I'm largely interested in topological data analysis, and in particular, persistent homology, in which I work on both theory and application. I'm also broadly interested in complex social systems, including models of opinion dynamics on networks. My advisor is Professor Mason Porter.
Before I landed in applied mathematics, my main interest was in algebra. In fact, I even wrote a Masters Thesis on algebra! For my masters, I worked with Professor Bill Jacob on quadratic forms over fields. More specifically, I worked towards building an analog of Witt ring over quadratic extensions of fields to the setting of abstract Witt rings.
Undergraduate Mentorship
Mentoring students is one of the things that I've really enjoyed, even moreso than research itself. My involvement on this front has largely been through the Directed Reading Program (DRP), although I've also co-mentored students with my advisor as well. If you're interested in some of the stuff I'm interested in, feel free to reach out!
Preprints and Publications
- Interval Decomposition for Persistence Modules Freely Generated over PIDs.
J. Luo, G. Henselman-Petrusek.
Preprint (2023). - Bounded-Confidence Models of Opinion Dynamics with Adaptive Confidence Bounds.
G. J. Li*, J. Luo*, M. A. Porter.
Preprint (2023). - Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites.
A. Hickok*, B. Jarman*, M. Johnson*, J. Luo*, M. A. Porter.
To Appear in SIAM Review (2024). - Pre-processing and classification of hyperspectral imagery via selective inpainting.
V. Chayes, K. Miller, R. Bhalerao, J. Luo, W. Zhu, A. L. Bertozzi, W. Liao, S. Osher.
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).