Titles & Abstracts
-
Speaker: Gustav Holzegel (Universität Münster)
Title: Quasilinear Wave Equations on Kerr spacetimes in the full subextremal range
Abstract:
I will discuss joint work with Dafermos, Rodnianski and Taylor establishing small data global existence, boundedness and decay for a general class of quasilinear wave equations on the Kerr spacetime in the full sub-extremal range |a| < M.
-
Speaker: Alec Metsch (Universität zu Köln)
Title: Local contractibility of the locus of multiple maximizing geodesics
Abstract:
On a globally hyperbolic spacetime (M,g), consider the set of points that are joined to a given point x by at least two different maximizing geodesics. The goal of this talk is to show that this set is locally contractible (in particular, it is locally path connected). This extends a recent result of Cannarsa, Cheng and Fathi from the Riemannian to the Lorentzian setting. The key idea is to introduce a time-dependent “q-Lorentzian distance function”, 0
-
Speaker: Jan Bohr (Universität Bonn)
Title: Zoll magnetic systems and ruled surfaces
Abstract:
On an oriented surface M, the dynamics of a charged particle in a magnetic field is governed by a pair (g,\lambda) that consists of a Riemannian metric g together with a smooth function \lambda modelling the magnetic field. If every unit speed particle moves on a closed orbit (and the minimal period depends continuously on the orbit), we call (g,\lambda) a Zoll magnetic system. We show that there is a plethora of such systems on every closed oriented surface: locally near a constant curvature and constant magnetic field, there is essentially one for every closed 1-form on M; globally they can be set into a 1:1 correspondence with certain twistor data. In negative Euler characteristic these are the first examples beyond the constant curvature models. The construction of Zoll magnetic systems is based on so-called transport twistor spaces and holomorphic blow-down maps into ruled surfaces. Based on joint work with Gabriel P. Paternain.
|