New Applications of the Container Method

During the funded period I began an investigation into a new area of research: the so-called container method. The original plan of the proposal was to prove several new applications of this method and to collaborate with one of the method’s inventors. Ultimately, we did not produce new research via the container method. However, as is often the case in mathematics, our pursuits lead in unplanned directions and the funded period ended up being very productive in two different (although related) research areas

Counting subgraphs in F-free graphs

During the funded period I continued what had been a preliminary investigation into a generalization of the central theory of extremal graph theory. With the help of funding from the UGP grant I was able to cover the travel expenses for several very productive visits