Department of Mathematics
Colorado State University
Fort Collins, CO 80523
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
- 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.
- May, 2021 “Expected distances on manifolds of partially oriented flags”, by Brenden Balch, Chris Peterson, and Clayton Shonkwiler, published in the Proceedings of the American Mathematical Society.
- April, 2021 Colin Roberts passed his Ph.D. preliminary examination. Congratulations, Colin!
- January, 2021 “Symplectic geometry and connectivity of spaces of frames”, by Tom Needham and Clayton Shonkwiler, published in Advances in Computational Mathematics.