Research
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:
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)
A geometric classification of rod complements in the 3-torus
Submitted for publication. Available at arXiv:2307.06317, 2023.
Modular links: Bunch algorithm and upper volume bounds
With José Andrés Rodríguez Migueles
Submitted for publication. Available at arXiv:2308.12847, 2023.
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.
Crushing Surfaces of Positive Genus
With Benjamin A. Burton, Thiago de Paiva and Alexander He
Submitted for publication. Available at arXiv:2403.11523, 2024.
Can you see the complement of the three rods in the 3-torus is the complement of the Borromean rings in the 3-sphere?
Non-destructive crushing
(Some notes taken during a mini-course given by Alex He in July 2023)
Projects with preprints in progress:
Volume bounds for hyperbolic rod complements in the 3-torus
With Norman Do and Jessica S. Purcell
Upper volume bounds for hyperbolic links in the 3-sphere
With Thiago de Paiva and José Andrés Rodríguez Migueles
Relationship between bunches of strands in a modular knot and its hyperbolic volume?