Abstract: The language and tools of dynamical systems have long provided an avenue to solving problems in arithmetic geometry, particularly in the setting of abelian varieties. Famous instances of this include Ullmo and Zhang's proof of the Bogomolov Conjecture and Vojta's proof of the Mordell Conjecture (Faltings' theorem). However, the arithmetic of dynamical systems is best understood in the case of rational functions on the projective line, leaving voids in the higher-dimensional setting that complicate attempted applications of dynamical tools. In this talk, I will discuss a potential-theoretic result in higher-dimensional dynamics and how it can be applied to problems about points of small canonical height on abelian varieties. As time allows, I'll talk about related open problems and future directions.