Objective
"Metric spaces, such as graphs, occur everywhere in mathematics and are used to model real life situations: in computer science e.g. they are used to model computer networks and in sociology, graphs are used to model interhuman relations.
In order to study metric spaces, one can embed them into an object which one understands quite well. The information that we know on the latter object may then provide useful information on the embedded metric space. A Hilbert space is a well understood mathematical object which can be studied by algebraic techniques (it is a vector space, with an inner product), by analytic techniques (least square methods) and by many more tools.
Around the 1990s, Gromov introduced the notion of metric spaces that `embed uniformly' into a Hilbert space. This relatively weak condition turned out to be connected with some major conjectures: it implies the coarse Baum-Connes and Novikov conjecture in the case of finitely generated groups. The equivariant version of uniform embeddability is Haagerup's property, a property with clear connections to the Baum-Connes conjecture and a subject of intense study.
Guentner and Kaminker define the (equivariant) Hilbert space compression of a f.g. group as a number between 0 and 1 which quantifies how ""well"" the group embeds uniformly into a Hilbert space (is Haagerup respectively). Moreover, they showed that if the value of the (equivariant) compression is strictly greater than 1/2, then the group has Yu's property (A) (is amenable respectively). This shows that the compression notions contain important information on the group, making them very interesting to study.
This Marie Curie project fits in this setting. We intend to study compression through new techniques such as persistent cohomology, determine the relations between compression and related properties such as Property A and amenability and apply compression in an interdisciplinary setting by using it to study data 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 pure mathematics algebra linear algebra
- social sciences sociology
- natural sciences computer and information sciences
- engineering and technology electrical engineering, electronic engineering, information engineering information engineering telecommunications telecommunications networks
- 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.
FP7-PEOPLE-2011-IEF
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.
Coordinator
SO17 1BJ Southampton
United Kingdom
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.