ResearchMy research interests are in computational topology and geometry, combinatorial topology, and applied topology. In particular, I like to study Vietoris-Rips and Čech simplicial complexes, Vietoris-Rips and Čech metric thickenings, applications of topology to data analysis, and applications of topology to sensor networks.
I am the co-director of the Applied Algebraic Topology Research Network, which hosts a weekly Online Seminar. Recordings of our seminar are available at our YouTube Channel, which has over 1,000 YouTube subscribers, and averages over 2,000 hours watched per year.
I am a member of the Descriptors of Energy Landscapes Using Topological Data Analysis (DELTA) leadership team.
Here is my PhD thesis, a related research highlight, and research statements from 2020, 2019, 2018, 2017, 2016. See section 4 of this column for some open (and some "closed") problems I am interested in.
An adaptation for iterative structured matrix completion.
With Lara Kassab and Deanna Needell.
Topological data analysis of collective motion.
With Maria-Veronica Ciocanel, Chad M. Topaz, and Lori Ziegelmeier.
SIAM News, January/February Issue (2020).
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