Objective
The principal methods of model theory, in its connections to algebraic geometry, have been quantifier elimination (e.g. Tarski's theorem)
and structural stability (used here in a wide sense, including simplicity, NIP and structural o-minimality.)
We propose to move beyond current limitations on both fronts, by means of three interrelated projects. (1) A study of definable sets in global fields. A successful quantifier elimination result in this setting would extend the reach of model theory to wide areas of number theory and geometry that have not been accessible before, including points of small height in number theory, and the Gromov-Witten invariants of a variety in geometry. (2) A study of limits of o-minimal metric structures as quotients of non-archimedean structures, extending similar measure and group-theoretic work that has led to a resolution of Pillay's conjectures in the o-minimal setting, and leading towards a model theory of Calabi-Yau degenerations. (3) Model theoretic asymptotic limits lead to measure and dimension theories, with associated dependence theories, that resemble known structures from stability theory but do not lie within the stable realm or its current extensions. Preliminary stability-theoretic considerations have already led to significant applications in combinatorics. We propose creating a structural stability theory based on pseudo-finite dimension, expected to create a long-term bridge between model theory and
additive combinatorics.
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 discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
- natural sciences mathematics pure mathematics algebra algebraic 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-2011-ADG_20110209
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
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.