Christina Kapatsori: Choosing the geometry of persistence

Abstract.

Persistent homology provides a way to extract topological information from data. However, turning this information into statistically useful, stable invariants requires a choice of pseudometric between persistence modules, a process known as hierarchical stabilization. This choice is far from canonical: different phenomena may require different notions of similarity, and what should be regarded as noise in one setting may carry important information in another. In this talk, we shall provide a recipe for constructing a zoo of pseudometrics on persistence modules, which allows us to choose the geometry flexibly as well as to investigate the properties of the spaces these distances define.