Publications and other writing

Conjugacy for homogeneous ordered graphs
With Paul Ellis. Archive for mathematical logic, 2019. (ordered graphs in journal)

Hyperbinary numbers and fraction trees
With Paul Ellis and Japheth Wood.

On the classification of automorphisms of trees
With Kyle Beserra. Accepted to Contributions to discrete mathematics.

The classification of countable models of set theory
With John Clemens and Samuel Dworetzky.

On the classification of vertex-transitive structures
With John Clemens and Stephanie Potter. Archive for mathematical logic, 2019. (vertex-transitive structures in journal)

The set splittability problem
With P. Bernstein, C. Bortner, S. Li, and C. Simpson.

Two articles on the classification of C* algebras
Review of “The isomorphism relation for separable C* algebras” by G. Elliott, I. Farah, et al, and “Completeness of the isomorphism problem for separable C* algebras” by M. Sabok. Bulletin of symbolic logic, 2015. (elliott review in journal)

The conjugacy problem for automorphism groups of homogeneous digraphs
With Paul Ellis. Contributions to discrete mathematics, 2017. (homogeneous digraphs in journal)

On generalizations of separating and splitting families
With Daniel Condon, Luke Serafin, and Cody Stockdale. Electronic journal of combinatorics, 2016. (separating families in journal)

The classification problem for finitely generated operator systems and spaces
With M. Argerami, M. Kalantar, M. Kennedy, M. Lupini, and M. Sabok. Research report, 2014.

The conjugacy problem for automorphism groups of countable homogeneous structures
With Paul Ellis. Mathematical logic quarterly, 2016. (homogeneous structures in journal)

A López-Escobar theorem for metric structures, and the topological Vaught conjecture
With Martino Lupini. Fundamenta mathematicae, 2016. (lopez-escobar in journal)

Ioana’s superrigidity theorem and orbit equivalence relations
ISRN algebra, 2013. (superrigidity applications in journal)

Generalized Choquet spaces
With Philipp Schlicht. Fundamenta mathematicae, 2016. (choquet spaces in journal)

The fundamental theorem on symmetric polynomials
History’s first whiff of Galois theory. With Ben Blum-Smith. College mathematics journal, 2017. (symmetric polynomials in journal)

Borel Tukey morphisms and combinatorial cardinal invariants
With Tamás Mátrai and Juris Steprāns. Fundamenta mathematicae, 2013. (tukey morphisms in journal)

Automorphisms of corona algebras, and group cohomology
With Ilijas Farah. Transactions of the American mathematical society, 2014. (corona algebras in journal)

The hierarchy of equivalence relations on the natural numbers under computable reducibility
With Joel Hamkins and Russell Miller. Computability, 2012. (computable reducibility in journal)

Review of Invariant descriptive set theory
Review of “Invariant descriptive set theory” by Su Gao. Bulletin of symbolic logic, 2011. (gao review in journal)

Cardinal characteristics and countable Borel equivalence relations
With Scott Schneider. Mathematical logic quarterly, 2017. (cardinal characteristics in journal)

Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
With Joel Hamkins. Appears in Effective mathematics of the uncountable, ASL Lecture Notes in Logic, 2014. (ittm applications in journal)

Infinite time decidable equivalence relation theory
With Joel Hamkins. Notre Dame journal of formal logic, 2011. (ittm reducibility in journal)

Borel reductions of profinite actions of SLn(Z)
Annals of pure and applied logic, 2010. (profinite actions in journal)

The complexity of classification problems for models of arithmetic
With Roman Kossak. Bulletin of symbolic logic, 2010. (peano arithmetic in journal)

The conjugacy problem for the automorphism group of the random graph
With Paul Ellis and Scott Schneider. Archive for mathematical logic, 2011. (random graph in journal)

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism
Transactions of the American mathematical society, 2012. (abelian groups in journal)

Descriptive aspects of torsion-free abelian groups
Doctoral thesis, Rutgers University, 2008. (descriptive aspects in repository)