Objetivo "Complex geometry is the study of manifolds that are defined over the complex numbers. Non-archimedean geometry is concerned with analytic spaces overfields endowed with a norm that satisfies the strong triangular inequality.The aim of this proposal is to explore the interactions between these seemingly different geometrieswith special emphasis on analytic and dynamical problems.We specifically plan to develop pluripotential theory over non-archimedean fields. This includes the search for analogs of the celebrated Yau's theorem. In a more local setting, we shall also look for possible applications of non-archimedean techniques to the ""Openness Conjecture"" on the structure of singularities of plurisubharmonic functions.A second axis of research concerns the problem of growth of degrees of iterates of complex rational maps in arbitrary dimensions. We especially aim at extending to arbitrary dimensions the successful non-archimedean techniques that are already available for surfaces.Finally we want to investigate the geometry of parameter spaces of complex dynamical systemsacting on the Riemann sphere using non-archimedean methods. This requires the development of the bifurcation theory of non-archimedean rational maps." Ámbito científico natural sciencesmathematicsapplied mathematicsdynamical systemsnatural sciencesmathematicspure mathematicsgeometry 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-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2012-StG_20111012 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Aportación de la UE € 787 232,52 Dirección RUE MICHEL ANGE 3 75794 Paris Francia Ver en el mapa Región Ile-de-France Ile-de-France Paris Tipo de actividad Research Organisations Investigador principal Charles Favre (Mr.) Contacto administrativo Bertrand Minault (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Aportación de la UE € 787 232,52 Dirección RUE MICHEL ANGE 3 75794 Paris Ver en el mapa Región Ile-de-France Ile-de-France Paris Tipo de actividad Research Organisations Investigador principal Charles Favre (Mr.) Contacto administrativo Bertrand Minault (Mr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos