Spanning Trees and Fair Voting Maps

Abstract: In the past decade, mathematicians have played an increasingly important role in evaluating the fairness of legislative district maps. We have contributed to legal challenges against gerrymandered maps and assisted commissions in drawing fair maps from the outset. Modern methods rely on MCMC algorithms that generate large ensembles of random maps. A central ingredient in these algorithms is a random spanning tree of a graph. After explaining this connection, I will describe some new results on spanning trees and graph partitions that were motivated by this application.

Speaker's bio: Dr. Kristopher Tapp is a mathematics professor at Saint Joseph's University. He is the author of 3 books and over 30 research papers ranging from Differential Geometry to Graph Theory applied to elections.

Moderator's bio: Matt Insall is a mathematician, father of four (two sons and two daughters), and grandfather of four boys and two girls. He’s written poems and a song, and performs occasionally at open mic events. Matt retired in September 2024 from his position in the faculty of the Missouri University of Science and Technology Department of Mathematics and Statistics after 35 years in that position.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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