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Dylan Shepardson works on mathematical problems that are motivated by applications in other disciplines, like biology, epidemiology, sociology, or archaeology. He is especially interested in new and unusual applications of optimization theory. In most physical, biological, and economic systems, a property is being optimized (like energy or entropy in physical systems, or reproductive success in evolutionary biology), and optimization techniques offer interesting insights into these systems. Shepardson's recent projects include voting theory and its connections to combinatorial geometry, infectious disease modeling, and the problem of using collections of radiocarbon data to estimate dates of the earliest human settlements of Pacific islands.