Objetivo 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. Ámbito científico natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programa(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) Tema(s) ERC-CG-2013-PE1 - ERC Consolidator Grant - Mathematics Convocatoria de propuestas ERC-2013-CoG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-CG - ERC Consolidator Grants Institución de acogida Westfälische Wilhelms-Universität Münster Aportación de la UE € 957 390,00 Dirección SCHLOSSPLATZ 2 48149 MUENSTER Alemania Ver en el mapa Región Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Investigador principal Emmanuel, François, Jean Breuillard (Prof.) Contacto administrativo Katharina Steinberg (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (2) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo Westfälische Wilhelms-Universität Münster Alemania Aportación de la UE € 957 390,00 Dirección SCHLOSSPLATZ 2 48149 MUENSTER Ver en el mapa Región Nordrhein-Westfalen Münster Münster, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Investigador principal Emmanuel, François, Jean Breuillard (Prof.) Contacto administrativo Katharina Steinberg (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos UNIVERSITE PARIS-SUD Francia Aportación de la UE € 326 610,00 Dirección RUE GEORGES CLEMENCEAU 15 91405 ORSAY CEDEX Ver en el mapa Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Nicolas Lecompte (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
