  We apply persistent homology, the main method in topological data analysis,
to the study of demographic data. Persistence diagrams efficiently summarize
information about clusters or peaks in a region's demographic data. To
illustrate how persistence diagrams can be used for exploratory analysis, we
undertake a study of the 100 largest U.S.~cities and their Black and Hispanic
populations. We use our method to find clusters in individual cities, determine
which cities are outliers and why, measure and describe change in demographic
patterns over time, and roughly categorize cities into distinct groups based on
the topology of their demographics. Along the way, we highlight the advantages
and disadvantages of persistence diagrams as a tool for analyzing geospatial
data.
