Published: Sept. 6, 2019

Henry Adams

Department of Mathematics, Colorado State University

An introduction to applied topology

 

This talk is an introduction to computational topology, as applied to data analysis and to sensor networks. The shape of a dataset often reflects important patterns within. Two such datasets with interesting shapes are a space of 3x3 pixel patches from optical images, which can be well-modeled by a Klein bottle, and the conformation space of the cyclo-octane molecule, which is a Klein bottle glued to a 2-sphere along two circles. I will introduce topological tools (persistent homology) for visualizing, understanding, and performing machine learning tasks on high-dimensional datasets. As a second application, I will describe how topology has been applied to coverage problems in mobile sensor networks.