Topological data analysis aims to discover structure in large, complex, finite datasets by examining the filtered (co)homology of nested CW complexes built over the data points. After briefly surveying this field, I will outline a new algorithm to extract the coarsest possible stratification of such a CW complex into cohomology manifolds.

There will be pictures. There will be cosheaves. And if time permits, there will be pictures of cosheaves.