RIGIDITY

"Rigidity: Groups, Geometry and Cohomology"

Coordinatore	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Switzerland [CH]
Totale costo	1˙332˙710 €
EC contributo	1˙332˙710 €
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-AdG_20100224
Funding Scheme	ERC-AG
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-03-01   -   2016-02-29

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE  Organization address address: BATIMENT CE 3316 STATION 1 city: LAUSANNE postcode: 1015 contact info Titolo: Ms. Nome: Caroline Cognome: Vandevyver Email: send email Telefono: +41 21 693 4977 Fax: +41 21 693 5585	CH (LAUSANNE)	hostInstitution	1˙332˙710.40
2	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE  Organization address address: BATIMENT CE 3316 STATION 1 city: LAUSANNE postcode: 1015 contact info Titolo: Prof. Nome: Nicolas Cognome: Monod Email: send email Telefono: +41 21 693 7928	CH (LAUSANNE)	hostInstitution	1˙332˙710.40

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 Obiettivo del progetto (Objective)

'Our proposal has three components:

1. Unitarizable representations.

2. Spaces and groups of non-positive curvature.

3. Bounds for characteristic classes.

The three parts are independent and each one is justified by major well-known conjectures and/or ambitious goals. Nevertheless, there is a unifying theme: Group Theory and its relations to Geometry, Dynamics and Analysis.

In the first part, we study the Dixmier Unitarizability Problem. Even though it has remained open for 60 years, it has witnessed deep results in the last 10 years. More recently, the PI and co-authors have obtained new progress. Related questions include the Kadison Conjecture. Our methods are as varied as ergodic theory, random graphs, L2-invariants.

In the second part, we study CAT(0) spaces and groups. The first motivation is that this framework encompasses classical objects such as S-arithmetic groups and algebraic groups; indeed, the PI obtained new extensions of Margulis' superrigidity and arithmeticity theorems. We are undertaking an in-depth study of the subject, notably with Caprace, aiming at constructing the full 'semi-simple theory' in the most general setting. This has many new consequences even for the most classical objects such as matrix groups, and we propose several conjectures as well as the likely methods to attack them.

In the last part, we study bounded characteristic classes. One motivation is the outstanding Chern Conjecture, according to which closed affine manifolds have zero Euler characteristic. We propose a strategy using a range of techniques in order to either attack the problem or at least obtain new results on simplicial volumes.'