**Office:** Weber 206C

**Phone:** (970) 491-1822

**Website: ** http://www.math.colostate.edu/~clayton/

**Curriculum Vitae: ** http://www.math.colostate.edu/~clayton/cv/cv.pdf

**Google Scholar: ** https://scholar.google.com/citations?user=MLHUVQwAAAAJ

**Education**

- Ph.D. in Mathematics, University of Pennsylvania, 2009
- B.S. in Mathematics, Sewanee: The University of the South, 2003

**About**

Differential and symplectic geometry, geometric probability, knot theory, and applications of these areas to polymer physics and signal processing

#### Publications

- Fusion frame homotopy and tightening fusion frames by gradient descent
*Journal of Fourier Analysis and Applications***29**, no. 4, 51, 2023 - New stick number bounds from random sampling of confined polygons
*Experimental Mathematics***31**, no. 4, 1373–1395, 2022 - Toric symplectic geometry and full spark frames
*Applied and Computational Harmonic Analysis***61**, no. 8, 254–287, 2022 - Symplectic geometry and connectivity of spaces of frames
*Advances in Computational Mathematics***47**, no. 1, 5, 2021 - Random triangles and polygons in the plane
*The American Mathematical Monthly***126**, no. 2, 113–134, 2019 - A fast direct sampling algorithm for equilateral closed polygons
*Journal of Physics A: Mathematical and Theoretical***49**, no. 27, 275202, 2016 (Selected as a**2016 Highlight of**)*J. Phys. A* - The symplectic geometry of closed equilateral random walks in 3-space
*Annals of Applied Probability***26**, no. 1, 549–596, 2016 - The expected total curvature of random polygons
*American Journal of Mathematics***137**, no. 2, 411–438, 2015 - Probability theory of random polygons from the quaternionic viewpoint
*Communications on Pure and Applied Mathematics***67**, no. 10, 1658–1699 , 2014 - Poincaré duality angles and the Dirichlet-to-Neumann operator
*Inverse Problems***29**, no. 4, 045007, 2013