Objective
The project consists of three distinct parts, on which the applicant will work in parallel.
Part 1 : We intend to work on analogues of Hilbert's tenth problem for various function rings, such as the rings of analytic functions and the fields of meromorphic functions on subsets of both the p-adicand the complex plane (for example on the unit discs). At a first stage we intend to develop new techniques in order to create new tools for the study of this kind of problems. The techniques that we have in mind relate to characterizing maps from (sufficiently large subsets of) algebraic curves (over the complex numbers) to elliptic surfaces.
Part 2: We will study the decidability problem for a field of power series in positive characteristic, in the language of addition, divisibility and the Frobenious map, and some variants. We expect to apply the results to problems rising in number theory.
Part 3: We will study a problem which has standed for a long time: what the elementary classes of function fields are. The field of complex rational functions is one of them. Despite various recent progresses towards a general answer to this question, some cases remain with no complete answer. This part of the project deals with the case of some elliptic fields with complex multiplication. The underlying theme of all the parts of the project is the connection of model theoretic notions to algebraic properties of various domains of interest in algebra, algebraic geometry and number theory .In recent years mathematical logic has been used increasingly for applications in other domains of mathematics, such as algebraic geometry. Also, knowledge in many domains, such as algebra, algebraic geometry, analysis, p-adic analysis and number theory, is a prerequisite in order to solve problems of interest in model theory. For example, the use of the theory of algebraic surfaces in order to solve some analogue of Hilbert's tenth problem will increase the ability of the applicant to make both fields interact. It will be an asset for his further research opportunities. Also the study of p-adic cases will strengthen the interaction that already exists intrinsically between Hilbert's tenth problem and number theory. Due to the large range of its research subjects, Oxford university would be an ideal place to carry out such a multi-disciplinary project. The expected impact for the host is to have some (probably young) researchers become interested and work on various aspects of the problems of the project, and thus to promote the interaction of ideas through discussions and seminars.
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 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.
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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.
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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
OX1 3LB OXFORD
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.