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## Seminar on** **

**Mathematical General Relativity**

* * *Organizers: *Sergiu Klainerman *(Princeton)*

#### Philippe G. LeFloch *(Univ. Pierre et Marie Curie) * Gabriele Veneziano *(Collège de France)*

#### With the financial support of the **Fondation des Sciences Mathématiques de Paris**

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**Monday January 31rst, 2011**

**Institut Henri Poincaré**

** Lecture room 314**

**Lecture room 314**

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### 11h Lydia Bieri (Ann Arbor), Geometry of Spacetimes Solving the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation

*Abstract. A major goal of mathematical General Relativity (GR) and astrophysics is to precisely describe and finally observe gravitational radiation, one of the predictions of GR. In order to do so, one has to study the null asymptotical limits of the spacetimes for typical sources. Among the latter we find binary neutron stars and binary black hole mergers. In these processes typically mass and momenta are radiated away in form of gravitational waves. D. Christodoulou showed that every gravitational-wave burst has a nonlinear memory. In this talk, we discuss the null asymptotics for spacetimes solving the Einstein-Maxwell (EM) equations, compute the radiated energy and derive limits at null infinity and compare them with the Einstein vacuum (EV) case. The physical insights are based on geometric-analytic investigations of the solution spacetimes.*

* *14h Jérémie Szeftel (ENS, Paris) Around the bounded L2 curvature conjecture in general relativity

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Abstract. We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation on a curved background, where the metric is a rough solution to the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L2 bounds on the curvature tensor of the metric is a major step towards the proof of the bounded L2 curvature conjecture. This is a joint work with Sergiu Klainerman and Igor Rodnianski.

*Abstract. A major goal of mathematical General Relativity (GR) and astrophysics is to precisely describe and finally observe gravitational radiation, one of the predictions of GR. In order to do so, one has to study the null asymptotical limits of the spacetimes for typical sources. Among the latter we find binary neutron stars and binary black hole mergers. In these processes typically mass and momenta are radiated away in form of gravitational waves. D. Christodoulou showed that every gravitational-wave burst has a nonlinear memory. In this talk, we discuss the null asymptotics for spacetimes solving the Einstein-Maxwell (EM) equations, compute the radiated energy and derive limits at null infinity and compare them with the Einstein vacuum (EV) case. The physical insights are based on geometric-analytic investigations of the solution spacetimes.*

*14h Jérémie Szeftel (ENS, Paris) Around the bounded L2 curvature conjecture in general relativity*

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