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#### Seminar at the

#### Laboratoire Jacques-Louis Lions

#### Université Pierre et Marie Curie, Paris

*Organizers*

#### Philippe G. LeFloch (Paris)

#### Jacques Smulevici (Orsay)

#### Jérémie Szeftel (Paris)

**Dates of the Seminar for this Academic year: **

**October 9, November 20, December 4, February 12, March 12**

**+ Conference from May 28 to June 1rst**

#### Monday March 12, 2018

*room 15-16 309*

#### 14h Carla Cederbaum (Tubingen)

**TBA**

Abstract. TBA

#### 15h30 Maxime Van de Moortel (Stanford)

**TBA**

Abstract. TBA

#### Monday February 12, 2018

*room 15-16 309*

#### 14h Shadi Tahvildar-Zadeh (Rutgers)

**TBA**

Abstract. TBA

#### 15h30 Thomas Johnson (Cambridge)

**TBA**

Abstract. TBA

#### Monday December 4, 2017

*room 16-26 113*

#### 14h Siyuan Ma (Potsdam)

**On Maxwell field and linearized gravity in Kerr**

Abstract. I will consider both Maxwell field and linearized gravity on Kerr backgrounds, and present recent results in obtaining energy and Morawetz estimates for the extreme Newman-Penrose components.

#### 15h30 Claudio Paganini (Potsdam)

**Mode stability on the real axis**

Abstract. I will discuss a generalization of the mode stability result of Whiting (1989) for the Teukolsky equation for the case of real frequencies. The main result states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish.

#### Monday November 20, 2017

*room 16-26 113 *

#### 14h Frederico Pasqualotto (Princeton)

**Nonlinear stability for the Maxwell–Born–Infeld system on a Schwarzschild background**

Abstract. The Maxwell–Born–Infeld (MBI) theory is a hyperbolic system of PDEs which describes nonlinear electromagnetism. Due to its tensorial and quasilinear nature, this system can be seen as a nonlinear model problem to study the stability properties of solutions to the Einstein vacuum equations. In this talk, I will present a nonlinear stability result for the MBI system on a fixed Schwarzschild background, when the initial data are constrained to be small. A crucial element of the proof is the observation that some null components of the MBI field satisfy “good” Fackerell–Ipser equations, as in the linear Maxwell case. However, in the MBI case, these equations are coupled through cubic nonlinear right hand sides, which contain all components of the MBI field. In order to resolve the coupling, we prove high-order energy decay and, subsequently, pointwise decay for all the components of the MBI field. This is achieved through the application of many ideas developed in recent years, regarding the decay of linear fields.

#### 15h30 Volker Schlue (Paris)

**On `hard stars’ in general relativity**

Abstract. I will review the classical picture of gravitational collapse in spherical symmetry, from the Oppenheimer-Snyder model (1939) to Christodoulou’s two phase model (1995). I will then turn to the possible end states of gravitational collapse, in particular discuss non-trivial static solutions to the two-phase model, which are idealized models of neutron stars. The main results concern a variational characterization of hard stars, and I will outline their relevance for the orbital stability problem of neutron stars in spherical symmetry. I hope to conclude with a discussion of the various remaining problems that have to be overcome for a global in time result, in particular related to possible phase transitions in this model.

#### Monday October 9, 2017

*room 15/16-309*

#### 14h Daniel Monclair (Orsay)

**Attractors in spacetimes and time functions**

Abstract. A time function on a Lorentzian manifold is a continuous real valued function which is increasing along all future directed causal curves. A result of Hawking states that the existence of a time function is equivalent to stable causality, i.e. the impossibility of generating timelike loops even after small perturbations of the metric. We will discuss a construction of time functions which is quite different from Hawking’s construction, in the sense that it produces functions that still have interesting properties for non stably causal spacetimes (while Hawking’s time functions fail to be continuous without stable causality). Our approach is based on a notion of attracting sets in spacetimes, following the work of Conley on Lyapunov functions.

#### 15h30 The-Cang Nguyen (Paris)

**Global dispersion of self-gravitating massive matter in spherical symmetry**

Abstract. We study massive matter fields evolving under their own gravitational field and we generalize results established by Christodoulou for the spherically symmetric evolution of massless scalar fields governed by the Einstein equations. We encompass both Einstein’s theory and the f(R)-theory of modified gravity defined from a generalized Hilbert-Einstein functional depending on a nonlinear function f(R) of the spacetime scalar curvature R. This is a joint work with P.G. LeFloch and F. Mena.