DYNRIGDIOPHGEOM

"Dynamics of Large Group Actions, Rigidity, and Diophantine Geometry"

Coordinatore	UNIVERSITY OF BRISTOL    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	629˙999 €
EC contributo	629˙999 €
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-2009-StG
Funding Scheme	ERC-SG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-02-01   -   2016-01-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITY OF BRISTOL  Organization address address: TYNDALL AVENUE SENATE HOUSE city: BRISTOL postcode: BS8 1TH contact info Titolo: Dr. Nome: Oleksandr Cognome: Gorodnyk Email: send email Telefono: +44 (0)117 331-5247 Fax: +44 (0)117 331-5264	UK (BRISTOL)	hostInstitution	629˙999.80
2	UNIVERSITY OF BRISTOL  Organization address address: TYNDALL AVENUE SENATE HOUSE city: BRISTOL postcode: BS8 1TH contact info Titolo: Mrs. Nome: Maria Cognome: Davies Email: send email Telefono: +44 117 331 7352 Fax: +44 117 925 0900	UK (BRISTOL)	hostInstitution	629˙999.80

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 Obiettivo del progetto (Objective)

'In our project we address several fundamental questions regarding ergodic-theoretical properties of actions of large groups. The problems that we plan to tackle are not only of central importance in the abstract theory of dynamical systems, but they also lead to solutions of a number of open questions in Diophantine geometry such as the Batyrev--Manin and Peyre conjectures on the asymptotics and the distribution of rational points on algebraic varieties, a generalisation of the Oppenheim conjecture on distribution of values of polynomial functions, a generalisation of Khinchin and Dirichlet theorems on Diophantine approximation in the setting of homogeneous varieties, and estimates on the number of integral points (with almost prime coordinates satisfying polynomial and congruence equations. The proposed research is expected to imply profound connections between diverse areas of mathematics simultaneously enriching each of them. For instance, we expect to establish a precise relation between the generalised Ramanujan conjecture in the theory of automorphic forms and the order of Diophantine approximation on algebraic varieties. We also plan to use our results on counting lattice points to derive estimates on multiplicities of automorphic representations and prove results in direction of Sarnak's density hypothesis. We investigate the problem of distribution of orbits, raised by Arnold and Krylov in sixties, the problem of multiple recurrence, pioneered by Furstenberg in seventies, and the problem of rigidity of group actions, formulated by Zimmer in eighties. We plan to compute the asymptotic distribution of orbits for actions on general homogeneous spaces, to establish multiple recurrence for large classes of actions of nonamenable groups, to prove isomorphism and factor rigidity of homogeneous actions and rigidity of actions under perturbations.'