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. Recovering a Structure from its Tree of Tuples (with J. Knight and M. Harrison-Trainor)
   Submitted for publication

2. Switching Categoricity Behavior with a Given Degree (with J.J. Valenzuela Morales and J. Villano)
   Submitted for publication

3. Tennenbaum-like Theorems for Cohesive Powers (with P. Shafer)
   Submitted for publication

4. Infinite Belligerent Jump Inversion and Computable Scott Analysis (with U. Andrews and H. Zhu)
   Submitted for publication

5. Scott Analysis below the Vaught Ordinal (with D. Rossegger and D. Turetsky)
   Submitted for publication

6. Computable Scott Sentences and the Friedman-Stanley Embedding (with J. Knight)
   To appear in J. Symb. Log.

7. Enumerative Combinatorics of Homogeneous Linear Orderings
   Submitted for publication

8. sp-Homogeneous Linear Orderings (with W. Calvert, D. Cenzer, V. Harizanov, and K. Ng)
   Submitted for publication

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

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

    Submitted for publication

11. Optimal Syntactic Definitions of Back-and-Forth Types (with M. Harrison-Trainor and R. Chen)
    To appear in Trans. Amer. Math. Soc.

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

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

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

15. 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

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

17. The Scott Sentence Complexity of Linear Orders (with D. Rossegger)
    J. Symb. Log., 90(2025), no. 4, 1563-1592.

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

19. 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.