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 […]
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 population counts will be carried out this year (2020). This Census is mandated by the US Constitution; it counts all people residing in the United […]
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 […]
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 […]
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 […]
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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 […]
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