Jonathan Luk (Mathematics) - Stanford University
Title: High-frequency limits in general relativity and a conjecture of Burnett
Abstract: It is known in the literature that ”high-frequency weak limits” of solutions to the Einstein vacuum equations are not necessarily vacuum solutions, but may have a non-trivial stress-energy-momentum tensor, which can be viewed physically as ”effective matter fields” arising from back-reaction of high-frequency gravitational waves. Burnett conjectured nonetheless that any such limit is isometric to a solution to the Einstein-massless Vlasov system; and conversely that any solution to the Einstein-massless Vlasov system arises as such limit. We discuss some recent progress on Burnett’s conjecture, as well as an application of it. This talk is based on joint works with Huneau, and with Rodnianski.
Bio: Jonathan Luk is an Associate Professor at the Stanford University Department of Mathematics. He received his PhD in Mathematics from Princeton University in 2012. His research interests are nonlinear partial differential equations, general relativity, and mathematical physics.