Department of Mathematics
Colorado State University
Fort Collins, CO 80523
This semester I am teaching:
Please see the course pages for more information. Previous courses can be found on the teaching page.
My primary research interest is in using geometry to solve topological and physical problems. I am currently working on a long-term project which uses Riemannian and symplectic geometry to develop a new framework for understanding the probability theory of topologically constrained random walks and polymer networks. A newer but very promising project uses symplectic geometry to answer long-standing questions in frame theory and statistical signal processing. Please see the research page for more.
- Harrison Chapman (2017–2019; software engineer at Google)
- Thomas D. Eddy (M.S. 2019; data scientist at Fountain)
- Yekaterina Aimukanova
- Laney Bowden
- Andrea Haynes
- Nikita Lavrenov
- Tucker Manton
- Nikolai Sannikov
- Aaron Shukert
- Gavin Stewart
- Bogdan Vasilchenko
- October, 2021 “Toric symplectic geometry and full spark frames”, by Tom Needham and Clayton Shonkwiler, posted to arXiv.
- August, 2021 “Admissibility and frame homotopy for quaternionic frames”, by Tom Needham and Clayton Shonkwiler, posted to arXiv.
- July, 2021 “New stick number bounds from random sampling of confined polygons”, by Thomas D. Eddy and Clayton Shonkwiler, published in Experimental Mathematics.
- June, 2021 Our project Collaborative Research: Applications of Symplectic Geometry to Frame Theory and Signal Processing has been funded by NSF (DMS–2107700). This project is a collaboration with Tom Needham at Florida State University.
- June, 2021 “Model and data reduction for data assimilation: Particle filters employing projected forecasts and data with application to a shallow water model”, by Aishah Albarakati, Marko Budišić, Rose Crocker, Juniper Glass-Klaiber, Sarah Iams, John Maclean, Noah Marshall, Colin Roberts, and Erik S. Van Vleck, published in Computers & Mathematics with Applications.
My research is partially supported by the National Science Foundation (DMS–2107700), and previously by the Simons Foundation (#354225 and #709150).