Objective
High-dimensional problems with a geometric flavor appear in quite a few branches of mathematics, mathematical physics and theoretical computer science. A priori, one would think that the diversity and the rapid increase of the number of configurations would make it impossible to formulate general, interesting theorems that apply to large classes of high-dimensional geometric objects. The underlying theme of the proposed project is that the contrary is often true. Mathematical developments of the last decades indicate that high dimensionality, when viewed correctly, may create remarkable order and simplicity, rather than complication. For example, Dvoretzky's theorem demonstrates that any high-dimensional convex body has nearly-Euclidean sections of a high dimension. Another example is the central limit theorem for convex bodies due to the PI, according to which any high-dimensional convex body has approximately Gaussian marginals. There are a number of strong motifs in high-dimensional geometry, such as the concentration of measure, which seem to compensate for the vast amount of different possibilities. Convexity is one of the ways in which to harness these motifs and thereby formulate clean, non-trivial theorems. The scientific goals of the project are to develop new methods for the study of convexity in high dimensions beyond the concentration of measure, to explore emerging connections with other fields of mathematics, and to solve the outstanding problems related to the distribution of volume in high-dimensional convex sets.
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 applied mathematics mathematical physics
- natural sciences computer and information sciences computational science
- natural sciences mathematics pure mathematics geometry
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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
See other projects for this call
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
7610001 Rehovot
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.