My research interests are in topology, geometry, and data analysis. More specific subfields of interest include applied topology, computational topology and geometry, combinatorial topology, metric geometry, machine learning, and sensor networks. I advance the study of Vietoris-Rips and Čech simplicial complexes, and I apply topology to data analysis, machine learning, and sensor networks. My research forms bridges between applied topology and nearby areas of mathematics, including quantitative topology, geometric group theory, Riemannian geometry, metric geometry, optimal transport, equivariant topology, and combinatorics, and I have experience working with datasets arising in interdisciplinary research areas such as computational chemistry, computer vision, collective motion in biological systems, sensor networks, and knowledge-guided machine learning.
You may find my research papers in my CV, on arXiv, or on Google Scholar.
Until my University of Florida webpage is setup, please see my prior webpage for information about my research: https://www.math.colostate.edu/~adams/research.