This Summer School “Mathematical General Relativity” is an event of the Trimester Program taking place at the Institut Henri Poincaré in order to celebrate the 100th Anniversary of General Relativity. It will provide an introduction to advanced methods in mathematical general relativity.

*Emile Borel Centre of Henri Poincaré Institute, Paris*

*September 14 to 18, 2015*

**SCHEDULE**

**Monday Sept. 14**

**:**Registration/coffee

**G. Huisken**

**H. Ringström**

**H. Ringström**

**Tuesday Sept. 15**

**:**coffee

**G. Galloway**

**G. Huisken**

**G. Huisken**

**Wednesday Sept. 16**

**:**coffee

**G. Huisken**

**H. Ringström**

**H. Ringström**

**Thursday Sept. 17**

**:**coffee

**G. Galloway**

**H. Ringström**

**H. Ringström**

**Friday Sept. 18**

**G. Galloway**

**LIST OF SPEAKERS**

Greg Galloway (Miami) *On the geometry and topology of initial data sets in General Relativity*

**Abstract.** An initial data set in a spacetime M is a triple (V,h,K), where V is a spacelike hypersurface in M, h is its induced (Riemannian) metric and K is its second fundamental form. A solution to the Einstein equations for physically relevant sources influences the curvature of V via the Einstein constraint equations, the geometric origin of which are the Gauss-Codazzi equations. After a brief introduction to Lorentzian manifolds and Lorentzian causality, we will study some topics of recent interest related to the geometry and topology of initial data sets. In particular, we will consider the topology of black holes in higher dimensional gravity, inspired by certain developments in string theory and issues related to black hole uniqueness. We shall also discuss recent work on the geometry and topology of the region of space exterior to all black holes, which is closely connected to the notion of topological censorship. Many of the results to be discussed rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry.

Gerhard Huisken (Tuebingen) Foliations in asymptotically flat 3-manifolds

**Abstract. **We study 1-parameter families of 2-dimensional hypersurfaces that sweep out asymptotically flat 3-manifolds that arise as spacelike slices in Lorentzian manifolds modelling isolated gravitating systems. In particular we investigate how constant mean curvature foliations as well as solutions of mean curvature flow and inverse mean curvature flow can be used to model physical concepts such as mass and center of mass geometrically. The lectures also give an introduction to the necessary analytical techniques from PDEs and the calculus of variations.

Hans Ringstrom (Stockholm) *The Cauchy problem in general relativity*

**Abstract.** The series will give a historical background to the Cauchy problem in general relativity; describe some of the questions that can (and have been) addressed using the corresponding perspective; explain the formulation of the Cauchy problem; describe some relevant aspects of non-linear wave equations that arise; and address the topic of global uniqueness in the form of the existence of a maximal Cauchy development.

**ORGANIZERS**

*Lars Andersson (Potsdam)*

*Sergiu Klainerman (Princeton) *

Philippe G. LeFloch *(Paris)*

This conference is part of the **Three-Month Program on MATHEMATICAL GENERAL RELATIVITY** — Institut Henri Poincaré, Paris