Colorado State University

Clayton Shonkwiler

Professor

Clayton.Shonkwiler@colostate.edu

Office: Weber 206C

Phone: 9704911822

Education:

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

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

Curriculum Vitae: View Curriculum Vitae

Google Scholar: View Google Scholar Profile

About

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

Publications

• “Optimization and the topology of spaces of Parseval frames” Anthony Caine, Tom Needham, and Clayton Shonkwiler SIAM Journal on Matrix Analysis and Applications 47, no. 3, 1375–1399, 2026
• “Looping animations using the modular flow and elliptic functions” Clayton Shonkwiler Proceedings of Bridges 2026: Mathematics and the Arts, 533–536, 2026
• “Approximately dual and pseudo-dual probabilistic frames” Dongwei Chen, Emily J. King, and Clayton Shonkwiler Applied and Computational Harmonic Analysis 84, 101885, 2026
• “Random knotting in very long off-lattice self-avoiding polygons” Jason Cantarella, Tetsuo Deguchi, Henrik Schumacher, Clayton Shonkwiler, and Erica Uehara Journal of Physics A: Mathematical and Theoretical 59, no. 14, 145205, 2026
• “Direct sampling of confined polygons in linear time” Clayton Shonkwiler and Kandin Theis SIAM Journal on Discrete Mathematics 40, no. 2, 505–535, 2026
• “New upper bounds on stick numbers” Jason Cantarella, Andrew Rechnitzer, Henrik Schumacher, and Clayton Shonkwiler Journal of Knot Theory and Its Ramifications 35, no. 8, 2650008, 2026
• “Factoring the Laplacian to understand topological polymers” Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara Europhysics Letters 152, no. 1, 12001, 2025
• “Geometric approaches to matrix normalization and graph balancing” Tom Needham and Clayton Shonkwiler Forum of Mathematics, Sigma 13, e149, 2025
• “An exact formula for the contraction factor of a subdivided Gaussian topological polymer” Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara Journal of Physics A: Mathematical and Theoretical 58, no. 35, 355201, 2025
• “On the existence of Parseval frames for vector bundles” Samuel A. Ballas, Tom Needham, and Clayton Shonkwiler Transactions of the American Mathematical Society, Series B 12, 395–416, 2025
• “A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting” Jason Cantarella, Henrik Schumacher, and Clayton Shonkwiler Journal of Physics A: Mathematical and Theoretical 57, no. 28, 285205, 2024
• “Three proofs of the Benedetto–Fickus theorem” Dustin G. Mixon, Tom Needham, Clayton Shonkwiler, and Soledad Villar In: Stephen D. Casey, M. Maurice Dodson, Paulo J.S.G. Ferreira, Ahmed Zayed, editors, Sampling, Approximation, and Signal Analysis: Harmonic Analysis in the Spirit of J. Rowland Higgins, Applied and Numerical Harmonic Analysis, Birkhäuser, Cham, 371–391, 2023
• “Fusion frame homotopy and tightening fusion frames by gradient descent” Tom Needham and Clayton Shonkwiler Journal of Fourier Analysis and Applications 29, no. 4, 51, 2023
• “Robocasting of ceramic Fischer–Koch S scaffolds for bone tissue engineering” Vail Baumer, Erin Gunn, Valerie Riegle, Claire Bailey, Clayton Shonkwiler, and David Prawel Journal of Functional Biomaterials 14, no. 5, 251, 2023
• “New stick number bounds from random sampling of confined polygons” Thomas D. Eddy and Clayton Shonkwiler Experimental Mathematics 31, no. 4, 1373–1395, 2022
• “Radius of gyration, contraction factors, and subdivisions of topological polymers” Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara Journal of Physics A: Mathematical and Theoretical 55, no. 47, 475202, 2022
• “New superbridge index calculations from non-minimal realizations” Clayton Shonkwiler Journal of Knot Theory and Its Ramifications 31, no. 10, 2250063, 2022
• “Toric symplectic geometry and full spark frames” Tom Needham and Clayton Shonkwiler Applied and Computational Harmonic Analysis 61, no. 8, 254–287, 2022
• “All prime knots through 10 crossings have superbridge index ≤ 5” Clayton Shonkwiler Journal of Knot Theory and Its Ramifications 31, no. 4, 2250023, 2022
• “Admissibility and frame homotopy for quaternionic frames” Tom Needham and Clayton Shonkwiler Linear Algebra and its Applications 645, 237–255, 2022
• “Exact evaluation of the mean square radius of gyration for Gaussian topological polymer chains” Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara In: Yasuyuki Tezuka and Tetsuo Deguchi, editors, Topological Polymer Chemistry: Concepts and Practices, Springer, Singapore, 37–63, 2022
