Mathematical General Relativity, Compressible Fluids, and More

Three-month Program at IHP (Paris) on MATHEMATICAL GENERAL RELATIVITY

In ALL SEMINARS AND CONFERENCES, GENERAL RELATIVITY on March 9, 2014 at 3:41 pm
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Three-Month Program on MATHEMATICAL GENERAL RELATIVITY at the Institut Henri Poincaré

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Organizers

Lars Andersson (Potsdam)

Sergiu Klainerman (Princeton) 

Philippe G. LeFloch (Paris) 

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From

September 14, 2015 to December 18, 2015

 

Main Themes of the Program

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 (Cauchy problem, cosmic censorship, asymptotic behavior). These developments have brought into focus the deep connections between the Einstein equation and other important geometric PDE’s, including the wave map equation, Yang-Mills equation, Yamabe problem, 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 breakthrough, concerning the uniqueness and stability of the Kerr black hole model, the formation of trapped surfaces, and the bounded L2 curvature problem. Specifically, the themes of mathematical interest that will be developed in the present Program and are currently most active include:

  •  The initial value problem for Einstein equation and the causal geometry of spacetimes with low regularity, formation of trapped surfaces
  • Techniques of Lorentzian geometry: injectivity radius estimates, geometry of null cones; construction of parametrices
  •  Geometry of black hole spacetimes: uniqueness theorems, censorship principles
  • Coupling of Einstein equation for self-gravitating matter models, weakly regular spacetimes with symmetry

Main Events

  • Sept. 14 to 18, 2015: Summer School INTRODUCTION TO MATHEMATICAL GENERAL RELATIVITY 

SPEAKERS (partial list):

Greg Galloway (Miami)

Gerhard Huisken (Tuebingen)

Alexandru Ionescu (Princeton)

Hans Ringstrom (Stockholm)

  • Sept. 23 to 25, 2015: Workshop MATHEMATICAL PROPERTIES OF SPACETIMES AND BLACK HOLES

SPEAKERS (partial list):

Greg Galloway  (Miami) *

Alexandru Ionescu (Princeton)

Hans Ringstrom (Stockholm)

  • Oct.: Workshop STATE OF THE ART ON BLACK HOLES

(This week hold in Montpelier and organized by Marc Herzlich and Erwann Delay)

SPEAKERS (partial list):

Piotr Chrusciel (Vienna)

Michael Eichmair (Zürich)

Mu-Tao Wang (New York)

  • Oct. 26 to 29, 2015: Workshop SELF-GRAVITATING MATTER MODELS
  • Nov. 16 to  20, 2015: International Conference MATHEMATICAL GENERAL RELATIVITY – A Celebration of the 100th Anniversary of General Relativity  

SPEAKERS (partial list):

Jean-Pierre Bourguignon (IHES)

Pieter Blue (Edinburgh)

Matthew Choptuik (Vancouver)

Demetrios Christodoulou (Zürich and Athens)

Mihalis Dafermos (Princeton)

Thibault Damour (Bures-sur-Yvette)

Richard Hamilton (New York) *

Jonathan Luk (Cambridge, US)

Juan Maldacena (Princeton) *

Roger Penrose (Oxford)

Igor Rodnianski (Cambridge) *

Richard Schoen (Stanford)

Jacques Smulevici (Orsay)

John Stachel (Boston)

Jérémie Szeftel (Paris)

Robert Wald (Chicago)

Qian Wang (Oxford)

* (to be confirmed)

  • Dec. 14 to 16, 2015: International Conference to CELEBRATE THE 100TH ANNIVERSARY OF THE BIRTH OF ANDRÉ LICHNEROWICZ 

(This week organized by Richard Kerner and Yvette Kosmann-Schwarzbach)


Program coordinated by the Centre Emile Borel at IHP. Financial support provided by the Institut Henri Poincaré and the ANR Project “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”.
 

