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*Organizers*

* *Philippe G. LeFloch *(Paris)*

*Jérémie Szeftel (Paris) *

*Ghani Zeghib (Lyon)*

**ANR Project**

#### “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

**Wednesday Sept. 17, 2014**

### Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

#### Lecture room 15-25-321

**14h Arick Shao (Imperial College) **Unique continuation from infinity for linear waves

Abstract. We prove various unique continuation results from infinity for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the solution must vanish in an open set in the interior. The parts of infinity where we must impose a vanishing condition depend strongly on the background geometry; in particular, for backgrounds with positive mass (such as Schwarzschild or Kerr), the required assumptions are much weaker than in Minkowski spacetime. These results rely on a new family of geometrically robust Carleman estimates near null cones and on an adaptation of the standard conformal inversion of Minkowski spacetime. Also, the results are nearly optimal in many respects. This is joint work with Spyros Alexakis and Volker Schlue.

**15h30 Claude Warnick (Warwick) ** Dynamics in anti-de Sitter spacetimes

Abstract. When solving Einstein’s equations with negative cosmological constant, the natural setting is that of an initial-boundary value problem. Data is specified on the timelike conformal boundary as well as on some initial spacelike hypersurface. Questions of local well-posedness and global stability are sensitive to the choices of boundary conditions. I will present recent work exploring the effects of non-trivial boundary data for the asymptotically AdS initial-boundary value problem, including a recent result in collaboration with Holzegel. I will also outline some interesting open problems in the area.