My primary area of research is in differential geometry, specifically geometric analysis, very specifically the study of harmonic maps into metric spaces.
My papers in this area are:
Rectifiability of the Singular Strata for Harmonic Maps to Euclidean Buildings, with C. Breiner. Preprint. 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.
Eigenvalues of Autoencoders in Training and at Initialization, with S. Agarwala and C. Lowman. Preprint.
Geometric instability of out of distribution data across autoencoder architecture, with S. Agarwala and C. Lowman. Preprint.