Research

Research Interests

Broadly speaking, my research interests include knot theory, categorification, and low-dimensional topology. Lately, I have spent most of my time thinking about (colored) sl(N) and HOMFLY-PT homology of rational tangles and links, as well as the Links-Quivers Correspondence. However, I am always interested in finding new problems to work on and people to collaborate with!

Papers

1. Minimal sl(N) Complexes of Rational Tangles via the Fukaya Category, in preparation

2. *Rational Knots, Quivers, and Tails of Colored HOMFLY-PT Polynomials (with Elijah Berry, Rongjiang Guo, Eduardo Perez, and Henry Zaslow), in preparation

3. A Geometric Approach to the Links-Quivers Correspondence I: Rational Tangles, preprint,  https://arxiv.org/abs/2603.01303

4. A Geometric Approach to the Links-Quivers Correspondence II: Rational Links, preprint,  https://arxiv.org/abs/2603.01312

5. **Minimal Prime Graphs of Finite Solvable Groups (with Chris Florez, Kyle Huang, Thomas M. Keller, Dawei Shen), preprint, accepted pending revisions by Rocky Mountain Journal of Mathematics, https://arxiv.org/pdf/2011.10403

6. **The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs (with Chris Florez, Kyle Huang, Thomas M. Keller, Dawei Shen), Involve (2024), https://arxiv.org/pdf/2011.08938

7. **The Prime Graphs of Some Classes of Finite Groups (with Chris Florez, Kyle Huang, Thomas M. Keller, Dawei Shen, Yong Yang), Journal of Pure and Applied Algebra (2022), https://arxiv.org/pdf/2101.00363

8. **A Groundwater Contaminant Extraction Model Using Complex Potentials (with Paul Isihara, Lucy Henneker, Andrew Luhmann, Nathaniel Bowden, Daws Bremner, Stephen McKay, Julio Reyes), UMAP Journal (2022)

*denotes papers written with undergrads in a mentoring capacity

**denotes papers during my time as an undergrad (mostly graph theory)