EQUIARITH

Equidistribution in number theory

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	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

#	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	0.00
2	ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE  Organization address address: BATIMENT CE 3316 STATION 1 city: LAUSANNE postcode: 1015 contact info Titolo: Prof. Nome: Philippe Cognome: Michel Email: send email Telefono: +41 21 69 32576 Fax: +41 21 69 35839	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.'