Bio
Major (Maj) Aaron A. Nelson is an Assistant Professor of Mathematics within the Department of Mathematical Sciences at the United States Air Force Academy, Colorado. He received his commission in the U.S. Air Force upon graduating from the University of Connecticut in May 2012. Maj Nelson is also a Distinguished Graduate of the Air Force Institute of Technology (March 2014) and went on to complete his Doctorate in Mathematics at the University of California San Diego in October 2019.
As an Operations Research Analyst (15A), Maj Nelson has experience in operational test and evaluation as well as on Combatant Command headquarters staff. He served as a test analyst at Air Force Operational Test and Evaluation Center Detachment 1, Edwards AFB, California, from April 2014 to September 2016 where he designed and analyzed experiments as part of the Joint Strike Fighter Operational Test Team. Notably, Maj Nelson participated in the first ever at-sea deployment of the F-35B onboard the USS Wasp (LHD-1) in May and June of 2015 and was the lead analyst for F-35 air-to-surface weapons testing. From October 2019 to October 2022, he served as a program analyst and staff officer within the Advanced Warfare Capabilities Division, Capability and Resource Directorate, at headquarters U.S. Strategic Command, Offutt AFB, Nebraska. As the Division’s focal point for advanced technology integration, Maj Nelson’s capability portfolio directly influenced the creation of new Concepts of Operations for multiple game-changing assured communications systems supporting the Nuclear Triad.
Maj Nelson’s academic interests span multiple topics within mathematical signal processing and analysis. His research regularly draws upon and develops tools in information theory, random matrix theory, frame theory, and geometric functional analysis to solve problems motivated by the acquisition, digitization, and processing of signals. Additionally, Maj Nelson has interest in problems related to machine learning, data science, and quantum information science.
Education
Doctor of Philosophy, Mathematics (with a specialization in Computational Science), University of California San Diego, 2019
Master of Science, Applied Mathematics, Air Force Institute of Technology, 2014
Bachelor of Science, Mathematics (with a minor in Physics), University of Connecticut, 2012
Professional Experience
Assistant Professor of Mathematics, Department of Mathematical Sciences, U.S. Air Force Academy, Colorado (Oct 2022 − Present)
Strategic Programs Analyst, Advanced Warfare Capabilities Division, Capability and Resource Directorate, U.S. Strategic Command, Offutt AFB, Nebraska (Oct 2019 − Oct 2022)
Effectiveness Test Analyst, Air Force Operational Test and Evaluation Center Detachment 1, Edwards AFB, California (Apr 2014 − Sep 2016)
Honors & Awards
Defense Meritorious Service Medal
Joint Service Achievement Medal
Air and Space Outstanding Unit Award
Air and Space Organizational Excellence Award (1 Oak Leaf Cluster)
Research and Scholarly Interests
Mathematical Signal Processing
Machine Learning and Data Science
Quantum Information Science
Publications
A. S. Bandeira, J. Cahill, D. G. Mixon, A. A. Nelson, Fundamental Limits of Phase Retrieval, In: Proceedings of the 10th International Conference on Sampling Theory and Applications (SampTA), 2013.
A. S. Bandeira, J. Cahill, D. G. Mixon, A. A. Nelson, Saving Phase: Injectivity and stability for phase retrieval, Applied and Computational Harmonic Analysis, 37(1):106–125, 2014.
M. Begue, D. J. Kelleher, A. Nelson, H. Panzo, R. Pellico, A Teplyaev, Random walks on barycentric subdivisions and the Strichartz hexacarpet, Experimental Mathematics, 21(4)402–417, 2012.
M. Fickus, D. G. Mixon, A. A. Nelson, Y. Wang, Phase retrieval with very few measurements, Linear Algebra and its Applications, 449:475–499, 2014.
M. A. Iwen, E. Lybrand, A. A. Nelson, R. Saab, New Algorithms and Improved Guarantees for One-Bit Compressed Sensing on Manifolds, In: Proceedings of the 13th International Conference on Sampling Theory and Applications (SampTA), 2019.
D. Molitor, D. Needell, A. A. Nelson, R. Saab, P. Salanevich, Classification scheme for binary data with extensions, In: Compressed Sensing and its Applications, Springer, 2018.
D. Needell, A. A. Nelson, R. Saab, P. Salanevich, O. Schavemaker, Random vector functional link networks for function approximation on manifolds, Frontiers in Applied Mathematics and Statistics, 10, 2024.
A. A. Nelson, About Phase: Synthetic Aperture Radar and the Phase Retrieval Problem, Air Force Institute of Technology Graduate School of Engineering and Management, Thesis No. AFIT-ENC-14-M-03, 2014.
A. A. Nelson, Modern Problems in Mathematical Signal Processing: Quantized Compressed Sensing and Randomized Neural Networks, University of California San Diego, ProQuest ID: Nelson_ucsd_0033D_18905, 2019.