Mathematical issues in AdS/CFT
Monday 3rd October 2005
|10:00 to 11:00||
CR Graham ([Washington])
Dirichlet-to-Neumann map for Poincare-Einstein metrics
An analogue of a Dirichlet-to-Neumann map for asymptotically hyperbolic Einstein metrics will be discussed. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the analysis of self-dual Poincare-Einstein metrics.
|11:30 to 12:30||
M Singer ([Edinburgh])
Toric Poincare-Einstein metrics
|14:30 to 15:30||
P Albin ([MIT])
The Gauss-Bonnet theorem for Poincare-Einstein metrics
A useful tool in the study of the AdS/CFT correspondence is the renormalized volume. For four dimensional Poincare-Einstein manifolds, a theorem of Mike Anderson relates the renormalized volume and the Euler characteristic of the underlying manifold with boundary. We will discuss the extension of the renormalization procedure to curvature integrals on these manifolds and the proof of the corresponding Gauss-Bonnet theorem in all even dimensions.
|16:00 to 17:00||
K Skenderis ([Amsterdam])
Conserved charges and positivity of energy for asymptotically locally AdS spacetimes