Advisors: Lorenzo Orecchia and Samantha J. Riesenfeld
I grew up in Nicholson, Georgia. After graduating high school in 2015, I attended MIT, wherein I changed my major twice. Interested in Biophysics, I took part in a research position with Dr. Aaron Meyer (now a professor at UCLA) wherein I helped develop a binding model for multivalent immune complexes to heterogeneous cell receptor species. This experience taught me the importance of robust mathematical frameworks to modern biological research, and it inspired me to change my major to Computational Biology. I continued to work with the Meyer lab on two biomathematical projects, and I was convinced by friends to switch my major to Mathematics. Before graduating with my B.S. in Mathematics, I worked with Dr. Jeremy Kepner at MIT Beaver Works to develop a method of de novo sparse neural network topologies with training accuracies matching those of dense neural networks that required no pruning.
I joined the Department of Computer Science at UChicago as a 2019 NSF Graduate Research Fellow. Inspired by the need for topologically and differential-geometrically robust tools for analyzing high-dimensional biological data, I decided to pursue research in automated manifold learning and Riemannian optimization. I am co-advised by Lorenzo Orecchia from the Department of Computer Science and Samantha J. Riesenfeld from the Pritzker School of Molecular Engineering. I have developed a mathematical framework for learning manifold representations of point cloud data that preserve homology, Riemannian metric, and other attributes intrinsic to the manifolds from which these data are generated. I am currently applying this framework to RNA sequencing data to elucidate mechanisms in the formation of Peyer’s patches in the gut.
My research is at the intersection of manifold learning and Riemannian optimization. Manifold learning is a branch of machine learning concerned with learning representations of data as topological, differentiable, or Riemannian manifolds. Manifold learning most often arises in application in the form of dimensionality reduction techniques, which have become ubiquitous and essential to computational biology. The purpose of my research is twofold: first, to write algorithms that learn manifold representations of point clouds which, in the case that the point clouds are generated from underlying manifolds, preserve all topological and differential-geometric properties of the manifold; second, to compute differential-geometric primitives and implement Riemannian optimization routines on said manifold representations.