Sequence Packings and STEM CLUSTERS: A Research Overview in Two Parts
Michael Ferrara, University of Colorado Denver
Starting from my early work in combinatorics and graph theory, my re- search has expanded in the last few years to include projects in mathematics and interdisciplinary STEM education. In this talk, I will give some results from my recent and ongoing work in these areas and hopefully give some insight into my overall approach to research.
Part I: New Results on Packing Graphic Sequences
The degree of a vertex v in a graph is the number of edges that include v. A sequence π = (d1,..., dn) is graphic if there is a simple graph G whose list of degrees is π; in this case we say that G is a realization of π. A given graphic sequence may have a diverse collection of realizations, and the prob- lem of determining when some or all realizations of a graphic sequence have a given property has attracted a great deal of interest.
Here, we present some recent results and ongoing work on when a pair of graphic sequences pack, meaning that they can be realized by edge-disjoint graphs on the same ordered vertex set. We prove several extremal degree sequence packing theorems that parallel central results and open problems from the graph packing literature. We will then discuss some ongoing work related to exploring the space of packed realizations of a pair of graphic se- quences, motivated in part by problems in network science.
The need for a more robust, well-trained STEM workforce is becoming increasingly acute in the U.S., and encompasses the need to recruit and retain a larger and more diverse population of undergraduate STEM majors. While many efforts centered in traditional P-16 classrooms have proven effective, it is also imperative to explore undergraduate student learning in other settings.
The STEM Club Leadership for Undergraduate STEM Education, Re- cruiting and Success (STEM-CLUSTERS) project is engaging undergradu- ate STEM majors in organizing middle and high school STEM clubs and teams in and around Denver, CO. Here, we describe the essential elements of our outreach model and discuss findings from our first cohort of eleven un- dergraduate outreach Fellows, related to their content knowledge, metacog- nition, communication skills, and identity as a future STEM professional.