I like to use math to solve problems and understand the world. Currently, I am working at a small company on applications of algebraic topology in machine learning. Previously I was a Visiting Assistant Professor in the Mathematics department at Ohio State university, as part of the Topological and Geometric Data Analysis group.
I graduated from the University of Pennsylvania in May 2020 with a PhD in Applied Mathematics and Computational Science, under the direction of Robert Ghrist.
Here are some interesting things I’ve done recently:
An updated version of my Gentle Introduction to Sheaves on Graphs is now posted. It includes a few exercises, a brief discussion of homological algebra, and sketches of several more applications.
I was an author on two papers in the NeurIPS workshop TDA and Beyond, both of which were selected for spotlight presentations: Sheaf Neural Networks, with Tom Gebhart, and Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions, with Hans Riess. You can see the presentations and posters at the workshop site.
I have a new preprint on Expansion in Matrix-Weighted Graphs. These are special kinds of sheaves on graphs that offer exciting opportunities to generalize results from spectral graph theory. A Twitter thread for your perusal.
A new paper with Rob Ghrist on using cellular sheaves and associated dynamics to model the evolution of opinions in social networks. Here’s a Twitter thread summarizing the central ideas, with lots of nice pictures.