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Zawartość zarchiwizowana w dniu 2024-06-18

Geometric analysis, complex geometry and gauge theory

Cel

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.

Zaproszenie do składania wniosków

ERC-2009-AdG
Zobacz inne projekty w ramach tego zaproszenia

System finansowania

ERC-AG - ERC Advanced Grant

Instytucja przyjmująca

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Wkład UE
€ 1 501 361,00
Adres
SOUTH KENSINGTON CAMPUS EXHIBITION ROAD
SW7 2AZ LONDON
Zjednoczone Królestwo

Zobacz na mapie

Region
London Inner London — West Westminster
Rodzaj działalności
Higher or Secondary Education Establishments
Kierownik naukowy
Simon Kirwan Donaldson (Prof.)
Kontakt administracyjny
Brooke Alasya (Ms.)
Linki
Koszt całkowity
Brak danych

Beneficjenci (1)