My primary research interest is in the branch of mathematical logic known as model theory.  In particular, I am interested in classification theory (stability theory), NIP theories, dp-minimality, theories of ordered structures, and applications to combinatorics.

My published articles can be grouped into four main lines of research:

•  Studying when (elementarily) bi-embeddable models of a first-order theory are necessarily isomorphic (the "Schröder-Bernstein property") using Shelahian classification theory (my Ph.D. thesis and articles co-authored with Chris Laskowski);

• Groups, and especially ordered groups and Abelian groups, which have finite dp-rank or finite burden (various articles, some with Jan Dobrowolski, Alfred Dolich and David Lippel);

• Type amalgamation properties in stable and simple theories and connections with elimination of generalized imaginaries and a homology theory for types (joint work with Byunghan Kim and Alexei Kolesnikov);

• Most recently, exploring applications of a parametrized version of Presburger arithmetic to combinatorial problems and when parametric counting problems yield eventually quasi-polynomial formulas (joint work with Tristram Bogart, Danny Nguyen and Kevin Woods).

All of my papers can be found on my Google Scholar profile, and the majority can be downloaded for free from the arXiv.

Some recent papers and preprints:

• "Discrete sets definable in strong expansions of ordered Abelian groups" (joint with Alfred Dolich), undergoing revisions, arXiv preprint 2208.06929, 2023.

• "Topological properties of definable sets in ordered Abelian groups of burden 2" (joint with Alfred Dolich), to appear in the Mathematical Logic Quarterly. See the arXiv preprint 2207.08741, 2022.

• "Sets definable in ordered Abelian groups of finite burden,'' RIMS Kôkyûroku 2249 (Proceedings of the RIMS Model Theory Workshop 2023), 2023. Availible online here .

• "Definable sets in dp-minimal ordered Abelian groups," RIMS Kôkyûroku 2218 (Proceedings of the RIMS Model Theory Workshop 2021), pages 40-52, 2022. Availible online here .

• "Tame topology over definable uniform structures" (with Alfred Dolich), Notre Dame Journal of Formal Logic, vol. 63 (2022), no. 1, 51-79, preprint version available here. 

• "Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic" (with Tristram Bogart and Kevin Woods), Semigroup Forum vol. 102 (2021), p. 340-356. Preprint version available here.

• "A parametric version of LLL and some consequences: parametc shortest and closed vector problems" (with Tristram Bogart and Kevin Woods), SIAM Journal on Discrete Mathematics vol. 34 (2020),  no. 4, p. 2363-2387. Preprint version available here.

• "Parametric Presburger arithmetic: complexity of counting and quantifier elimination" (with Tristram Bogart, Danny Nguyen, and Kevin Woods), Mathematical Logic Quarterly vol. 65 (2019) no. 2, p. 237-250.  Preprint version available here.

• "A characterization of strongly dependent ordered Abelian groups" (with Alfred Dolich), Revista Colombiana de Matemáticas, vol 52 (2018), no. 2, p. 139-159. Preprint version of the article is available here.

• "Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior" (with Tristram Bogart and Kevin Woods), Discrete Analysis 2017:4, 34 pp., article available here.

• "Bounding quantification in parametric expansions of Presburger arithmetic," Archive for Mathematical Logic, vol. 57 (2018), p. 577-591, preprint version available here.

• "Homology groups of types in stable theories and the Hurewicz correspondence" (with Alexei Kolesnikov and Byunghan Kim) Annals of Pure and Applied Logic, volume 168 (2017), issue 9, p. 1710-1728.

• "Some remarks on inp-minimal and finite burden groups" (with Jan Dobrowolski), Archive for Mathematical Logic, vol. 58 (2019), no. 3-4, p. 267-274. Preprint version available here.

• "Strong theories of ordered Abelian groups" (with Alfred Dolich), Fundamenta Mathematicae volume 236 (2017), number 3, p. 267-296, preprint version available here.

My thesis advisor was Thomas Scanlon and my Ph.D. thesis was titled "When are elementarily bi-embeddable models isomorphic?" You can download it here .