The HADES seminar on Tuesday, September 22nd will be given by Jonathan Luk via Zoom from 3:40 to 5 pm.

Speaker: Jonathan Luk, Stanford

Abstract: I will discuss the construction of a class of low-regularity (merely $W^{1,2}$) solutions to the Einstein vacuum equations which have the property that the solutions are foliated by $2$-spheres so that the metric is more regular along the tangential directions of the $2$-spheres. I will first discuss a model semi-linear problem, then introduce the relevant geometric setup and give a sketch of the proof. This type of singular solutions is relevant to the problems of impulsive gravitational waves, high-frequency limits, null dust shells and the formation of trapped surfaces in general relativity (discussed in the Analysis and PDE seminar on 9/21).