Discrete Mathematics Seminar

Speaker: Zoe Wellner, Arizona State
Title: “The topology connecting graph colorings, graph matchings, and discrete geometry”
Abstract: The classical Borsuk--Ulam theorem states that for any continuous map from the sphere to Euclidean space, $f\colon S^d\to \mathbb{R}^d$, there is a pair of antipodal points that are identified, so $f(x)=f(-x)$. Through a generalization of this theorem, we provide a new proof of topological Hall's theorem that relates directly to chromatic number bounds and Radon's theorem in discrete geometry. By tying these results together, we can provide more structural insights to the combinatorial structures.

The Discrete Math Seminar (DMS) is intended for Kennesaw State faculty working in the various areas of algebra, number theory, and discrete mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone interested in attending.