ANALYTIC
"ANALYTIC PROPERTIES OF INFINITE GROUPS: limits, curvature, and randomness"
| Coordinatore | UNIVERSITAT WIEN
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
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITAT WIEN
Organization address
address: UNIVERSITATSRING 1 contact info |
AT (WIEN) | hostInstitution | 1˙065˙500.00 |
| 2 |
UNIVERSITAT WIEN
Organization address
address: UNIVERSITATSRING 1 contact info |
AT (WIEN) | hostInstitution | 1˙065˙500.00 |
Mappa
Word cloud
Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.
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.'