My primary area of research is in differential geometry, specifically geometric analysis, very specifically the study of harmonic maps into metric spaces.
For those craving even more specificity, I study harmonic maps into CAT(0) metric spaces, primarily Euclidean buildings, seeking both to apply these maps to prove certain kinds of fixed point theorems for group actions on those buildings, and to investigate the regularity and other properties of such maps as an area of interest in and of itself.
My papers in this area are:
Rectifiability of the Singular Strata for Harmonic Maps to Euclidean Buildings, with C. Breiner. Transactions of the American Mathematical Society, Series B 12 (2025), 1156--1187. https://arxiv.org/abs/2502.14049
Harmonic Maps into Euclidean Buildings and Non-Archimedean Superrigidity, with C. Breiner and C. Mese. Preprint. https://arxiv.org/abs/2408.02783
Rectifiability of the Singular Set of Harmonic Maps into Buildings. The Journal of Geometric Analysis 32 (205) 2022. https://arxiv.org/abs/2106.06670
I also have some contributions in the field of machine learning:
Geometry and Generalization: Eigenvalues as predictors of where a network will fail to generalize, with S. Agarwala, A. Gearheart, and C. Lowman. Foundations of Data Science, 2022, 4(2): 217--242. https://arxiv.org/abs/2107.06386
Eigenvalues of Autoencoders in Training and at Initialization, with S. Agarwala and C. Lowman. Preprint. https://arxiv.org/abs/2201.11813
Geometric instability of out of distribution data across autoencoder architecture, with S. Agarwala and C. Lowman. Preprint. https://arxiv.org/abs/2201.11902