Mathematical Problems in General Relativity
Student No.:200
Time:Mon. / Wed. 10:10-12:00
Instructor:Richard Schoen  [Stanford University]
Place:Lecture Hall, Floor 3, Jin Chun Yuan West Building (近春园西楼3层报告厅)
Starting Date:2012-3-28
Ending Date:2012-5-30

Course description:

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made.

Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetimes. We will describe recent progress on mass/angular momentum inequalities.

We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.



Basic Riemannian geometry including submanifold theory, basic functional analysis, Sobolev and Hölder spaces, knowledge of elliptic PDE on manifolds.


Reference for the course:

General Relativity, Robert M. Wald, University of Chicago Press
Lecture notes and some recent papers to be posted