Objectif "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." Champ scientifique natural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicsapplied mathematicsstatistics and probability Mots‑clés Enumerative combinatorics Algebraic combinatorics combinatorial maps graphs on surfaces bijective combinatorics random discrete structures random graphs Brownian map scaling limits Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-STG - ERC Starting Grant Appel à propositions ERC-2016-STG Voir d’autres projets de cet appel Régime de financement ERC-STG - Starting Grant Institution d’accueil CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 1 045 625,00 Adresse RUE MICHEL ANGE 3 75794 Paris France Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 086 125,00 Bénéficiaires (2) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS France Contribution nette de l'UE € 1 045 625,00 Adresse RUE MICHEL ANGE 3 75794 Paris Voir sur la carte Région Ile-de-France Ile-de-France Paris Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 086 125,00 Tiers Entité juridique autre qu’un sous-traitant qui est affiliée ou juridiquement liée à un participant. L’entité réalise des travaux dans les conditions prévues par la convention de subvention, fournit des biens ou des services pour l’action, mais n’a pas signé la convention de subvention. Le tiers respecte les règles applicables au participant qui lui est lié dans le cadre de la convention de subvention en ce qui concerne l’éligibilité des coûts et le contrôle des dépenses. ECOLE NORMALE SUPERIEURE DE LYON France Contribution nette de l'UE € 40 500,00 Adresse PARVIS RENE DESCARTES 15 69342 Lyon Voir sur la carte Région Auvergne-Rhône-Alpes Rhône-Alpes Rhône Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 40 500,00