Innovating Works

GroIsRan

Financiado
Growth Isoperimetry and Random walks on Groups
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... 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. ver más
31/08/2023
CNRS
2M€
Duración del proyecto: 78 meses Fecha Inicio: 2017-02-28
Fecha Fin: 2023-08-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2023-08-31
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2016-COG: ERC Consolidator Grant
Cerrada hace 8 años
Presupuesto El presupuesto total del proyecto asciende a 2M€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5