Tools from Computational Topology, with applications in medicine and the life science

The field of topology, and in particular computational topology, has produced a powerful set of tools for studying both model systems and data measured directly from physical systems.  I will focus on three classes of topological tools:  computational homology, topological persistence, and Conley index theory.   To illustrate their use, I will discuss recent projects studying coupled-patch population dynamics, flickering red blood cells, and pulse-coupled neurons.