Title: Lecture I: Persistence Beyond Vector Spaces
Speaker: Amit Patel (Colorado State University)
Abstract: In classical persistent homology, we start with a filtration of a space indexed by the real line and apply homology with field coefficients. The result is a persistence module of vector spaces. As the filtration parameter increases, homology is born and homology dies. These births and deaths are encoded in the persistence diagram of the module. The original definition of the persistence diagram generalizes very naturally to persistence modules valued in any skeletally small abelian category. I will talk about these generalized persistence diagrams.
- Patel. Generalized persistence diagrams.
- McCleary, Patel. Bottleneck stability for generalized persistence diagrams.
Seminar URL: https://tgda.osu.edu/