Topological Data Analysis : Persistent Homology and Applications

An extremely powerful tool in the field of topological data analysis (TDA) is persistent homology which seeks to quantify structure in a large data set. In particular, persistence can find homology classes for an underlying manifold even when obscured by noise. These homology classes can then give information about the underlying manifold, and thus, about the data of interest. In this talk, we will discuss the basics of persistence with no prior knowledge assumed. Time permitting, we will also discuss recent advancements for using statistical methods with TDA, as well as applications to signal processing and sensor networks.