Pure PGR Seminar - "An Excision Theorem for Persistent Homology", Megan Palser (University of Southampton) Seminar

Event details

Persistent homology has become an increasingly popular area of research since its invention around the beginning of the century, partly due to its power as a tool in data analysis. Aside from its practical applications, there is also much research to be done into the formal properties of persistent homology. In 2008, Robert Ghrist described persistent homology as "a homology theory for point-cloud data". In light of this description, in this talk we will investigate whether some classical homological properties can be said to hold - at least in some form - for persistence. In particular I will present a new result - an excision theorem for persistent homology. This can be used to recover Barbara DiFabio and Claudia Landi's 2011 result concerning a Mayer-Vietoris sequence for persistent homology, which has been applied in the field of shape recognition.