Research

While my primary interest lies in computable structure theory, this area intersects with many areas in mathematical logic and beyond. In the boldface version of the theory, the analysis is highly structural and resembles countable model theory or, in practice, a sort of countable combinatorics. This relates tightly to problems in descriptive set theory, which views these same problems from a topological perspective.

I am also actively working on projects in reverse mathematics, which aims to understand the combinatorial core of proofs and theorems.

Publications and preprints:

  1. Computability of Separation Axioms in Countable Second Countable Spaces (with A. DeLapo)
    Submitted for publication

  2. Classifying the Complexities of Models of Arithmetic (with M. Łełyk, D. Rossegger and P. Szlufik)

    Submitted for publication

  3. Optimal Syntactic Definitions of Back-and-Forth Types (with M. Harrison-Trainor and R. Chen)
    Submitted for publication

  4. Scott Spectral Gaps are Bounded for Linear Orderings (with M. Harrison-Trainor)
    Submitted for publication

  5. Scott analysis, linear orders and almost periodic functions (with M.Harrison-Trainor and M. Ho)
    To appear in Bull. Lond. Math. Soc., 57 (2025), no. 4, 1118-1139

  6. Hybrid Maximal Filter Spaces
    Twenty Years of Theoretical and Practical Synergies, 85–99. Lecture Notes in Comput. Sci., 14773 (2024)

  7. The Borel Complexity of the Class of Models of First-Order Theories (with U. Andrews, S. Lempp, D. Rossegger and H. Zhu)
    Proc. Amer. Math. Soc., 153 (2025), 4013-4024

  8. Generically Computable Linear Orderings (with W. Calvert, D. Cenzer and V. Harizanov)
    Ann. Pure Appl. Log., 176 (2025), no. 8, 103612

  9. The Scott Sentence Complexity of Linear Orders (with D. Rossegger)
    To appear in J. Symb. Log.

  10. The omega-Vaught’s Conjecture (with A. Montalban)
    Trans. Amer. Math. Soc., 376 (2023), no. 8, 5989–6008.

  11. An Upper Bound for the Restricted Online Ramsey Number (with X. He and H. Zheng)
    Discrete Math., 342 (2019), no. 9, 2565-2569

For more information on fellowships, awards, and conference talks, please refer to my CV. For more information about my research, please refer to my research statement. My thesis can be found here.

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