My research is in applied topology. In particular, I am interested in the structure of Vietoris–Rips simplicial complexes, discrete Morse theory, and persistent homology.
"On the nonlinear statistics of optical flow." With Henry Adams, Johnathan Bush, Brittany Carr, and Lara Kassab. To appear in Pattern Recognition Letters, special issue Topological Analysis and Recognition (2018+). [Publisher link, arXiv:1812.00875, Slides, Abstract]
"A fractal dimension for measures via persistent homology" With Henry Adams, Manuchehr Aminian, Elin Farnell, Michael Kirby, Rachel Neville, Chris Peterson, and Clayton Shonkwiler. Submitted September 2018. [arXiv:1808.01079, Abstract]