Obiettivo The proposal is for work in Geometric Analysis aimed at two different problems. One is to establish necessary and sufficient conditions for the existence of extremal metrics on complex algebraic manifolds. These metrics are characterised by conditions on their curvature tensor a paradigm being the Riemannian version of the Einstein equation of General Relativity The standard conjecture is that the right condition should be the stability of the manifold, a condition defined entirely in the language of algebraic geometry. But there are very few cases where this conjecture has been verified. The problem comes down to proving the existence of a solution to highly nonlinear partial differential equation. The aim is to advance this theory by a detailed study of interesting but more amenable cases, for example where there is a large symmetry group. The second problem is to develop new invariants and structures associated to a particular class of manifolds of dimension 6 and 7 (with holonomy SU(3) and G2). These would be derived from the solutions of versions of the Yang-Mills equation over the manifolds, in a similar manner to familiar theories in 3 and 4 dimensions. In higher dimensions there are fundamental new difficulties to overcome to set up a theory rigorously and the main point of this part of the proposal is to attack these. It is likely that the new structures, if they do exist, will have interesting connections to other developments in this general area, involving string theory and algebraic geometry. Campo scientifico natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Invito a presentare proposte ERC-2009-AdG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-AG - ERC Advanced Grant Istituzione ospitante IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Contributo UE € 1 501 361,00 Indirizzo SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Regno Unito Mostra sulla mappa Regione London Inner London — West Westminster Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Simon Kirwan Donaldson (Prof.) Contatto amministrativo Brooke Alasya (Ms.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Regno Unito Contributo UE € 1 501 361,00 Indirizzo SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Mostra sulla mappa Regione London Inner London — West Westminster Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Simon Kirwan Donaldson (Prof.) Contatto amministrativo Brooke Alasya (Ms.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
