Dr. Abigail Hickok (Dept. of Mathematics, Columbia)

2/1/2024  3:10pm

Abstract: Analyzing spatial data is often a complex task. In this talk, we will explore applications of topological data analysis (TDA) to several geospatial and geospatiotemporal data sets. First, we’ll use persistent homology to quantify the accessibility of geographically-distributed “resources” (e.g., polling places, medical care centers, and public green spaces) and to identify “holes in coverage.” We consider case studies in both polling-place accessibility as well as public-park accessibility. For the former, we construct a filtration that takes into account real-world factors such as waiting time and travel time, and for the latter, we formulate a multiparameter persistent homology framework in order to take into account the heterogeneous quality of the parks. Then, I’ll discuss an application of TDA to two COVID-19 data sets (LA infection rates and NYC vaccination rates). We use persistent homology to identify “anomalies” (local maxima in the infection-rate data and local minima in the vaccination data) and analyze global spatial structure; we use vineyards to study how the data changes with time. Each data set requires a unique choice of filtration (or bifiltration) in order to model the problem appropriately, and in each case, I will emphasize why TDA should be the right tool for the job.