Obiettivo Statistical physics is a theory allowing the derivation of the statistical behavior of macroscopic systems from the description of the interactions of their microscopic constituents. For more than a century, lattice models (i.e. random systems defined on lattices) have been introduced as discrete models describing the phase transition for a large variety of phenomena, ranging from ferroelectrics to lattice gas.In the last decades, our understanding of percolation and the Ising model, two classical exam- ples of lattice models, progressed greatly. Nonetheless, major questions remain open on these two models.The goal of this project is to break new grounds in the understanding of phase transition in statistical physics by using and aggregating in a pioneering way multiple techniques from proba- bility, combinatorics, analysis and integrable systems. In this project, we will focus on three main goals:Objective A Provide a solid mathematical framework for the study of universality for Bernoulli percolation and the Ising model in two dimensions.Objective B Advance in the understanding of the critical behavior of Bernoulli percolation and the Ising model in dimensions larger or equal to 3.Objective C Greatly improve the understanding of planar lattice models obtained by general- izations of percolation and the Ising model, through the design of an innovative mathematical theory of phase transition dedicated to graphical representations of classical lattice models, such as Fortuin-Kasteleyn percolation, Ashkin-Teller models and Loop models.Most of the questions that we propose to tackle are notoriously difficult open problems. We believe that breakthroughs in these fundamental questions would reshape significantly our math- ematical understanding of phase transition. Campo scientifico natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Parole chiave Statistical Physics Phase transition percolation theory Ising model Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-2017-STG - ERC Starting Grant Invito a presentare proposte ERC-2017-STG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-STG - Starting Grant Istituzione ospitante INSTITUT DES HAUTES ETUDES SCIENTIFIQUES Contribution nette de l'UE € 1 301 459,31 Indirizzo ROUTE DE CHARTRES 35 91440 Bures Sur Yvette Francia Mostra sulla mappa PMI L’organizzazione si è definita una PMI (piccola e media impresa) al momento della firma dell’accordo di sovvenzione. Sì Regione Ile-de-France Ile-de-France Essonne 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 € 1 301 459,31 Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto INSTITUT DES HAUTES ETUDES SCIENTIFIQUES Francia Contribution nette de l'UE € 1 301 459,31 Indirizzo ROUTE DE CHARTRES 35 91440 Bures Sur Yvette Mostra sulla mappa PMI L’organizzazione si è definita una PMI (piccola e media impresa) al momento della firma dell’accordo di sovvenzione. Sì Regione Ile-de-France Ile-de-France Essonne 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 € 1 301 459,31 UNIVERSITE DE GENEVE Svizzera Contribution nette de l'UE € 198 452,69 Indirizzo RUE DU GENERAL DUFOUR 24 1211 Geneve Mostra sulla mappa Regione Schweiz/Suisse/Svizzera Région lémanique Genève Tipo di attività Higher or Secondary Education Establishments 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 € 198 452,69
