Objectif The goal of the project is to develop new techniques for estimation and evaluation of well-known asymptotic invariants of groups, including growth of groups, isoperimetric profiles, entropy and probability to return to the origin of random walks as well as of some more recent invariants related to the geometric criteria for construction of quotients of groups, which appeared in the joint work of PI with A.Karlsson (2010), and in a recent work of Ozawa (2015) giving a short functional analytic proof of the Polynomial Growth Theorem. We plan to work on the Gap conjecture of Grigorchuk, which states that any group of growth asymptotically strictly less than exp(n1/2) has polynomial growth, the question about the forms of Foelner sets in groups of intermediate and exponential growth and Kaimanovich and Vershik conjecture about characterisation of groups of exponential growth in terms of non-triviality of the Poisson boundary of some symmetric random walks. We plan to develop methods sharpening previous results of PI about isoperimetric inequalities for wreath products and relation between growth of groups and isoperimetry, and apply them for growth estimates and the description of the boundary. A further goal of the project is to introduce new constructions of non-elementary amenable groups which can show that necessary conditions in growth conjecture and isoperimetric inequalities cannot be weakened. Mots‑clés Growth of Groups Groups of Intermediate Growth Isoperimetric inequalities entropy random walks on groups Poisson boundary Grigorchuk conjecture Grigorchuk groups Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-COG - ERC Consolidator Grant Appel à propositions ERC-2016-COG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS Contribution nette de l'UE € 1 789 438,00 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 € 1 789 438,00 Bénéficiaires (1) 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 € 1 789 438,00 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 € 1 789 438,00
