Mini-course: Foundations of Topological Data Analysis

Michael Lesnick, IMA, University of Minnesota, Jose A. PereaDuke University and Matthew Wright, IMA, University of Minnesota.

Abstract: In the last 15 years, there has been surge of interest and activity in the application of topological methods to the analysis of data, yielding not only practical new tools for studying data, but also some pleasant mathematical surprises.

We will present an introduction to topological data analysis, with an emphasis on persistent homology, a primary tool of the field.  Topics will include the algebraic structure of persistence modules, computation of persistence barcodes, zig-zag persistent homology, and the stability of persistence.