10:00 to 11:00 Global convergence of the Yamabe flow INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Rough initial data The story of constant mean curvature $H^s$ solutions of the constraint equations with $s>3/2$ has largely been completed, both for asymptotically Euclidean and compact manifolds. It turns out that the standard existence results for smooth solutions extend fully and naturally to the low regularity setting. In this talk I will describe how these results were obtained. One point of interest, even for smooth solutions, is that the rough theory leads to a unified and simpler approach for working with the various cases of the CMC conformal method on compact manifolds. INI 1 12:30 to 13:30 Lunch at Wolfson Court 18:30 to 19:45 Dinner at Wolfson Court (Residents only)
 10:00 to 11:00 GJ Galloway ([Miami])Rigidity and positivity of mass for asymptotically hyperbolic manifolds We discuss an approach to the proof of positivity of mass without spin assumption, for asymptotically hyperbolic Riemannian manifolds, based on the general methodology of Schoen and Yau. Our approach makes use of the "BPS brane action" introduced by Witten and Yau in their work on the AdS/CFT correspondence, and takes hints from work of Lohkamp. This is joint work with Lars Andersson and Mingliang Cai. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 On problems related to Bartnik's definition of quasi-local mass (sponsored by CQG) INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:30 to 15:00 Positive energy theorem for asymptotically hyperbolic manifolds General Relativity is a geometrical theory of gravity which asserts that the geometry of space-time is closely related to matter. There exists some consistent definition for total energy (and momentum) of isolated systems which by definition are manifolds whose metric approaches a background metric (Euclidean or hyperbolic). The positive mass theorem can be considered as attempts at understanding the relationship between the local energy density (namely the stress-energy tensor) and the total energy of a space-time. On one hand P. T. Chrusciel and G. Nagy rigorously defined in a recent work notions of mass and momentum for manifolds which are asymptotic to a standard hyperbolic slice of Minkowski space-time. On the other hand P. T. Chrusciel and M. Herzlich proved a positive mass theorem for Riemannian asymptotically hyperbolic manifolds. My work extends this result for orientable 3-dimensional manifolds which are asymptotic to a standard hyperbolic slice of anti-de Sitter space-time in the following way: we define a sesquilinear form Q which is closely related to the energy-momentum and prove, under the relevant energy condition, that Q is a nonnegative Hermitian form which is in fact definite unless our manifold is isometrically embeddable in anti-de Sitter. INI 1 15:00 to 15:30 N O'Murchadha ([University College, Cork])Why we should not take the Liu-Yau quasi-local mass seriously The Liu-Yau mass is a true mass, it is frame independent. However, the Liu-Yau mass is bigger than the Brown-York energy on any surface for which both can be defined. Further, if I take a sequence of coordinate spheres' on any spacelike slice, both the Liu-Yau mass and the Brown-York energy asymptote to the ADM mass (which is really an energy, the 0'-th component of a Lorentz covariant 4-vector). This means that in any asymptotically flat spacetime, I can find a 2-surface with unboundedly large Liu-Yau mass. This is even true for Minkowski space. INI 1 15:30 to 16:00 Tea 18:30 to 19:45 Dinner at Wolfson Court (Residents only)