Burnett's conjecture in general relativity

In this talk I will present a conjecture of Burnett, which characterizes weak limits of solutions to the Einstein vacuum equations from general relativity. After a brief review of the Cauchy problem for these equations, I will show how their seemingly messy nonlinear structure actually leads to some beautiful cancellations. I will conclude by discussing potential Riemannian versions of Burnett's conjecture, in connection with results by Gromov and Lohkamp.