EQUIARITH
Equidistribution in number theory
| Coordinatore | ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Switzerland [CH] |
| Totale costo | 866˙000 € |
| EC contributo | 866˙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-2008-AdG |
| Funding Scheme | ERC-AG |
| Anno di inizio | 2008 |
| Periodo (anno-mese-giorno) | 2008-12-01 - 2013-11-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Organization address
address: BATIMENT CE 3316 STATION 1 contact info |
CH (LAUSANNE) | hostInstitution | 0.00 |
| 2 |
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Organization address
address: BATIMENT CE 3316 STATION 1 contact info |
CH (LAUSANNE) | hostInstitution | 0.00 |
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Obiettivo del progetto (Objective)
'The purpose of this proposal is to investigate from various perspectives some equidistribution problems associated with homogeneous spaces of arithmetic type: a typical problem (basically solved) is the distribution of the set of representations of a large integer by an integral quadratic form. Another harder problem is the study of the distribution of special points on Shimura varieties. In a different direction (linked with quantum chaos), the study of the concentration of Laplacian (Maass) eigenforms or of sections of holomorphic bundles is related to similar problems. Given X such a space and G>L the underlying algebraic group and its corresponding lattice L, the above questions boil down to studying the distribution of H-orbits x.H (or more generally H-invariant measures)on the quotient LG for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on LG one studies the period integral of f along x.H. This may be done by automorphic methods. In favorable circumstances, the above periods are related to L-functions which one may hope to treat by methods from analytic number theory (the subconvexity problem). Ergodic Theory (ET): one studies the properties of weak*-limits of the measures supported by x.H using rigidity techniques: depending on the nature of H, one might use either rigidity of unipotent actions or the more recent rigidity results for torus actions in rank >1. In fact, HA and ET are intertwined and complementary : the use of ET in this context require a substantial input from number theory and HA, while ET lead to a soft understanding of several features of HA. In addition, the Langlands correspondence principle make it possible to pass from one group G to another. Based on earlier experience, our goal is to develop these interactions systematically and to develop new approaches to outstanding arithmetic problems :eg. the subconvexity problem or the Andre/Oort conjecture.'