Cel 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 L\G for some subgroups H. This question may be studied different methods: Harmonic Analysis (HA): given a function f on L\G 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. Dziedzina nauki natural sciencesmathematicspure mathematicsarithmeticsL-functions Słowa kluczowe L-functions automorphic forms ergodic theory homogeneous spaces periods Program(-y) 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) Temat(-y) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Zaproszenie do składania wniosków ERC-2008-AdG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-AG - ERC Advanced Grant Instytucja przyjmująca ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Wkład UE € 866 000,00 Adres BATIMENT CE 3316 STATION 1 1015 Lausanne Szwajcaria Zobacz na mapie Region Schweiz/Suisse/Svizzera Région lémanique Vaud Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Philippe Michel (Prof.) Kontakt administracyjny Caroline Vandevyver (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE Szwajcaria Wkład UE € 866 000,00 Adres BATIMENT CE 3316 STATION 1 1015 Lausanne Zobacz na mapie Region Schweiz/Suisse/Svizzera Région lémanique Vaud Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Philippe Michel (Prof.) Kontakt administracyjny Caroline Vandevyver (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych