Objective
The goal of this project is to study random walks on groups, with the focus on boundary theory. We plan to establish new criteria for estimates of the entropy and Poisson-Furstenberg boundary triviality and apply this method to study the following question: which groups admit simple random walks with trivial boundary? In particular, we want to produce a classification for classes of
solvable groups, more generally elementary amenable groups, and groups acting on rooted trees. We plan to make a contibution in the solution of the conjecture of Vershik and Kaimanovich, posed in the early eighties, that states that any group of exponential growth admits a symmetric measure with non-trivial boundary. We plan to study applications of random walks to growth of groups. In my previous work I have produced a method to use boundaries in order to obtain new low estimates for groups of Grigorchuk of intermediate growth. We plan to construct new classes of groups of intermediate growth, and to refine the existing method to obtain sharp bounds of the growth function. We also want to address Grigorchuk's conjecture about the gap in the range of possible growth functions of groups. Further applications include large scale geometrical properties of amenable groups, including amenable groups acting on rooted trees, as well as groups of orientation preserving diffeomorphisms of the interval, in particular, Richard Thompson group F
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2010-StG_20091028
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Host institution
75794 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.