Jerry Luo

Research

Here is a copy of my Research Statement.

I'm a mathematician interested in socially-motivated problems, working as a postdoc at the Knowledge Lab under the mentorship of Professor James Evans. Lately I've been thinking about how to use persistent homology to study the topological structure of spaces of knowledge and how it changes in time.

My research interests can be characterized as an amalgamation of topological data analysis and complex social systems. Within topological data analysis, I've worked in persistent homology, including both theory and application. Within complex social systems, my work includes the agent-based modeling of opinion dynamics on networks.

Here is a link to my thesis. My PhD advisor was 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! 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.

Mentorship

**I am always open to mentoring students. If my research areas are of interest to you, please feel free to reach out if you're interested in working with me!**

Mentoring students is one of the things that I've really enjoyed, even moreso than research itself. As a PhD student, I was involved in the Directed Reading Program (DRP) in the mathematics department at UCLA. I also co-mentored students with my advisor. If you're interested in some of the stuff I'm interested in, feel free to reach out!

Preprints and Publications

*Equal Contribution

  1. Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain.
    J. Luo, G. Henselman-Petrusek.
    Preprint (2025). arXiv

  2. Bounded-Confidence Models of Multi-Dimensional Opinions with Topic-Weighted Discordance.
    G. J. Li, J. Luo, W. Chu.
    To appear in SIAM Journal on Applied Dynamical Systems (2025). arXiv

  3. Interval Decomposition of Persistence Modules over a Principal Ideal Domain.
    J. Luo, G. Henselman-Petrusek.
    Published in Foundations of Computational Mathematics (2025). Journal arXiv

  4. Bounded-Confidence Models of Opinion Dynamics with Adaptive Confidence Bounds.
    G. J. Li*, J. Luo*, M. A. Porter.
    Published in SIAM Journal on Applied Dynamical Systems (2025). Journal arXiv

  5. Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites.
    A. Hickok*, B. Jarman*, M. Johnson*, J. Luo*, M. A. Porter.
    Published in SIAM Review (2024). Journal arXiv

  6. 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). Conference Proceeding