Research

I work in mathematical logic, in model theory. Model theory studies the information encoded in well-known mathematical objects such as linear orders, lattices, graphs, groups and fields. For a particular graph, the question is not so much what we can say about the graph, but what the graph can “say about itself.” My research has focused on classification theory which aims to categorize objects along certain lines according to the complexity of information encoded within the object. As a result of this focus, my work intersects areas of structural Ramsey theory, or, the theory of patterns that can be found in large and diverse enough initial configurations.

Slides:

“Transfer of the Ramsey Property between Classes” (BLAST 2015@UNT)

“Tree indiscernibles and a Ramsey Class of Trees” (JMM 2013)

Publications:

  • “Indiscernibles, EM-types, and Ramsey Classes of Trees,” Notre Dame Journal of Formal Logic
    56 (2015), no. 3, pp. 429-447. on arxiv
  • (with Byunghan Kim and Hyeung-Joon Kim) “Tree Indiscernibilities, Revisited,” Archive for
    Mathematical Logic 53 (2014), no. 1-2, pp. 211-232. on SpringerLink on arxiv
  • “Characterization of NIP theories by ordered graph-indiscernibles,” Annals of Pure and Applied Logic 163 (2012), pp. 1624-1641. on sciencedirect on arxiv
  • A draft of my thesis: Characterization Theorems by Generalized Indiscernibles.

Work in Progress:

  • (with Dragan Masulovic) “Categorical Constructions and the Ramsey Property,” (submitted) on arxiv
  • (with Vincent Guingona and Cameron Donnay Hill) “Characterizing Model-Theoretic Dividing Lines via Collapse of
    Generalized Indiscernibles,” (submitted) on arxiv

Notes: