*Organizers*

*Lars Andersson (Potsdam)*

*Sergiu Klainerman (Princeton) *

#### Philippe G. LeFloch *(Paris) *

**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”.*