Persistent homology: an introduction and some example applications

Katharine Turner (EPFL)


Sometimes we may want to study a set of objects that contain interesting geometrical or topological structure. For example each piece of data may be a random packing of spheres, an image, a network, or the surface of a bone. In such a scenario it is sensible to calculate some summary of its topological and/or geometrical structure and then compare these summaries instead of the original complicated objects. Persistent homology is a popular tool. In this talk I will define persistent homology and the topological summaries of the persistent diagram and the persistent homology rank function. I will also show some examples of applications.