Objective
The ultimate goal of the project is the design of algorithmic criteria for the global integrability of physical field theories, which may later serve as the basis of new modelling and analysis technologies for industry. While the local integrability theory of partial differential equations is reasonably well understood and advanced mathematical techniques for its investigation exist, the study of global integrability has remained a challenging and highly risky task in mathematical physics for over a century. The proposed methodology combines hitherto unrelated results from various domains including algebraic topology, computer algebra, differential Galois theory, integrable systems and the formal theory of differential equations.
This approach originates in and relies on the complementary experiences of the partners in a research consortium newly formed specifically for this project. Recent advances in the mentioned domains and the inter-disciplinarity of the consortium let a real breakthrough in this old problem appear possible. Given the great importance of differential equations for the mathematical modelling in almost all sciences, such a breakthrough would lead to completely new possibilities in a wide range of fields spanning from fundamental physics over real-world engineering problems to social and economic sciences.
This includes the potential discovery of novel classes of topologically non-trivial solutions describing new physical phenomena, new approaches in non-linear stability and bifurcation theory or more powerful numerical methods rendering currently inaccessible problems tractable. The strong emphasis on algorithmic solutions will allow the later development of automatised toolboxes making sophisticated mathematical techniques avail able to industry.
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 mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences mathematics applied mathematics numerical analysis
- natural sciences mathematics applied mathematics mathematical model
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.
FP6-2003-NEST-A
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
KARLSRUHE
Germany
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.