsen Leipzig Leipzig Activity type Higher or Secondary Education Establishments Administrative Contact Gerhard Fuchs Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
