For k >= 2, the k-coloring graph C(G) of a base graph G has a vertex set consisting of the proper k-colorings of G with edges connecting two vertices corresponding to two different colorings of G if those two colorings differ in the color assigned to a single vertex of G. A base graph whose […]
Opioid addiction has become a national health crisis in recent years, with involvement in 66% of all drug overdose deaths in 2016 and high economic costs. In contrast to the dynamics of a classic disease or illicit drug epidemic, opioid addiction has its roots in legal, prescription medication - a fact which greatly increases the […]
TOPIC: The Mathematics of Reapportionment and Census Data Every ten years, the United States Census Bureau conducts a count of all persons living in the United States; one of those […]
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms […]
The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In this talk, we will define the orthosymplectic Lie superalgebras, realize $\mathfrak{osp}(1|2n)$ as differential operators on complex polynomials, and describe the space of polynomials in commuting […]
In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana’s the claim to fame for his discovery. About the time the debate about the bill concluded, Purdue University professor Clarence A. Waldo serendipitously came […]
David Hilbert's Grundlagen der Geometrie is a rare example of a historical mathematics text that is still profitably read today and continues to inspire research in mathematics, computer science, and philosophy. The effort of publishing an English translation of Hilbert in 1902 involved a diverse swath of the American mathematical community. Edgar Jerome Townsend completed a first draft […]
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In this talk, I'll attempt to give an introduction to the beautiful world of tropical geometry. As an application, I'll describe work with Siddarth Kannan (Pomona 2018) and Shiyue Li (Mudd 2017) using tropical geometry to compute the cohomology of certain moduli spaces, called heavy/light Hassett spaces, which are of interest in a wide range of […]
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