My research is in mathematical logic, specifically set theory and computability.
In computability, my current work is in the connections between computable model theory and the model-theoretic concept of ultrahomogeneity. This includes classifying which structures satisfy a weaker version of being ultrahomogeneous and comparing this weak homogeneity to computable categoricity.
In set theory, I am investigating properties of definable (closed, Borel, etc.) graphs on Polish spaces as well as more general topological spaces. A focus of this work is on characteristics of graphs other than the chromatic number; namely the coloring number and the loose number, along with definable versions of these invariants.
Computability and Categoricity of Weakly Homogeneous Boolean Algebras and Abelian p-Groups. Accepted for Downey Festschrift (with Doug Cenzer and Selwyn Ng), World Scientific Press. Abelian p-groups and Boolean Algebras
Cardinal Invariants of Closed Graphs (with Jindrich Zapletal). Published in Israel Journal of Mathematics. Closed Graphs Loose Number
Computability and Categoricity of Weakly Ultrahomogeneous Structures (with Douglas Cenzer). Published in Computability. CompCat of WUH Structures
Construction of Directed Strongly Regular Graphs: DSRG Paper
Google Scholar Page: https://scholar.google.com/citations?user=wFvBmqMAAAAJ&hl=en