• “Expected distances on manifolds of partially oriented flags” Brenden Balch, Chris Peterson, and Clayton Shonkwiler Proceedings of the American Mathematical Society 149, no. 8, 3553–3567, 2021
• “Symplectic geometry and connectivity of spaces of frames” Tom Needham and Clayton Shonkwiler Advances in Computational Mathematics 47, no. 1, 5, 2021
• “Distributions of distances and volumes of balls in homogeneous lens spaces” Brenden Balch, Chris Peterson, and Clayton Shonkwiler Differential Geometry and its Applications 74, 101712, 2021
• “New computations of the superbridge index” Clayton Shonkwiler Journal of Knot Theory and Its Ramifications 29, no. 14, 2050096, 2020
• “Knots with exactly 10 sticks” Ryan Blair, Thomas D. Eddy, Nathaniel Morrison, and Clayton Shonkwiler Journal of Knot Theory and Its Ramifications 29, no. 3, 2050011, 2020
• “A fractal dimension for measures via persistent homology” Henry Adams, Manuchehr Aminian, Elin Farnell, Michael Kirby, Joshua Mirth, Rachel Neville, Chris Peterson, and Clayton Shonkwiler In: Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, and Marius Thaule, editors, Topological Data Analysis: The Abel Symposium 2018, volume 15 of Abel Symposia, Springer, Cham, 2020, 1–31, 2020
• “Stiefel manifolds and polygons” Clayton Shonkwiler Proceedings of Bridges 2019: Mathematics, Art, Music, Architecture, Education, Culture, 187–194, 2019
• “Random triangles and polygons in the plane” Jason Cantarella, Tom Needham, Clayton Shonkwiler, and Gavin Stewart The American Mathematical Monthly 126, no. 2, 113–134, 2019
• “Spherical geometry and the least symmetric triangle” Laney Bowden, Andrea Haynes, Clayton Shonkwiler, and Aaron Shukert Geometriae Dedicata 198, 19–34, 2019
• “Open and closed random walks with fixed edgelengths in R^d” Jason Cantarella, Kyle Chapman, Philipp Reiter, and Clayton Shonkwiler Journal of Physics A: Mathematical and Theoretical 51, no. 43, 434002, 2018
• “The geometry of constrained random walks and an application to frame theory” Clayton Shonkwiler 2018 IEEE Statistical Signal Processing Workshop (SSP), 343–347, 2018
• “Homotopy string links and the κ-invariant” Frederick R. Cohen, Rafał Komendarczyk, Robin Koytcheff, and Clayton Shonkwiler Bulletin of the London Mathematical Society 49, no. 2, 246–260, 2017
• “A fast direct sampling algorithm for equilateral closed polygons” Jason Cantarella, Bertrand Duplantier, Clayton Shonkwiler, and Erica Uehara 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” Jason Cantarella and Clayton Shonkwiler Annals of Applied Probability 26, no. 1, 549–596, 2016
• “The expected total curvature of random polygons” Jason Cantarella, Alexander Y. Grosberg, Robert Kusner, and Clayton Shonkwiler American Journal of Mathematics 137, no. 2, 411–438, 2015
• “Homotopy Brunnian links and the κ-invariant” Frederick R. Cohen, Rafał Komendarczyk, and Clayton Shonkwiler Proceedings of the American Mathematical Society 143, no. 3, 1347–1362, 2015
• “Probability theory of random polygons from the quaternionic viewpoint” Jason Cantarella, Tetsuo Deguchi, and Clayton Shonkwiler Communications on Pure and Applied Mathematics 67, no. 10, 1658–1699 , 2014
• “Generalized Gauss maps and integrals for three-component links II” Dennis DeTurck, Herman Gluck, Rafał Komendarczyk, Paul Melvin, Haggai Nuchi, Clayton Shonkwiler, and David Shea Vela-Vick Algebraic & Geometric Topology, 13, no. 5, 2897–2923, 2013
• “Poincaré duality angles and the Dirichlet-to-Neumann operator” Clayton Shonkwiler Inverse Problems 29, no. 4, 045007, 2013
• “Generalized Gauss maps and integrals for three-component links” Dennis DeTurck, Herman Gluck, Rafał Komendarczyk, Paul Melvin, Clayton Shonkwiler, and David Shea Vela-Vick Journal of Mathematical Physics 54, no. 1, 013515, 2013
• “The complete Dirichlet-to-Neumann map for differential forms” Vladimir Sharafutdinov and Clayton Shonkwiler Journal of Geometric Analysis 23, no. 4, 2063–2080, 2013
• “Legendrian contact homology and nondestabilizability” Clayton Shonkwiler and David Shea Vela-Vick Journal of Symplectic Geometry 9, no. 1, 33–44, 2011
• “Higher-dimensional linking integrals” Clayton Shonkwiler and David Shea Vela-Vick Proceedings of the American Mathematical Society 139, no. 4, 1511–1519, 2011
• “Poincaré duality angles for Riemannian manifolds with boundary” Clayton Shonkwiler Ph.D. thesis, University of Pennsylvania, 2009
• “Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links” Dennis DeTurck, Herman Gluck, Rafał Komendarczyk, Paul Melvin, Clayton Shonkwiler, and David Shea Vela-Vick Matemática Contemporânea 34, 251–283, 2008