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## Seminar on

**Mathematical General Relativity**

*Organizers:*

* *Philippe G. LeFloch *(Paris)*

*Jérémie Szeftel (Paris) *

*Ghani Zeghib (Lyon)*

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**ANR Project**

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

**February 12, 2014**

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

**Lecture room ** 1525-103

**Lecture room**

**14h Florian Beyer (Dunedin) **Graceful exit from inflation for minimally coupled Bianchi A scalar field models

Abstract. We consider the dynamics of Bianchi A scalar field models which undergo inflation. The main question is under which conditions does inflation come to an end and is succeeded by a decelerated epoch. This so-called ‘graceful exit’ from inflation is an important ingredient in the standard model of cosmology, but is, at this stage, only understood for restricted classes of solutions. We present new results obtained by a combination of analytical and numerical techniques.

**15h30 Cécile Huneau (ENS, Paris)** Vacuum constraint equations for asymptotically flat space-times with a translational Killing field

Abstract. In the presence of a space-like translational Killing field, vacuum Einstein equations in 3+1 dimensions reduces to 2+1 Einstein equations with a scalar field. Minkowski space-time is a trivial solution of vacuum Einstein equation with a translational Killing field. A natural question is therefore the nonlinear stability of Minkowski solution in this setting. A first step in addressing this problem is the study of the constraint equations. The main difficulty in that case is due to the delicate inversion of the Laplacian. In particular, we have to work in the non constant mean curvature setting, which enforces us to consider the intricate coupling of the Einstein constraint equations.