Cel Our proposed research lies at the interface of Geometry, Group Theory, Number Theory and Combinatorics. In recent years, striking results were obtained in those disciplines with the help of a surprise newcomer at the border between mathematics and logic: Model Theory. Bringing its unique point of view and its powerful formalism, Model Theory made a resounding entry into several different fields of mathematics. Here shedding new light on a classical phenomenon, there solving a long-standing open problem via a completely new method.Recent examples of concrete mathematical problems where Model Theory interacted in a fruitful manner abound: the local version of Hilbert's 5th problem by Goldbring and van den Dries, Szemeredi's theorems in combinatorics and graph theory, the André-Oort conjecture in diophantine geometry (Pila, Wilkie, Zannier), etc. In this vein, and building on Hrushovski's model-theoretic work, Green, Tao and myself recently settled a conjecture of Lindenstrauss pertaining to the structure of approximate groups.Our plan in this project is to put these methods into further use, to collaborate with model theorists, and to start looking through this prism at a small collection of familiar problems coming from combinatorics, group theory, analysis and spectral geometry of metric spaces, or from arithmetic geometry. Among them: extend our study of approximate groups to the general setting of locally compact groups, obtain uniform estimates on the spectrum of Cayley graphs of large finite groups, prove an analogue for character varieties of the Pink-Zilber conjectures in relation with rigidity theory for discrete subgroups of Lie groups, and clarify the links between uniform spectral gaps and height lower bounds in diophantine geometry with a view towards Lehmer's conjecture. Dziedzina nauki natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry 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-CG-2013-PE1 - ERC Consolidator Grant - Mathematics Zaproszenie do składania wniosków ERC-2013-CoG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-CG - ERC Consolidator Grants Instytucja przyjmująca Westfälische Wilhelms-Universität Münster Wkład UE € 957 390,00 Adres SCHLOSSPLATZ 2 48149 MUENSTER Niemcy Zobacz na mapie Region Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Emmanuel, François, Jean Breuillard (Prof.) Kontakt administracyjny Katharina Steinberg (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych Beneficjenci (2) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko Westfälische Wilhelms-Universität Münster Niemcy Wkład UE € 957 390,00 Adres SCHLOSSPLATZ 2 48149 MUENSTER Zobacz na mapie Region Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Rodzaj działalności Higher or Secondary Education Establishments Kierownik naukowy Emmanuel, François, Jean Breuillard (Prof.) Kontakt administracyjny Katharina Steinberg (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych UNIVERSITE PARIS-SUD Francja Wkład UE € 326 610,00 Adres RUE GEORGES CLEMENCEAU 15 91405 ORSAY CEDEX Zobacz na mapie Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Nicolas Lecompte (Mr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych
