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

Speaker: 
Niky Kamran
Date: 
Mon, Apr 7, 2014
Location: 
PIMS, University of British Columbia
Conference: 
CRM-Fields-PIMS Prize Lecture
Abstract: 

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.