Objetivo 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. Ámbito científico natural sciencesphysical sciencesrelativistic mechanicsnatural sciencesphysical sciencestheoretical physicsstring theorynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programa(s) 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) Tema(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Convocatoria de propuestas ERC-2009-AdG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-AG - ERC Advanced Grant Institución de acogida IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Aportación de la UE € 1 501 361,00 Dirección SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Reino Unido Ver en el mapa Región London Inner London — West Westminster Tipo de actividad Higher or Secondary Education Establishments Investigador principal Simon Kirwan Donaldson (Prof.) Contacto administrativo Brooke Alasya (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE Reino Unido Aportación de la UE € 1 501 361,00 Dirección SOUTH KENSINGTON CAMPUS EXHIBITION ROAD SW7 2AZ LONDON Ver en el mapa Región London Inner London — West Westminster Tipo de actividad Higher or Secondary Education Establishments Investigador principal Simon Kirwan Donaldson (Prof.) Contacto administrativo Brooke Alasya (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
