Background and Description

As a graduate student, I learned that the best way to understand something was to explain it to a colleague or write it down with clarity. Often times during my career, I found myself making observations or connections that were not necessarily explicitly stated in literature, but not significant enough for publication. I was convinced that these ideas would one-day lead to publications - and they very well still could - but my time in academia has since come to an end. This document is an exposition of a few seemingly unrelated connections that I made during my graduate career.