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Contenuto archiviato il 2024-06-18

Geometry and Analysis of Group Rings

Obiettivo

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.

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
Costo totale
Nessun dato

Beneficiari (2)