FURTHER INFORMATIONS TO BE ADDED SOON

 

 




 

 

 

 

J. Hyperbolic Differential Equations (JHDE)

In GENERAL RELATIVITY, J. Hyperbolic Differential Equations (JHDE) on September 7, 2009 at 11:20 am

 

Main Editor: Philippe G. LeFloch

contact@philippelefloch.org

Laboratoire Jacques-Louis Lions
Centre National de la Recherche Scientifique (CNRS)
Université Pierre et Marie Curie
(Paris 6), 4 Place Jussieu
75252 Paris, FRANCE

Co-editor:  Jian-Guo Liu, Duke Univ.

Editorial Board

  • Lars Andersson (Potsdam)
  • François Bouchut (Paris-Est)
  • Shuxing Chen (Shanghai)
  • James Colliander (Toronto)
  • Rinaldo Colombo (Brescia)
  • Constantine Dafermos (Providence)
  • Helmut Friedrich (Potsdam)
  • Kenneth H Karlsen (Oslo)
  • Shuichi Kawashima (Fukuoka)
  • Sergiu Klainerman (Princeton)
  • Peter Lax (New York)
  • Tai-Ping Liu (Taipei)
  • Pierro Marcati (L’Aquila)
  • Nader Masmoudi (New York)
  • Frank Merle (Bures-sur-Yvette)
  • Cathleen S Morawetz (New York)
  • Tatsuo Nishitani (Osaka)
  • Alan Rendall (Potsdam)
  • Denis Serre (Lyon)
  • Eitan Tadmor (College Park)

This journal publishes original research papers on nonlinear hyperbolic problems and related topics, especially on the theory and numerical analysis of hyperbolic conservation laws and on hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:

  • Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
  • Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models.
  • Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
  • Nonlinear hyperbolic systems arising in continuum physics such as hyperbolic models of fluid dynamics, mixed models of transonic flows.
  • General problems that are dominated by finite speed phenomena such as dissipative and dispersive perturbations of hyperbolic systems, and models relevant to the derivation of fluid dynamical equations.

JHDE aims to provide a forum for the community of researchers working in the very active area of nonlinear hyperbolic problems and nonlinear wave equations, and will also serve as a source of information for the applications.

Seminar on Mathematical General Relativity – Wednesday Sept. 17, 2014

In ALL SEMINARS AND CONFERENCES, GENERAL RELATIVITY on August 29, 2014 at 9:27 pm
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Seminar on

Mathematical General Relativity

 

Organizers:

 Philippe G. LeFloch (Paris)

 

Jérémie Szeftel (Paris) 

Ghani Zeghib (Lyon)

 

ANR Project

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

Wednesday Sept. 17, 2014

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

Lecture room ???

 


14h Arick Shao (Imperial College) Unique continuation from infinity for linear waves

Abstract. We prove various unique continuation results from infinity for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the solution must vanish in an open set in the interior. The parts of infinity where we must impose a vanishing condition depend strongly on the background geometry; in particular, for backgrounds with positive mass (such as Schwarzschild or Kerr), the required assumptions are much weaker than in Minkowski spacetime. These results rely on a new family of geometrically robust Carleman estimates near null cones and on an adaptation of the standard conformal inversion of Minkowski spacetime. Also, the results are nearly optimal in many respects. This is joint work with Spyros Alexakis and Volker Schlue.

15h30 Claude Warnick (Warwick)  Dynamics in anti-de Sitter spacetimes

Abstract. When solving Einstein’s equations with negative cosmological constant, the natural setting is that of an initial-boundary value problem. Data is specified on the timelike conformal boundary as well as on some initial spacelike hypersurface. Questions of local well-posedness and global stability are sensitive to the choices of boundary conditions. I will present recent work exploring the effects of non-trivial boundary data for the asymptotically AdS initial-boundary value problem, including a recent result in collaboration with Holzegel. I will also outline some interesting open problems in the area.

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