**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 with symmetry

General schedule for the Trimester available here

**SCIENTIFIC ACTIVITIES during the Trimester**

**Weekly Seminar on Mathematical General Relativity,**organized by L. Andersson, jointly with S. Klainerman, P.G. LeFloch, J. Szeftel (Paris), and A. Zeghib (Lyon). Begin on October 7 at 2pm-4:30pm, and the following Wednesdays.**On the Mathematical Theory of Black Holes,**Graduate course given**An Introduction to Self-Gravitating Fluids**__,__Graduate course given by PG. LeFloch. Begins on October 9 at 2pm-4:30pm, and the following Fridays.**Workshops and Conferences:**see below.- 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)

Todd Oliynyk (Monash)

Bernd Schmidt (Potsdam)

Jared Speck (Cambridge, USA)

Marc Mars (Salamanca)

David Maxwell (Fairbanks)

Volker Schlue (Toronto)

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 **

Jean-Pierre Bourguignon (Bures-sur-Yvette)

Pieter Blue (Edinburgh)

Matthew Choptuik (Vancouver)

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)

Igor Rodnianski (Princeton)

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- 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**

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)

Edward Frenkel (Berkeley)

Simone Gutt (Bruxelles)

James Isenberg (Eugene)

Sergiu Klainerman (Princeton)

Maxim Kontsevich (Gif-Sur-Yvette)

Alan Weinstein (Berkeley)

**LIST OF LONG TERM VISITORS for THE TRIMESTER **

**(partial list) **

Lars Andersson (Potsdam)

Thierry Barbot (Avignon)

Florian Beyer (Dunedin)

Mattias Dahl (Stockholm)

Romain Gicquaud (Tours)

Jean-Claude Guillot (Palaiseau)

Jim Isenberg (Eugene)

Sergiu Klainerman (Princeton)

Philippe LeFloch (Paris)

Hand Lindblad (Baltimore)

Lionel Mason (Oxford)

Vincent Moncrief (Yale)

Vincent Pecastaing (Orsay)

Jérémie Szeftel (Paris)

Jared Wunsch (Evanston)

Ghani Zeghib (Lyon)

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”.*