Objective
The research proposal concerns nonlinear Galois theory and applications to study of continuous and discrete dynamical systems. Recently, two theories were proposed by H. Umemura (with an algebraic and arithmetical flavour) and B.Malgrange (with a geometrical and dynamical flavour).
The purpose of this proposal is to:
- develop the theory of Lie groupoid using fruitful interrelations between the formal theory of partial differential equations and differential algebra,
- apply Galois theory to irreducibility problems, especially for Painleve equations and Garnier systems,
- unify integrability notions of both continuous and discrete dynamical systems using differential Galois theory and to give integrability and non integrability criteria for hamiltonian systems,
- study analytic and algebraic geometry of holomorphic singular foliations with a view toward deformations of geometric structures,
-give a Tannakian unification of these two theory.
This will provide numbers of new relations between arithmetic and dynamic.
This research is important to set up a complete differential Galois theory as important as the classical one. The numbers of applications and used tools give a concrete view of the transversal and interdisciplinary nature of the proposal. Research methodology contains regular discussion sessions with the scientific in charge and other local mathematicians and intermediate goals leading to the objectives. Scientific credibility and feasibility of the project is increase by many examples already computed and numerous discussions with international level mathematicians.
Practical arrangements for the management of the project include organisation of a work shop on differential Galois theory at the end of the first year, invitation of international level mathematicians. Algebraic and geometric studies of differential equations are fields in which Europe and Japan excel. This project contributes to the enhancement of European scientific excellence.
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 dynamical systems
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences mathematics pure mathematics algebra algebraic geometry
You need to log in or register to use this function
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.
FP6-2004-MOBILITY-5
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
BELLATERRA (CERDANYOLA DEL VALL
Spain
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.