Publications
I. Anderson, B. Ashley. Darboux Integrable f-Gordon Equations and Rank 2 Distributions in Five Variables. (In preparation).
B. Ashley, A. Eskenazi. 7-Dimensional Symmetry Subalgebras of Maximally Symmetric Monge Equations on 6-Manifolds and Darboux Integrability. (In preparation).
B. Ashley, M. Schultz. Geometric Aspects of Rank-3 Vector Bundles Over Surfaces and 2-Plane Distributions on 5-Manifolds. Journal of Differential Geometry and Its Applications. (Submitted).
B. Ashley, M. Schultz. Projective Differential Geometry of Surfaces and Rank-2 Distributions on 5-Manifolds. In: Lie Theory and Its Applications to Physics (2025). Springer Proceedings in Mathematics & Statistics. (Submitted).
B. Ashley. Transformation Groups and The Method of Darboux. Dissertation, Utah State University, 2021.
B. Ashley, W. Liu. Asymptotic Tracking and Disturbance Rejection of the Blood Glucose Regulation System. Mathematical Biosciences, Volume 289, 2017, Pages 78-88. ISSN 0025-5564.
D. Arrigo, B. Ashley, S. Bloomberg, T. Deatherage. Nonclassical Symmetries of a Nonlinear Diffusion-Convection/Wave Equation and Equivalent Systems. Symmetry, 2016, 8(12), 140.
Conferences and Presentations
Virginia Tech Geometry/Topology Seminar, Blacksburg, VA (2024)
Invited Talk: On the Geometry of Darboux Integrable Equations
Texas A&M University Geometry Seminar, College Station, TX (2024)
Invited Talk: A Group-Theoretic Approach to Darboux Integrable f-Gordon Equations
AMS/MAA Joint Mathematics Meeting, San Francisco, CA (2024)
Invited Talk: Intransitive Symmetry Groups of 2-Plane Distributions and Darboux Integrable f-Gordon Equations
Cal Poly Humboldt Math Colloquium, Arcata, CA (2023)
Invited Talk: Transformations and Symmetry
Winter Meeting on Geometry and Differential Equations, Warsaw, Poland (2022)
Invited Talk: Intransitive Symmetry Groups of 2-Plane Distributions and Darboux Integrability
Invited Talk: Quotient Construction of Symmetric Powers of Differential Equations
Whiskeytown Lake Mathematics Congress, Whiskeytown Lake, California (2022)
Invited Talk: Transformations, Symmetries, and Applications to Differential Equations
AMS/MAA Joint Mathematics Meeting, Denver, Colorado (2020)
Invited Talk: Transformation Groups and The Method of Darboux
Together We Teach Conference, Logan, Utah (2020)
Invited Talk: Promoting Progressive Problems in the Classroom
Together We Teach Conference, Logan, Utah (2019)
Invited Talk: Design and Implementation of Proficiency-Based Homeworks
USU Math & Stat Department Summer Research Symposium, Logan, Utah (2018)
Poster: Extensions of AFV Theory of Darboux Integrable Equations
DGCAMP Student Daze Conference, Logan, Utah (2018)
Talk: Finding Zero Curvature Representations of Hyperbolic Darboux Integrable Equations
Together We Teach Conference, Logan, Utah (2018)
Talk: A Consideration of Pre-Lecture Calculus Video Podcasts (with Kaitlin Murphy)
DGCAMP Student Workshop, Logan, Utah (2017)
Talk: Making New Differential Equations from Old