Workshop

The mathematical study of the dynamics of the Einstein equations forms a central part of both partial differential equations and geometry, and is intimately related to our current physical understanding of gravitational collapse. The celebrated singularity theorems of Penrose, proven in the 1960s, showed that geodesic incompleteness is inevitable provided that initial data contain what is known as a closed trapped surface. Trapped surfaces are also related to the presence of black holes. A breakthrough into the understanding of trapped surface formation has recently been achieved by Christodoulou in his 600 page monograph: "The formation of black holes in General Relativity", Publications of the EMS, January 2009, where it is shown that trapped surfaces form in evolution for the Einstein vacuum equations from completely dispersed initial confgurations, a phenomenon caused purely by the focussing of gravitational waves. The proof brings together ideas from geometric analysis and non-linear hyperbolic equations and at the same time introduces new techniques adapted to large data problems. The methods will undoubtedly have many future applications in both general relativity and other equations of mathematical physics. Inparticular, the work provides the first global "large data" result in general relativity (without symmetry assumptions) and opens the possibility for many new developments on dynamical problems relating to black holes. Accomodations: A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. The cut-off date for reservations is August 31, 2009. A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: BLACKHOLESMSRI. The cut-off date for reservations is August 13, 2009. We also hold a block of rooms at the Doubletree Hotel. Please mention the MSRI as a reference when making reservations by calling 510-548-7920 OR directly on their website. The Doubletree Hotel offers complementary shuttle to and from MSRI. The room rate is $99 per night. New, completely renovated Hotel Shattuck Plaza has rooms available for you as well! Click here to book online Or, you can make reservations calling the main line, 510-845-7300, and asking for the rate for Hot Topics: Black Holes in Relativity. The room rate is $119 per night plus tax.