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
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITE PARIS-SUD
Organization address
address: RUE GEORGES CLEMENCEAU 15 contact info |
FR (ORSAY) | hostInstitution | 0.00 |
| 2 |
UNIVERSITE PARIS-SUD
Organization address
address: RUE GEORGES CLEMENCEAU 15 contact info |
FR (ORSAY) | hostInstitution | 0.00 |
Mappa
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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.'