Organized by Philippe LeFloch, Mike Anderson, Sergiu Klainerman, and Jared Speck

Dates: January 19 – 23, 2015

Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, including the Cauchy problem, cosmic censorship, and asymptotic behavior. These developments have brought into focus the deep connections between the Einstein equation and other important geometric partial differential equations, including the wave map equation, Yang-Mills equation, Yamabe equation, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthroughs concerning the uniqueness and stability of black hole models, the formation of trapped surfaces, and the bounded L2 curvature problem. The themes of mathematical interest that will be particularly developed in the present Program include the formation of trapped surfaces and the nonlinear interaction of gravitational waves. The new results are based on a vast extension of the earlier technique by Christodoulou and Klainerman establishing the nonlinear stability of the Minkowski space. This Program will be an excellent place in order to present the recent breakthrough on the bounded L2 curvature problem for the Einstein equation, which currently provides the lower regularity theory for the initial value problem, as well as the recently developed theory of weakly regular Einstein spacetimes with distributional curvature.

This workshop is a part of the Spring 2015 program, Mathematical Problems in General Relativity, which is organized by Philippe LeFloch, Mike Anderson, Sergiu Klainerman, and Jared Speck. This program takes place from January 5 – February 6, 2015.

First day of the workshop (January 19th, 2015) is the U.S. holiday of Martin Luther King Day. This will be an informal day during the workshop.

Workshop Application is now closed.

#### Mathematical Problems in General Relativity Workshop Schedule

Time | Title | Presenters | Video |

9:30am | Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations | Sung-Jin Oh | video |

10:30am | Coffee Break | ||

11:00am | Stationarity of Time-Periodic Vacuum Spacetimes | Volker Schlue | video |

12:00pm | Lunch | ||

1:30pm | The Euler–Maxwell system for electrons: global solutions in 2D | Alexandru Ionescu | video |

3:00pm | Concentration Compactness for the Critical Maxwell Klein Gordon Equation | Joachim Krieger | video slides |

5:00pm | Della Pietra Lecture Series and Reception, “The Story of Flat Surfaces” | Etienne Ghys | video |

Time | Title | Presenters | Video |

9:30am | Two Results on Formation of Trapped Surfaces | Xinliang An | video slides |

10:30am | Coffee Break | ||

11:00am | The Dirac electron and the Kerr-Newman spacetime | A. Shadi Tahvildar-Zadeh | video slides |

12:00pm | Lunch | ||

1:30pm | Lecture | Mihalis Dafermos | video slides |

3:00pm | Asymptotically Hyperbolic Shear-Free Solutions of the Einstein Constraint Equations | James Isenberg | video |

Time | Title | Presenters | Video |

9:30am | Stability in exponential time of Minkowski | Cécile Huneau | video |

10:30am | Coffee Break | ||

11:00am | Vector field methods for transport equations with applications to the Vlasov-Poisson system. |
Jacques Smulevici | video |

12:00pm | Lunch | ||

1:30pm | Quasi-local angular momentum and the limit at infinity | Mu-Tao Wang | video |

3:00pm | The Penrose inequality for perturbations of the Schwarzschild exterior | Spyros Alexakis | video |

6:00pm | Workshop Banquet Dinner |

Time | Title | Presenters | Video |

9:30am | Pointwise decay for the Maxwell system on black holes | Mihai Tohaneanu | video |

10:30am | Coffee Break | ||

11:00am | Lecture | Qian Wang | video |

12:00pm | Lunch | ||

1:30pm | Revisiting decay of fields outside a Schwarzschild black hole | Peter Blue | video |

3:00pm | Weak solutions to the Einstein equations in spherical or T2 symmetry | Phillipe LeFloch | video |