Starting summer 2024, I worked under Lori Ziegelmeier and Russell Funk to use topological data analysis (TDA) to analyze how knowledge develops over time.
We focus our analysis on knowledge networks constructed by connecting scientific concepts that cooccur in published papers. The TDA tools allow us to analyze where there are missing links in the network between closely related concepts. Using persistent homology (PH) and filtrating over time, we examine how gaps in knowledge open, exist, and close over time.
My role in the project was focused on getting representatives of each of the gaps. PH tools make it easy to pinpoint how many holes there are and when they open or close, but examining exactly what nodes and edges surround the gaps and how they fill in can be harder. I use linear programming to get better representatives of the gaps.
I’m expanding on my work in this project in my honors project in mathematics. I’m looking into new, network-specific approaches to optimizing the representatives of cycles and performing an empirical analysis of the role the papers in the gaps play in scientific literature.
At the 2025 JMM, I presented my work in this project in a special session and the undergraduate poster session. In the future, I’ll update this page with drafts of my honors and any other papers we work on.