Objective
We propose to study the fractal geometry of invariant sets for endomorphisms of compact abelian groups, specifically a family of conjectures by Furstenberg on the dimensions of orbit closures under such dynamics, and on the size of sums and intersections of invariant sets. These conjectures are related to problems on expansion in integer bases, in Diophantine approximation, measure rigidity, analysis and equidistribution. The project focuses on the conjectures themselves and some related problems, e.g. Bernoulli convolutions, and on applications to equidistribution on tori. Our approach combines tools from ergodic theory, geometric measure theory and additive combinatorics, building on recent progress in these fields and recent partial results towards the main conjectures.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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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-2012-StG_20111012
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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
91904 JERUSALEM
Israel
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.