Objectif 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. Champ scientifique natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) 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) Thème(s) ERC-CG-2013-PE1 - ERC Consolidator Grant - Mathematics Appel à propositions ERC-2013-CoG Voir d’autres projets de cet appel Régime de financement ERC-CG - ERC Consolidator Grants Institution d’accueil Westfälische Wilhelms-Universität Münster Contribution de l’UE € 957 390,00 Adresse SCHLOSSPLATZ 2 48149 MUENSTER Allemagne Voir sur la carte Région Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Type d’activité Higher or Secondary Education Establishments Chercheur principal Emmanuel, François, Jean Breuillard (Prof.) Contact administratif Katharina Steinberg (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (2) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire Westfälische Wilhelms-Universität Münster Allemagne Contribution de l’UE € 957 390,00 Adresse SCHLOSSPLATZ 2 48149 MUENSTER Voir sur la carte Région Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Type d’activité Higher or Secondary Education Establishments Chercheur principal Emmanuel, François, Jean Breuillard (Prof.) Contact administratif Katharina Steinberg (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée UNIVERSITE PARIS-SUD France Contribution de l’UE € 326 610,00 Adresse RUE GEORGES CLEMENCEAU 15 91405 ORSAY CEDEX Voir sur la carte Type d’activité Higher or Secondary Education Establishments Contact administratif Nicolas Lecompte (Mr.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée