Persistent homology is a key method in topological data analysis, a young but
rapidly growing field at the intersection of computational geometry and
algebraic topology. Persistence is used to describe the shape of data in a way
that generalizes clustering: besides considering what connected components
(clusters) are present in the data, it also describes their topology.
This talk will introduce persistence and some of its applications in materials
science, neuroscience, and cosmology. We will also discuss computation of
persistence at scale, and how lock-free and distributed data structures help
solve this problem.