My interests lie in the intersection of functional analysis, harmonic analysis, and algebraic combinatorics. Currently, my work involves leveraging analytical tools and existing combinatorial objects to discover rich mathematical configurations. Fundamentally this research is anchored in pure mathematics, yet it sees many applications in fields such as signal processing and quantum information theory.
As an undergraduate, I also did some work in extremal combinatorics, in particular (anti-)Ramsey theory, some of which carried on after I graduated. Last but not least, I have taken a recent interest in data science, machine learning, and AI.
Research_Statement_Fallon.pdf