An Introduction to Multiparameter Persistence

Understand

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology.

• However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led to consider multiparameter persistence, which associates to the data a space equipped with a multiparameter filtration.
• Multiparameter persistence has become one of the most active areas of research within TDA, with exciting progress on several fronts.
• In this article, we introduce multiparameter persistence and survey some of this recent progress, with a focus on ideas likely to lead to practical applications in the near future.