  We introduce a novel set of observables associated to the rapidly developing
field of persistent homology for the quantitative characterization of nuclear
collisions and their evolution. Persistent homology allows for the
identification of topological and homological characteristics of distributions
in multi-dimensional spaces. We demonstrate here how to apply the toolset of
persistent homology to the extraction of novel clustering signatures and the
identification of long-range flow correlations in the particle production
process of nuclear collisions.
