My research focuses on interactions between computational complexity, topology, and logic. More specifically, I am pursuing research into the topology of reconfiguration problems and how this reflects the computational complexity of related decision problems. Additionally, I am pursuing research into descriptive complexity theory over first-order structures, where complexity classes are defined using Blum-Shub-Smale machines. One complexity class of special interest is the class ER, whose defining complete problem is the existential theory of the reals. I am also interested in software for mathematical research and education, such as Julia and SageMath.