Hyperbolic & Dispersive PDE Seminar

Speaker: Christoph Kehle MIT

Title: Extremal black hole formation as a critical phenomenon

Abstract: I will present a proof which shows that extremal black holes arise on the threshold of gravitational collapse. More precisely, I will present a construction of one-parameter families of smooth solutions to the Einstein-Maxwell-Vlasov system which interpolates between dispersion and collapse and for which the critical solution is an extremal black hole. This is joint work with Ryan Unger (Stanford).

Speaker: Leonhard Kehrberger University of Leipzig

Title: Scattering, polyhomogeneity and explicit asymptotics for nonlinear wave equations from past to future null infinity, with applications to relativity

Abstract: Consider a quasilinear wave equation that is a perturbation of the Minkowskian wave equation: Given semi-global scattering data along an ingoing cone towards past null infinity and along past null infinity, then under what conditions can we show scattering solutions to exist, and, if they exist, what are the asymptotics of these solutions towards spacelike and future null infinity? I will discuss a theorem with Istvan Kadar concerning existence, optimal-in-decay weighted energy estimates and propagation of polyhomogeneity for these solutions. The propagation of polyhomogeneity ensures that the solution has expansions towards spacelike and future null infinity. I will then present an algorithm that allows to iteratively compute the coefficients in the latter expansions. Finally, I will put these results in the context of the Einstein vacuum equations, where they have consequences on the asymptotics of gravitational radiation and on the regularity properties of null infinity.

Speaker: Fabio Pusateri University of Toronto

Title: TBC

Abstract: TBC

Speaker: Warren Li Princeton University

Title: TBC

Abstract: TBC