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Geometry and Analysis of Group Rings

Ziel

Eversince, the study of discrete groups and their group rings has attracted researchers from various
mathematical 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 the
study 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 groups
rings by contributing to a better understanding of conjectures of Dixmier’s and Atiyah’s. The field of
Algebraic Approximation is new, and has already been successfully used by G. Cortinas and myself to
resolve a longstanding conjecture in Algebraic K-theory due to Jonathan Rosenberg.

Aufforderung zur Vorschlagseinreichung

ERC-2011-StG_20101014
Andere Projekte für diesen Aufruf anzeigen

Gastgebende Einrichtung

TECHNISCHE UNIVERSITAET DRESDEN
EU-Beitrag
€ 460 847,92
Adresse
HELMHOLTZSTRASSE 10
01069 Dresden
Deutschland

Auf der Karte ansehen

Region
Sachsen Dresden Dresden, Kreisfreie Stadt
Aktivitätstyp
Higher or Secondary Education Establishments
Hauptforscher
Andreas Thom (Prof.)
Kontakt Verwaltung
Friederieke Noack (Mrs.)
Links
Gesamtkosten
Keine Daten

Begünstigte (2)