Seminar on theory of function spaces

Wasserstein distances in the space of Cartesian currents

The first half of this two-part will give a grand tour through some interrelated topics from the study of harmonic maps, geometric measure theory, currents and mathematical relaxation techniques as well as optimal transport. The aim will be to give brief introductions and some overview of intuitions and recurring concepts, so to be understandable without much prior knowledge. This will then set the stage for the second half, which will use those ideas to present an attempt to connect those ideas and develop a theory which can be used to attack problems that combine evolutionary PDEs with geometric/topological aspects.