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SUMMARY:Unique continuation of waves on asymptotically Anti-de Sitter spac
etimes
DTSTART;VALUE=DATE-TIME:20170703T133000Z
DTEND;VALUE=DATE-TIME:20170703T143000Z
DTSTAMP;VALUE=DATE-TIME:20210413T103703Z
UID:indico-event-2400@indico.math.cnrs.fr
DESCRIPTION:Séminaire de Relativité Générale Mathématique\n\n \n\n\n
In theoretical physics\, it is often conjectured that a correspondence exi
sts between the gravitational dynamics of asymptotically Anti-de Sitter (A
dS) spacetimes and a conformal field theory of their boundaries. In the co
ntext of classical relativity\, one can attempt to rigorously formulate su
ch a correspondence statement as a unique continuation problem for PDEs: I
s an asymptotically AdS solution of the Einstein equations uniquely determ
ined by its data on its conformal boundary at infinity? In this presentati
on\, we establish a key step: we prove such a unique continuation result f
or wave equations on fixed asymptotically AdS spacetimes. In particular\,
we highlight the analytic and geometric features of AdS spacetime which en
able this uniqueness result\, as well as obstacles preventing such a resul
t from holding in other cases. If time permits\, we will also discuss some
applications of this result toward symmetry extension and rigidity theore
ms.\n\n\nhttps://indico.math.cnrs.fr/event/2400/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2400/
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