My research interests lie mainly in the fields of low-dimensional topology and hyperbolic geometry.  In particular, I have been learning hyperbolic knot theory and working on knots and links in Seifert-fibred spaces such as the 3-torus and the unit tangent bundle of the modular surface.  

Publications and preprints: 

1. On the geometry of rod packings in the 3-torus

With Jessica S. Purcell 

Bulletin of the London Mathematical Society. 

Published open access Feb 2024. 

https://doi.org/10.1112/blms.12993 

(arXiv version: arXiv:2212.04662) 

2. A geometric classification of rod complements in the 3-torus

Proceedings of the American Mathematical Society. 

Published in Oct 2024. 

https://doi.org/10.1090/proc/16949

(arXiv version: arXiv:2307.06317)  

3. Volume bounds for hyperbolic rod complements in the 3-torus

With Norman Do and Jessica S. Purcell

Pacific Journal of Mathematics. 

Published in Sept 2025. 

https://doi.org/10.2140/pjm.2025.339.167 

(arXiv version: arXiv:2409.02357v2) 

4. Modular links: Bunch algorithm and upper volume bounds

With José Andrés Rodríguez Migueles

Accepted by Algebraic & Geometric Topology. 

Available at arXiv:2308.12847, 2023.  

5. Crushing Surfaces of Positive Genus

With Benjamin A. Burton, Thiago de Paiva and Alexander He 

Accepted by Algebraic & Geometric Topology. 

Available at arXiv:2403.11523, 2024. 

6. A lower bound for the volumes of modular link complements

With Dionne Ibarra and José Andrés Rodríguez Migueles 

Submitted for publication. Available at arXiv:2402.00400, 2024.  

7. Volumes, Lorenz-like templates, and braids 

With Thiago de Paiva and José Andrés Rodríguez Migueles 

Submitted for publication. Available at arXiv:2410.04391, 2024. 

8. A robot that unknots knots

With Dionne Ibarra, Louis H. Kauffman,  Emma N. McQuire, Gabriel Montoya-Vega, Sujoy Mukherjee, and Corbin Reid 

Submitted for publication. Available at arXiv:2504.01254, 2025.