SIGNATURE WORK
CONFERENCE & EXHIBITION 2022

This paper looks at the classical problems of gerrymandering and districting under the framework of Topological Data Analysis (TDA), a newly developed tool from algebraic topology, which helps to analyze data without using the notion of distance. Although the number of applications of TDA is growing rapidly, it was not applied to study geospatial data until recently. In this paper, we leverage the pipeline created by Duchin et al. that employs the Markov chain Monte Carlo method to generate an ensemble of maps and analyze it using algebraic topology concepts like persistence diagrams. We applied the pipeline to study Texas and Arizona elections (including the Presidential elections of 2012 and 2016). We also used the method to look at the racial demographics of Texas.