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Séminaire de Mathématique

Unique continuation of waves on asymptotically Anti-de Sitter spacetimes

by Prof. Arick SHAO (London)

lundi 3 juillet 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Séminaire de Relativité Générale Mathématique


In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Anti-de Sitter (AdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate such a correspondence statement as a unique continuation problem for PDEs: Is an asymptotically AdS solution of the Einstein equations uniquely determined by its data on its conformal boundary at infinity? In this presentation, we establish a key step: we prove such a unique continuation result for wave equations on fixed asymptotically AdS spacetimes. In particular, we highlight the analytic and geometric features of AdS spacetime which enable this uniqueness result, as well as obstacles preventing such a result from holding in other cases. If time permits, we will also discuss some applications of this result toward symmetry extension and rigidity theorems.
Organisé par S. Klainerman (Princeton University & IHES), P. G. LeFloch (LJLL, Paris), J. Smulevici (Université Paris-Sud) et J. Szeftel (LJLL, Paris)
Contact Email: cecile@ihes.fr