Wesley Hamilton – GMA Seminar

Title: Homology: Redux

Abstract: Topological Data Analysis (TDA) is a relatively recent area of applied topology, in which tools from algebraic topology are used to understand the topology of data sets. The TDA pipeline is, in short, the following: a simplicial complex (to be defined) is associated to the data set, the persistent homology (to be defined) is computed, and the collection of birth/death times of topological features/the barcode (to be defined) is reported. During this talk, we’ll define all of the terms above and see a few instances of TDA in action. In particular, we’ll see a number of different ways for constructing simplicial complexes (specialized to different types of data), how to interpret barcodes, and finally some results on the statistics of barcodes. No previous TDA or algebraic topology experience is required.