ANALYTIC

"ANALYTIC PROPERTIES OF INFINITE GROUPS: limits, curvature, and randomness"

Coordinatore	UNIVERSITAT WIEN    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Austria [AT]
Totale costo	1˙065˙500 €
EC contributo	1˙065˙500 €
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-2010-StG_20091028
Funding Scheme	ERC-SG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-04-01   -   2016-03-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAT WIEN  Organization address address: UNIVERSITATSRING 1 city: WIEN postcode: 1010 contact info Titolo: Dr. Nome: Helmut Cognome: Schaschl Email: send email Telefono: +43 1 427718218 Fax: +43 1 42779182	AT (WIEN)	hostInstitution	1˙065˙500.00
2	UNIVERSITAT WIEN  Organization address address: UNIVERSITATSRING 1 city: WIEN postcode: 1010 contact info Titolo: Prof. Nome: Gulnara Cognome: Arzhantseva Email: send email Telefono: +43 1 4277506 49 Fax: +43 1 42779 506	AT (WIEN)	hostInstitution	1˙065˙500.00

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 Obiettivo del progetto (Objective)

'The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.

My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?

My motivation is two-fold: - Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious. - In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.

The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior.'