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.

Publications:

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