In progress
A Brief Modern Functional Analytic Tour of the Fourier–Bessel Transform
A Partner to the Fourier–Bessel Transform and an Associated Uncertainty Principle
Optimal Quantum Error-Correcting Codes From Constitutent Codes of Quasi-Cyclic Codes
In-print
Williams, C.L. Segal–Bargmann Transforms Associated to a Family of Coupled Supersymmetries. Complex Anal. Oper. Theory 16, 94 (2022). https://doi.org/10.1007/s11785-022-01272-1
Williams, C. L., Pandya, N. N., Bodmann, B. G., & Kouri, D. J. (2018). Coupled supersymmetry and ladder structures beyond the harmonic oscillator. Molecular Physics, 116(19–20), 2599–2612. https://doi.org/10.1080/00268976.2018.1473655
Williams, C.L., Bodmann, B.G. & Kouri, D.J. Fourier and Beyond: Invariance Properties of a Family of Integral Transforms. J Fourier Anal Appl 23, 660–678 (2017). https://doi.org/10.1007/s00041-016-9482-x
Presentations
Coupled Supersymmetry and the Fourier–Bessel Transform, Joint Mathematics Meetings, 2025
The Segal–Bargmann Transform and Coupled Supersymmetry, Eighth Exchange of Mathematical Ideas, 2022
Some Coupled Supersymmetries and Their Associated Bargmann Transforms, Canadian Operator Symposium, 2020
Coupled Supersymmetry: Unifying the Harmonic Oscillator and Supersymmetric Quantum Mechanics, University of Connecticut, 2017
An Alternate Characterization and Generalization of the Fourier Transform, University of Mathematics, 2015
Beyond Harmonic Analysis with Fourier-like Transforms, Fifth International Conference on Computational Harmonic Analysis, 2014
Learning Seminars
Modern Algebra Seminar, with Brent Solie, Summer 2023
Representation Theory of Finite Groups, SUNY Potsdam, 2019
An Introduction to the Representation Theory of Finite Groups, University of Houston, 2014
Several Complex Variables, University of Waterloo, 2013