Objetivo "The purpose of this project is to use the ubiquitous nature of certain combinatorial topological objects called maps in order to unveil deep connections between several areas of mathematics. Maps, that describe the embedding of a graph into a surface, appear in probability theory, mathematical physics, enumerative geometry or graph theory, and different combinatorial viewpoints on these objects have been developed in connection with each topic. The originality of our project will be to study these approaches together and to unify them.The outcome will be triple, as we will:1. build a new, well structured branch of combinatorics of which many existing results in different areas of enumerative and algebraic combinatorics are only first fruits;2. connect and unify several aspects of the domains related to it, most importantly between probability and integrable hierarchies thus proposing new directions, new tools and new results for each of them;3. export the tools of this unified framework to reach at new applications, especially in random graph theory and in a rising domain of algebraic combinatorics related to Tamari lattices.The methodology to reach the unification will be the study of some strategic interactions at different places involving topological expansions, that is to say, places where enumerative problems dealing with maps appear and their genus invariant plays a natural role, in particular: 1. the combinatorial theory of maps developped by the ""French school"" of combinatorics, and the study of random maps; 2. the combinatorics of Fermions underlying the theory of KP and 2-Toda hierarchies; 3; the Eynard-Orantin ``topological recursion'' coming from mathematical physics.We present some key set of tasks in view of relating these different topics together. The pertinence of the approach is demonstrated by recent research of the principal investigator." Ámbito científico natural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicsapplied mathematicsstatistics and probability Palabras clave Enumerative combinatorics Algebraic combinatorics combinatorial maps graphs on surfaces bijective combinatorics random discrete structures random graphs Brownian map scaling limits Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-2016-STG - ERC Starting Grant Convocatoria de propuestas ERC-2016-STG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-STG - Starting Grant Coordinador CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Aportación neta de la UEn € 1 045 625,00 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 Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 086 125,00 Beneficiarios (2) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Aportación neta de la UEn € 1 045 625,00 Dirección Rue michel ange 3 75794 Paris Ver en el mapa Región Ile-de-France Ile-de-France Paris Tipo de actividad Research Organisations Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 086 125,00 Tercero Entidad jurídica distinta de un subcontratista que está afiliada o vinculada jurídicamente con un participante. Dicha entidad lleva a cabo su trabajo en las condiciones establecidas en el acuerdo de subvención, proporciona bienes o presta servicios para la acción, pero no firma dicho acuerdo. El tercero acata las normas aplicables a su participante en virtud del acuerdo de subvención en lo que respecta a la subvencionalidad de los costes y el control de los gastos. ECOLE NORMALE SUPERIEURE DE LYON Francia Aportación neta de la UEn € 40 500,00 Dirección Parvis rene descartes 15 69342 Lyon Ver en el mapa Región Auvergne-Rhône-Alpes Rhône-Alpes Rhône Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 40 500,00