Objective
"In recent years, the importance of superimposing the contribution of the measure to that of the metric, in determining the underlying space's (generalized Ricci) curvature, has been clarified in the works of Lott, Sturm, Villani and others, following the definition of Curvature-Dimension introduced by Bakry and Emery. We wish to systematically incorporate
this important idea of considering the measure and metric in tandem, in the study of questions pertaining to isoperimetric and concentration properties of convex domains in high-dimensional Euclidean space, where a-priori there is only a trivial metric (Euclidean) and trivial measure (Lebesgue).
The first step of enriching the class of uniform measures on convex domains to that of non-negatively curved (""log-concave"") measures in Euclidean space has been very successfully implemented in the last decades, leading to substantial progress in our understanding of volumetric properties of convex domains, mostly regarding concentration of linear functionals. However, the potential advantages of altering the Euclidean metric into a more general Riemannian one or exploiting related Riemannian structures have not been systematically explored. Our main paradigm is that in order to progress in non-linear questions pertaining to concentration in Euclidean space, it is imperative to cast and study these problems in the more general Riemannian context.
As witnessed by our own work over the last years, we expect that broadening the scope and incorporating tools from the Riemannian world will lead to significant progress in our understanding of the qualitative and quantitative structure of isoperimetric minimizers in the purely Euclidean setting. Such progress would have dramatic impact on long-standing fundamental conjectures regarding concentration of measure on high-dimensional convex domains, as well as other closely related fields such as Probability Theory, Learning Theory, Random Matrix Theory and Algorithmic Geometry."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics applied mathematics statistics and probability
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
ERC-STG - Starting Grant
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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.
(opens in new window) ERC-2014-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
32000 Haifa
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.