Working under an undergraduate research award, Elyot was presented with a list of well-known open problems and rapidly proceeded to solve several of them. The most important relates to Kuratowski's theorem on closures in topological spaces and how it relates to formal languages. In particular, he discovered a clever and subtle proof that there is a clopen partition between two words if, and only if, the words do not commute. In the short time since then, Elyot's ideas on the topological separation of words have already been taken up by researchers in Europe, which shows that these ideas are important and in the mainstream of theoretical computer science.

After completing the work above, Elyot joined a separate research project in the area of Combinatorics and Optimization, and produced interesting results on approximation algorithms for NP-hard covering problems. In addition to possessing mathematical skills, Elyot is an expert programmer and has had a number of programming jobs while in college.