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 […]
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 […]
Biological invasions often have outsized consequences for the invaded ecosystem and represent an interesting challenge to model mathematically. Landscape heterogeneity, non-local or time-dependent spreading mechanisms, coarse data, and air or […]
It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful […]
In this talk I will discuss a rather unique collection of tools and how they have been used to understand the spread of Influenza virus in the State of Montana. […]
Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules, generalizing both the quiver invariant and the quandle module […]
Data coming from Monte Carlo experiments is often analyzed in the same way as data from more traditional sources. The unique nature of Monte Carlo data, where it is easy […]
Let S be a set of k > n points in n-dimensional Euclidean space. How many parallel hyperplanes are needed to cover it? In fact, it is easy to prove that every such set can be covered by k-n+1 parallel hyperplanes, but do there exist sets that cannot be covered by fewer parallel hyperplanes? We […]
Let K be a field and S = K be the polynomial ring in n variables over K. For a graded S-module M with minimal free resolution the Castelnuovo-Mumford regularity is defined. We survey a number of recent studies of the Castelnuovo-Mumford regularity of the ideals related to a graph and their (symbolic) powers. Our […]
Antibodies are the standard biomolecule for marking molecular structures and delivering drugs due to their specific binding capabilities. However, they are expensive to produce and their relatively large size prevents […]
Several conditions are known for a self-inversive polynomial that ascertain the location of its roots, and we present a framework for comparison of those conditions. We associate a parametric family of polynomials p_α(x) to each such polynomial p, and define cn(p), il(p) to be the sharp threshold values of α that guarantee that, for all […]
In this talk, I will describe an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express […]
