An Introduction to Applied Topology

Abstract: This talk is an introduction to topology, as applied to data analysis and to sensor networks. The shape of a dataset often reflects important patterns within, and topology can help us visualize and understand these shapes. One example dataset with an interesting shape is the conformation space of the cyclo-octane molecule, which is a Klein bottle glued inside a sphere. As a second application of topology, we consider coverage problems for sensor networks. Suppose ball-shaped sensors are scattered in a domain, but unfortunately the sensors can't measure their locations (they're not equipped with GPS), and instead they only measure which sensors overlap. Can we determine if the sensors cover the entire domain? What if the sensors are moving?