I am interested in to varying degrees ordered sets, general topology, point-free topology, Boolean algebras, set-theory, universal algebra, and model theory. Most of my previous mathematics research involves dualities that are similar to Stone duality. I am currently interested in using the Boolean-valued approach to forcing to study objects such as Boolean algebras and frames in the ground model (i.e. Boolean-valued point-free topology). Furthermore, I am also interested in self-distributive algebras with operations of arbitrary finite arity and their relations with algebras of rank-into-rank elemetary embeddings and other mathematical structures.