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September 14, 2015 to December 18, 2015
Trimester Program at the
Centre Emile Borel
Financial support provided by Institut Henri Poincaré
and ANR Project “Mathematical General Relativity”
Organizers
Lars Andersson (Potsdam)
Sergiu Klainerman (Princeton)
Philippe G. LeFloch (Paris)
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 parametrix
- Geometry of black hole spacetimes: uniqueness theorems, censorship principles
- Coupling of Einstein equation for self-gravitating matter models, weakly regular spacetimes, nonlinear stability of Minkowski space with matter
General schedule for the Trimester
SCIENTIFIC ACTIVITIES during the Trimester
- Workshops and Conferences (see below)
- On the Mathematical Theory of Black Holes, Course by S. Klainerman.
- Begins on October 13 from 2pm to 4:30pm, and the following Tuesdays.
- Video of the lectures
- An Introduction to Self-Gravitating Matter, Course by P.G. LeFloch.
- Begins on October 9 from 2pm to 4:30pm, and the following Fridays.
- LECTURE NOTES for this course
- Video 1: An introduction to self-gravitating matter
- Video 2: Modified gravity and weakly regular spacetimes
- Video 3: Weak solutions to the Einstein equations
- Video 4: Weakly regular Cauchy developments
- Video 5: Self-gravitating fluids with bounded variation
- Video 6: The geometry of weakly regular spacetimes
- Video 7: Nonlinear stability of Minkowski space for massive fields
- Weekly Seminar on Mathematical General Relativity
- organized by L. Andersson, jointly with S. Klainerman, P.G. LeFloch, J. Szeftel (Paris), and A. Zeghib (Lyon).
- Begins on October 7 from 2pm to 4:30pm, and the following Wednesdays.
- Speakers in the Seminar :
- Bruno Premoselli (Cergy-Pontoise), Martin Taylor (Cambridge, UK)
- Steffen Aksteiner (Potsdam), Lars Andersson (Potsdam)
- Jesus Oliver (San Diego)
- Anne Franzen (Utrecht), Jared Wunsch (Evanston)
- Sung-Jin Oh (Berkeley), Anna Sakovich (Vienna)
- Hans Lindblad (Baltimore), Florian Beyer (Dunedin)
- VIDEOS available (courses, main conference)
- Tea break every day 3pm-3:30pm
WORKSHOPS AND CONFERENCES
Sept. 14 to 18, 2015 Summer School – INTRODUCTION TO MATHEMATICAL GENERAL RELATIVITY
List of speakers
Greg Galloway (Miami)
Gerhard Huisken (Tuebingen)
Hans Ringstrom (Stockholm)
Sept. 23 to 25, 2015 Workshop – RECENT ADVANCES IN MATHEMATICAL GENERAL RELATIVITY
List of speakers
Spyros Alexakis (Toronto)
Piotr Chrusciel (Vienna)
Joao Costa (Lisbon)
Semyon Dyatlov (Cambridge, USA)
Stefan Hollands (Cardiff)
Alexandru Ionescu (Princeton)
Lionel Mason (Oxford)
Vincent Moncrief (Yale)
Jean-Philippe Nicolas (Brest)
Harvey Reall (Cambridge, UK)
Hans Ringstrom (Stockholm)
Mu-Tao Wang (New York)
Sept. 28 to Oct. 1, 2015 Workshop – GEOMETRIC ASPECTS OF MATHEMATICAL RELATIVITY (Hold in Montpellier and organized by Marc Herzlich and Erwann Delay)
List of speakers
Piotr Chrusciel (Vienna)
Michael Eichmair (Zürich)
Mu-Tao Wang (New York)
Oct. 26 to 29, 2015 Workshop – DYNAMICS OF SELF-GRAVITATING MATTER
List of speakers
Hakan Andreasson (Gothenburg)
Thierry Barbot (Avignon)
Robert Beig (Vienna)
David Fajman (Vienna)
Marc Mars (Salamanca)
David Maxwell (Fairbanks)
Todd Oliynyk (Monash)
Volker Schlue (Toronto)
Bernd Schmidt (Potsdam)
Jared Speck (Cambridge, USA)
Shadi Tahvildar-Zadeh (Rutgers)
Eric Woolgar (Alberta)
Nov. 16 to 20, 2015 International Conference – GENERAL RELATIVITY – A Celebration of the 100th Anniversary
List of speakers Schedule and title
Jean-Pierre Bourguignon (Bures-sur-Yvette)
Demetrios Christodoulou (Zürich & Athens)
Mihalis Dafermos (Princeton)
Thibault Damour (Bures-sur-Yvette)
Georges Ellis (Cape Town)
Richard Hamilton (New York)
Gustav Holzegel (London)
Jonathan Luk (Cambridge, UK)
Roger Penrose (Oxford)
Richard Schoen (Stanford & Irvine)
Jacques Smulevici (Orsay)
Jérémie Szeftel (Paris)
Robert Wald (Chicago)
Qian Wang (Oxford)
Dec. 14 to 16, 2015 International Conference- RELATIVITY AND GEOMETRY – IN MEMORY OF A. LICHNEROWICZ (Organized by Giuseppe Dito, Jean-Pierre Francoise, Paul Gauduchon, Richard Kerner, Yvette Kosmann-Schwarzbach et Daniel Sternheimer)
List of speakers
Olivier Biquard (Paris 6)
Robert Bryant (Durham)
Pierre Cartier (Gif-Sur-Yvette)
Thibault Damour (Gif-Sur-Yvette)
Nathalie Deruelle (Paris 7)
Simon Donaldson (Stony Brook & London)
Michel Dubois-Violette (Paris 11)
Charles Francès (Strasbourg)
Edward Frenkel (Berkeley)
Christian Fronsdal (Los Angeles)
Simone Gutt (Bruxelles)
James Isenberg (Eugene)
Sergiu Klainerman (Princeton)
Maxim Kontsevich (Gif-Sur-Yvette)
Alan Weinstein (Berkeley)
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”.
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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 June 17, 2015
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
Lecture room 15/25-326
11h Emmanuel Hebey (Cergy-Pontoise) Systèmes de Kirchhoff critiques stationnaires sur des variétés compactes
14h Lydia Bieri (Ann Arbor) Gravitational radiation and two types of memory
Abstract. We are believed to live on the verge of detection of gravitational waves, which are predicted by General Relativity. In order to understand gravitational radiation, we have to investigate analytic and geometric properties of corresponding solutions to the Einstein equations. Gravitational waves leave a footprint in the spacetime regions they pass, changing the manifold – and therefore displacing test masses – permanently. This is known as the memory effect. It has been believed that for the Einstein equations, being nonlinear, there exists one such effect with a small `linear’ and a large `nonlinear’ part. In this talk, I present some of my joint work with D. Garfinkle showing that these are in fact two different effects.