Speaker: Peter Bubenik
Abstract. Topological Data Analysis (TDA) is a new approach to analyzing complicated geometric and/or high dimensional data for which traditional approaches don't work as well one would like. The central mathematical object of TDA is the persistence module, which can be understood using the language of a number of different branches of mathematics. It turns out that taking an applied viewpoint on this algebraic object leads us to new mathematics. I will give an introduction to TDA focusing on its mathematical foundations. I will also describe the pipeline of turning input data into persistence modules and then representing these persistence modules in a way that can be combined with tools from statistics and machine learning.