Henry Adams
Department of Mathematics, Colorado State University
An introduction to applied topology
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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.
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