DIFFERENTIALGEOMETR

"Geometric analysis, complex geometry and gauge theory"

Coordinatore	IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	United Kingdom [UK]
Totale costo	1˙501˙361 €
EC contributo	1˙501˙361 €
Programma	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)
Code Call	ERC-2009-AdG
Funding Scheme	ERC-AG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-04-01   -   2015-03-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE  Organization address address: SOUTH KENSINGTON CAMPUS EXHIBITION ROAD city: LONDON postcode: SW7 2AZ contact info Titolo: Ms. Nome: Brooke Cognome: Alasya Email: send email Telefono: +44 207 594 1181 Fax: +44 207 594 1418	UK (LONDON)	hostInstitution	1˙501˙361.00
2	IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE  Organization address address: SOUTH KENSINGTON CAMPUS EXHIBITION ROAD city: LONDON postcode: SW7 2AZ contact info Titolo: Prof. Nome: Simon Kirwan Cognome: Donaldson Email: send email Telefono: +44 2075895111 Fax: +44 2075948483	UK (LONDON)	hostInstitution	1˙501˙361.00

Mappa

 Word cloud

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 Obiettivo del progetto (Objective)

'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.'