Research

My research interests include knot theory, categorification, representation theory, and low-dimensional topology. Nowadays, I spend most of my time thinking about colored HOMFLY-PT and type-A invariants for rational links.

Here is an ever-growing list of mathematical topics I want to think about someday (in no particular order):

• Non type-A link homology

• The AJ Conjecture

• The Volume Conjecture

• Skein lasagna modules

• Skein algebras

• Incompressible surfaces in knot exteriors

• Graph homology 

• Annular Khovanov homology

• Knotted surfaces

• (Quantum) cluster algebras

My previous research was in graph theory, where I studied algebraic and combinatorial properties of prime graphs as part of an REU with Texas State University. I also participated in a project for my undergraduate complex analysis course, which resulted in a publication.

Here is a list of my undergrad publications:

1. Minimal Prime Graphs of Finite Solvable Groups, Chris Florez, Jonathan Higgins, Kyle

Huang, Thomas M. Keller, Dawei Shen, preprint, accepted pending revisions by Rocky

Mountain Journal of Mathematics, arXiv:2011.10403 [math.CO]

2. The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs, Chris

Florez, Jonathan Higgins, Kyle Huang, Thomas M. Keller, Dawei Shen, Involve, Vol. 17

(2024), No. 1, 107–120, arXiv:2011.08938 [math.CO]

3. **The Prime Graphs of Some Classes of Finite Groups, Chris Florez, Jonathan Higgins, Kyle Huang, Thomas M. Keller, Dawei Shen, Yong Yang, Journal of Pure and Applied Algebra, 226 (2022), 106990, 19 pp., arXiv:2101.00363 [math.GR]

4. A Groundwater Contaminant Extraction Model Using Complex Potentials, Paul Isihara, Lucy Henneker, Andrew Luhmann, Nathaniel Bowden, Daws Bremner, Jonathan Higgins,

Stephen McKay, Julio Reyes, UMAP Journal 43.1, 2022, 39-76

**I am listed as an author of this paper as part of the REU group, but I did not work on this paper in particular.