GADA

Group Actions: Interactions between Dynamical Systems and Arithmetic

 Coordinatore UNIVERSITE PARIS-SUD 

Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.

 Nazionalità Coordinatore France [FR]
 Totale costo 750˙000 €
 EC contributo 750˙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-2007-StG
 Funding Scheme ERC-SG
 Anno di inizio 2008
 Periodo (anno-mese-giorno) 2008-12-01   -   2013-11-30

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITE PARIS-SUD

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Mr.
Nome: Nicolas
Cognome: Lecompte
Email: send email
Telefono: + 33 (0)1 69 15 55 89
Fax: +33 (0)1 69 15 55 99

FR (ORSAY) hostInstitution 0.00
2    UNIVERSITE PARIS-SUD

 Organization address address: RUE GEORGES CLEMENCEAU 15
city: ORSAY
postcode: 91405

contact info
Titolo: Prof.
Nome: Emmanuel
Cognome: Breuillard
Email: send email
Telefono: +33 (0) 6 63 18 26 98
Fax: +33 (0)1 69 15 63 48

FR (ORSAY) hostInstitution 0.00

Mappa


 Word cloud

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ergodic    groups    arithmetic    theory    subgroups    spectral    spaces    forms    parts    group    conjecture    harmonic    combinatorics    mathematics   

 Obiettivo del progetto (Objective)

'Our main goal is to apply the powerful analytical tools that are now emerging from areas of more 'applicable' parts of mathematics such as ergodic theory, random walks, harmonic analysis and additive combinatorics to some longstanding open problems in more theoretical parts of mathematics such as group theory and number theory. The recent work of Green and Tao about arithmetic progressions of prime numbers, or Margulis' celebrated solution of the Oppenheim Conjecture about integer values of quadratic forms are examples of the growing interpenetration of such seemingly unrelated fields. We have in mind an explicit set of problems: a uniform Tits alternative, the equidistribution of dense subgroups, the Andre-Oort conjecture, the spectral gap conjecture, the Lehmer problem. All these questions involve group theory in various forms (discrete subgroups of Lie groups, representation theory and spectral theory, locally symmetric spaces and Shimura varieties, dynamics on homogeneous spaces of arithmetic origin, Cayley graphs of large finite groups, etc) and have also a number theoretic flavor. Their striking common feature is that each of them enjoys some intimate relationship, whether by the foreseen methods to tackle it or by its consequences, with ergodic theory on the one hand and harmonic analysis and combinatorics on the other. We believe that the new methods being currently developed in those fields will bring crucial insights to the problems at hand. This proposed research builds on previous results obtained by the author and addresses some of the most challenging open problems in the field.'

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