Primož Škraba, An Overview of Persistent Homology

This talk will be designed as an introduction to persistent homology or more generally persistence. Persistence comes in many different flavors: homology, cohomology, local, robustness, to name a few. In addition to reviewing definitions and properties, I will motivate the uses of the different various flavors through applications. Time permitting,  I will discuss what theorems we need to prove to obtain theoretical guarantees for algorithms based on persistence. In particular I will discuss various sampling conditions required for computing the various flavors on point clouds.