Obiettivo 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. Campo scientifico natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysisnatural sciencesmathematicsapplied mathematicsmathematical model Parole chiave Computer Algebra Constructive Methods Field Theory Global integrability Integrable System Programma(i) FP6-POLICIES - Policy support: Specific activities covering wider field of research under the Focusing and Integrating Community Research programme 2002-2006. Argomento(i) NEST-2003-1 - Adventure activities Invito a presentare proposte FP6-2003-NEST-A Vedi altri progetti per questo bando Meccanismo di finanziamento STREP - Specific Targeted Research Project Coordinatore UNIVERSITAET KARLSRUHE (TECHNISCHE HOCHSCHULE) Contributo UE Nessun dato Indirizzo Kaiserstrasse 12 KARLSRUHE Germania Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato Partecipanti (5) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto LANCASTER UNIVERSITY Regno Unito Contributo UE Nessun dato Indirizzo BAILRIGG LANCASTER Mostra sulla mappa Costo totale Nessun dato RUPRECHT-KARLS-UNIVERSITAET HEIDELBERG Germania Contributo UE Nessun dato Indirizzo Seminarstrasse 2 HEIDELBERG Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato UNIVERSITE JOSEPH FOURIER Francia Contributo UE Nessun dato Indirizzo Avenue Centrale 621, Campus Universitaire GRENOBLE Mostra sulla mappa Costo totale Nessun dato UNIVERSITE PAUL SABATIER-TOULOUSE III Francia Contributo UE Nessun dato Indirizzo Route de Narbonne, 118 TOULOUSE Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato VRIJE UNIVERSITEIT AMSTERDAM Paesi Bassi Contributo UE Nessun dato Indirizzo De Boelelaan 1105 AMSTERDAM Mostra sulla mappa Collegamenti Sito web Opens in new window Costo totale Nessun dato