My research lies at the intersection of Topology, Combinatorics, and Data Science. It loosely fits under the umbrella of Topological Data Analysis (TDA), a burgeoning field over the past 25 years.

Data is increasingly relevant in our world, but also increasingly complex. My research attempts to deal with this complexity in two ways: the models used to represent the data, and the methods used to analyze it.

Mathematicians have been modeling data problems with graphs for a long time. Think of the travelling salesperson problem, or Euler's Bridges of Königsberg. Graphs are fantastic tools for displaying pairwise information. However, it is often beneficial to model data with relationships of higher order. For example, biologists have found examples of three-way symbiotic relationships. I use combinatorial objects called hypergraphs to model data. Hypergraphs are generalizations of graphs in which edges can have any number of vertices. The image above shows a hypergraph with various edge sizes, visualized using the python package HypernetX.