Obiettivo "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." Campo scientifico natural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicsapplied mathematicsstatistics and probability Parole chiave Enumerative combinatorics Algebraic combinatorics combinatorial maps graphs on surfaces bijective combinatorics random discrete structures random graphs Brownian map scaling limits Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-2016-STG - ERC Starting Grant Invito a presentare proposte ERC-2016-STG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-STG - Starting Grant Coordinatore CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 1 045 625,00 Indirizzo Rue michel ange 3 75794 Paris Francia Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 086 125,00 Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Francia Contribution nette de l'UE € 1 045 625,00 Indirizzo Rue michel ange 3 75794 Paris Mostra sulla mappa Regione Ile-de-France Ile-de-France Paris Tipo di attività Research Organisations Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 086 125,00 Terza parte Soggetto giuridico diverso da un subappaltatore che è affiliato o legalmente collegato a un partecipante. Il soggetto svolge le attività secondo le condizioni stabilite nell’accordo di sovvenzione, fornisce beni o servizi per l’azione, ma non ha sottoscritto l’accordo di sovvenzione. Una terza parte rispetta le regole applicabili al suo partecipante correlato ai sensi dell’accordo di sovvenzione per quanto riguarda l’ammissibilità dei costi e il controllo delle spese. ECOLE NORMALE SUPERIEURE DE LYON Francia Contribution nette de l'UE € 40 500,00 Indirizzo Parvis rene descartes 15 69342 Lyon Mostra sulla mappa Regione Auvergne-Rhône-Alpes Rhône-Alpes Rhône Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 40 500,00