Topological Data Analysis of Voting-Site Coverage

Abstract: In many cities in the United States, it can take a very long time to go to a polling site to cast a vote in an election. To find such "voting deserts" in an algorithmic way, we use persistent homology (PH), which is a type of topological data analysis (TDA) that allows one to detect "holes" in data. In this talk, we'll give an introduction to TDA and PH. We will then discuss our recent work on PH to detect voting deserts and in the coverage of other resources.

Mathematics

Audience: general audience

Comments: (Use interactive livestream for Q&A but the view-only livestream should have better sound.)

Abigail Hickok is an NSF postdoctoral fellow in the Department of Mathematics at Columbia University. Prior to joining Columbia, she completed a PhD in applied mathematics at UCLA in 2023, and she received her undergraduate degree in mathematics at Princeton in 2018. Her research is on the theory and applications of geometric and topological data analysis.

Mason Porter is a professor in the Department of Mathematics at University of California, Los Angeles (UCLA). He earned a B.S. in Applied Mathematics from Caltech in 1998 and a Ph.D. from the Center for Applied Mathematics at Cornell University in 2002. Mason held postdoctoral positions at Georgia Tech, the Mathematical Sciences Research Institute, and California Institute of Technology (Caltech). He joined as faculty at University of Oxford in 2007 and moved to UCLA in 2016. Mason is a Fellow of the American Mathematical Society, the American Physical Society, and the Society for Industrial and Applied Mathematics. In recognition of his mentoring of undergraduate researchers, Mason won the 2017 Council on Undergraduate Research (CUR) Faculty Mentoring Award in the Advanced Career Category in the Mathematics and Computer Science Division. To date, 26 students have completed their Ph.D. degrees under Mason's mentorship, and Mason has also mentored several postdocs, more than 30 masters students, and more than 100 undergraduate students on various research projects. Mason's research interests lie in theory and (rather diverse) applications of networks, complex systems, and nonlinear systems.

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NYU CDS Math and Democracy Seminar

Series comments: The Math and Democracy Seminar features research on contact points between the mathematical sciences and the structure of democratic society. The purpose of the seminar is to stimulate mathematical activity on problems relating to democracy, and to foster interdisciplinary collaboration between mathematicians and other scholars and democratic stakeholders.

Examples of topics of interest include detection of gerrymandering, fairness and accountability of algorithms used in social decision-making, voting and apportionment theory, applications of statistics to discrimination law and the census, and mathematical modeling of democratic processes. The scope is not limited to these and is expected to expand as further applications emerge.

Seminars currently conducted via Zoom (with some events also in person). Look for links in individual talk descriptions.

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