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- Date de réalisation : 1 Juillet 2014
- Durée du programme : 62 min
- Classification Dewey : Mathématiques
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- Catégorie : Conférences
- Niveau : niveau Doctorat (LMD), Recherche
- Disciplines : Mathématiques et physique
- Collections : Ecoles d'été, 2014
- ficheLom : Voir la fiche LOM
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- Réalisateur(s) : Bastien Fanny
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- Langue : Anglais
- Mots-clés : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
- Conditions d’utilisation / Copyright : CC BY-NC-ND 4.0
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Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories ``at infinity'', to the asymptotic phenomena of an interior (pseudo-‐)-‐Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. I will describe how the notion of conformal compactification can be linked to Cartan holonomy reduction. This leads to a conceptual way to define other notions of geometric compactification. The idea will be taken up, in particular, for the case of compactifying pseudo-‐ Riemannian manifolds using projective geometry. A new characterisation of projectively compact metrics will be given, and some results on their asymptotics near the conformal infinity. This is joint work with Andreas Cap.
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