Speaker: Facundo Mémoli
Abstract. Persistent Homology can be viewed as a method for extending tools of homotopy theory to discrete objects, namely finite metric spaces.
Persistent Homology assigns a tower of vector spaces to a finite metric space. These towers of vector spaces can be characterized up to isomorphism by multisets of points in the plane. These multisets are typically referred to as persistence diagrams or persistence barcodes, can be computed in time polynomial on the cardinality of the finite metric spaces, and are used in practical data analysis applications as features.
Several methods exist for constructing these towers, with the most prominent arising from the so called Vietoris-Rips simplicial construction. Interestingly, the persistence diagrams arising from this construction are Lipschitz continuous with respect to the Gromov-Hausdorff distance.
In this talk we will overview ideas related to the persistent homology of finite metric spaces and describe some open questions.