Cel We propose to study the fractal geometry of invariant sets for endomorphisms of compact abelian groups, specifically a family of conjectures by Furstenberg on the dimensions of orbit closures under such dynamics, and on the size of sums and intersections of invariant sets. These conjectures are related to problems on expansion in integer bases, in Diophantine approximation, measure rigidity, analysis and equidistribution. The project focuses on the conjectures themselves and some related problems, e.g. Bernoulli convolutions, and on applications to equidistribution on tori. Our approach combines tools from ergodic theory, geometric measure theory and additive combinatorics, building on recent progress in these fields and recent partial results towards the main conjectures. Dziedzina nauki natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics 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-SG-PE1 - ERC Starting Grant - Mathematical foundations Zaproszenie do składania wniosków ERC-2012-StG_20111012 Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-SG - ERC Starting Grant Instytucja przyjmująca THE HEBREW UNIVERSITY OF JERUSALEM Wkład UE € 1 107 000,00 Adres EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Izrael Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Hani Ben-Yehuda (Ms.) Kierownik naukowy Michael Hochman (Dr.) 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 THE HEBREW UNIVERSITY OF JERUSALEM Izrael Wkład UE € 1 107 000,00 Adres EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Hani Ben-Yehuda (Ms.) Kierownik naukowy Michael Hochman (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych
