Title: Lecture 2: The coherent matching distance in 2D persistent homology.
Speaker: Patrizio Frosini (University of Bolohna)
Abstract: Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions associated with lines having a positive slope, it has two main drawbacks. First, it forgets the natural link between the homological properties of filtrations associated with lines that are close to each other. As a consequence, part of the interesting homological information is lost. Second, its intrinsically discontinuous definition makes it difficult to study its properties. In this lecture we illustrate a new matching distance for 2D persistent Betti numbers, called coherent matching distance and based on matchings that change coherently with the lines we take into account. Its definition is not trivial, as it must face the presence of monodromy in multidimensional persistence.
Seminar URL: http://www.tgda.osu.edu/mini-course-frosini.html