We consider the simultaneous movement of finitely many colored points in space, calling it a \emph{spatial sorting process}. The name suggests a purpose that drives the collection to a configuration of increased or decreased order. Mapping such a process to a subset of space-time, we use persistent homology measurements of the time function to characterize the process topologically.
joint work with Herbert Edelsbrunner, Carl-Phillip Heisenberg and Gabriel Krens (IST Austria)