The magnetization of a ferromagnetic sample is typically given by a vector field of constant length, so we can think of a map into the unit 2-sphere. The topology of the target sometimes gives rise to defects in the magnetization. When we study ferromagnetic samples in the shape of a
thin film, then these defects have a lot in common with the Ginzburg-Landau vortices that have been studied in the context of superconductors and superfluids.

We study the evolution of the vortices under the Landau-Lifshitz-Gilbert equation. Again this problem has strong similarites with the corresponding theory for Ginzburg-Landau vortices, but there are some significant differences, too. In particular the
geometry of the target (the 2-sphere) gives rise to some new phenomena and some technical difficulties as well.

This is joint work with Matthias Kurzke (Bonn), Christof Melcher (Aachen), and Daniel Spirn (Minnesota).