Objective
The project is in model theory (mathematical logic), which concerns the expressibility in logical languages of properties of mathematical structures (e.g. graphs, groups, rings). Model theory aims to identify borders between `tame' and `wild' objects in mathematics, and to pin down abstract notions of independence and dimension and understand the geometry of `definable sets' in a structure, often with wide-ranging applications. This project focusses on classes of finite structures (e.g. the class of all finite fields), and on the `ultraproduct' construction which converts a class of finite structures to an infinite `pseudofinite' structure' which inherits properties of the class and is amenable to model-theoretic methods, with applications for the finite structures. Key objectives include:
(i) proving a trichotomy for pseudofinite geometries -- they should be `trivial', `group-like', or `field-like';
(ii) developing current concepts from abstract model theory for pseudofinite structures;
(iii) identifying first order properties of pseudofinite groups, and constraints on their possible quotients;
(iv) finding links between the model-theoretic `independence theorem', Gowers' notion of `quasi-random groups', and the Szemeredi regularity theorem in graph theory.
(v) model theory of finite ordered structures, and links to finite model theory.
To support his future academic research career, the Fellow, Garcia, will receive training through research in the model theory groups in Leeds and (through a secondment) Lyon. There will be knowledge transfer to Garcia of expertise in model-theoretic algebra of Leeds and Lyon, and Garcia will also build knowledge of finite model theory and its computer science applications. He will receive complementary training in many research skills (including outreach), and will transfer to Leeds expertise he has gained in the excellent model theory groups in Berkeley and Bogota, while deepening EU-Colombia mathematics links.
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 geometry
- natural sciences mathematics pure mathematics discrete mathematics graph theory
- 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.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF-EF-ST - Standard EF
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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) H2020-MSCA-IF-2014
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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.
LS2 9JT Leeds
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.