GEOMANGROUP

Geometry and Analysis of Group Rings

Coordinatore	TECHNISCHE UNIVERSITAET DRESDEN    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Germany [DE]
Totale costo	900˙000 €
EC contributo	900˙000 €
Programma	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)
Code Call	ERC-2011-StG_20101014
Funding Scheme	ERC-SG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-10-01   -   2016-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAET LEIPZIG  Organization address address: RITTERSTRASSE 26 city: LEIPZIG postcode: 4109 contact info Nome: Gerhard Cognome: Fuchs Email: send email Telefono: +49 341 9735012 Fax: +49 341 9735009	DE (LEIPZIG)	beneficiary	443˙306.80
2	TECHNISCHE UNIVERSITAET DRESDEN  Organization address address: HELMHOLTZSTRASSE 10 city: DRESDEN postcode: 1069 contact info Titolo: Mrs. Nome: Friederieke Cognome: Noack Email: send email Telefono: +49 351 463 42191 Fax: +49 351 463 39742	DE (DRESDEN)	hostInstitution	456˙693.20
3	TECHNISCHE UNIVERSITAET DRESDEN  Organization address address: HELMHOLTZSTRASSE 10 city: DRESDEN postcode: 1069 contact info Titolo: Prof. Nome: Andreas Cognome: Thom Email: send email Telefono: +49 351 463 37579 Fax: +49 351 463 36027	DE (DRESDEN)	hostInstitution	456˙693.20

Mappa

 Word cloud

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 Obiettivo del progetto (Objective)

'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.'