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GroIsRan SIGNED

Growth, Isoperimetry and Random walks on Groups

Total Cost €

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EC-Contrib. €

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Partnership

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Project "GroIsRan" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙789˙438 €
 EC max contribution 1˙789˙438 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-COG
 Funding Scheme ERC-COG
 Starting year 2017
 Duration (year-month-day) from 2017-09-01   to  2022-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙789˙438.00

Map

 Project objective

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.

 Publications

year authors and title journal last update
List of publications.
2017 Anna Erschler, Tianyi Zheng
Isoperimetric inequalities, shapes of Følner sets and groups with Shalom\'s property HFD
published pages: , ISSN: , DOI:
to appear in Annales de l\'Institut Fourier 2019-06-06
2018 Anna Erschler, Tianyi Zheng
Growth of periodic Grigorchuk groups
published pages: , ISSN: , DOI:
2019-06-06
2017 Johannes Cuno, Ecaterina Sava-Huss
Random walks on Baumslag-Solitar groups
published pages: , ISSN: , DOI:
2019-06-06
2019 Anna Erschler, Vadim Kaimanovich
Arboreal structures on groups and the associated boundaries
published pages: , ISSN: , DOI:
2019-06-06
2018 Markus Steenbock, Thomas Delzant
Product set growth in groups and hyperbolic geometry
published pages: , ISSN: , DOI:
2019-06-06
2018 Yanis Amirou
ELEMENTS OF UNIFORMLY BOUNDED WORD-LENGTH IN GROUPS
published pages: , ISSN: , DOI:
2019-06-06
2019 Anna Erschler
Almost invariance of distributions for random walks on groups
published pages: , ISSN: , DOI:
to appear in Probability Theory and related fields 2019-06-06
2019 Anna Erschler, Alexei Kanel Belov
No iterated identities satisfied by all finite groups
published pages: , ISSN: , DOI:
to appear in Israel Journal of Mathematics 2019-06-06
2018 Bogdan Stankov
Non-triviality of the Poisson boundary of random walks on the group H(ℤ) of Monod
published pages: , ISSN: , DOI:
2019-06-06
2018 Johannes Cuno, Gerald Williams
A class of generalized graph groups defined by balanced presentations
published pages: , ISSN: , DOI:
2019-06-06

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