General Relativity, Differential Geometry and Differential Equations; Stories From a Successful Menage-a-trois

Niky Kamran
Mon, Apr 7, 2014
PIMS, University of British Columbia
CRM-Fields-PIMS Prize Lecture

N.B. Due to problems with the microphone, the audio quality of this video is significantly lower than expected.


It is well known that Einstein's general theory of relativity provides a geometrical description of gravity in terms of space-time curvature. Einstein's theory poses some fascinating and difficult mathematical challenges that have stimulated a great deal of research in geometry and partial differential equations. Important questions include the well-posedness of the evolution problem, the definition of mass and angular momentum, the formation of black holes, the cosmic censorship hypothesis, the linear and non-linear stability of black holes and boundary value problems at conformal infinity arising in the analysis of the AdS/CFT correspondence. I will give a non-technical survey of some significant advances and open problems pertaining to a number of these questions.