About Your Instructor

W. Riley Casper

• Email: wcasper@fullerton.edu
• Webpage: caspermath.com (Links to an external site.)

About Me

I obtained concurrently a B.S. in Mathematics, a B.S. in Physics, and a M.S. in Mathematics from North Dakota State University in 2010. Following this, I did a stint at Los Alamos National Lab (LANL) as a post-baccalaureate researcher before continuing on to a graduate program at the University of Washington in Seattle (UW), while continuing research at LANL during summers. After obtaining my Ph.D. in Mathematics from UW in 2017, I spent three years as a post-doc at Louisiana State University and joined CSUF in 2020.

My research focuses on applications of algebra and algebraic geometry to various problems in pure and applied mathematics. Specific research interests include orthogonal polynomials, integrable systems, spectral theory of integral and differential operators, and noncommutative crepant resolutions. Additionally, my research includes work in computational fluid dynamics and high performance computing.

Past/Current Research Projects with Students (as of 2021)

• Exploring maximal cliques in derangement graphs with connections to orthogonal Latin squares
• Determinants of special matrices related to Vandermonde matrices
• Using orthogonal matrix polynomials for nonlinear eigenvalue problems
• Exploring exact equations and recurrence relations for matrix-valued Chebyshev-type polynomials
• Solving Battleship puzzle problems using discrete tomography and quantum computing

My Publications (as of 2022)

• The matrix Bochner problem
  American J. Mathematics (2022)
• Reflective prolate-spheroidal operators and the adelic Grassmannian
  Communications in Pure and Applied Mathematics (2022)
• Algebras of commuting differential operators for integral kernels of Airy type
  Operator Theory: Advances and Applications (2022)
• Bivariate cont. q-Hermite polynomials and quantum Serre relations
  J. Algebra Appl. (2020)
• Reflective prolate-spheroidal operators and the KP/KdV equations
  Proc. Natl. Acad. of Sci. USA (2019)
• Integral operators, bispectrality and growth of Fourier algebras
  J. Reine Angew. Math “Crelle’s Journal” (2019)
• Elementary examples of solutions to Bochner’s problem for matrix differential operators
  J. Approx. Theory (2018)
• Quantum Algorithm Implementations for Beginners
  arXiv preprint (2018)
• Ensemble-based global ocean data assimilation
  J. Ocean Modelling (2013)