casper

Contact Information

Office: MH 160A

Phone: 657-278-7455

Email: wcasper@fullerton.edu 

Riley Casper

Assistant Professor

Degrees

PhD, University of Washington

MS, North Dakota State University

BS, North Dakota State University

Research Areas

Orthogonal polynomials, integrable systems, spectral theory of integral and differential operators, and noncommutative crepant resolutions. Additional research areas include computational fluid dynamics and high performance computing.

Courses Regularly Taught

Lower Division: Calculus, Computational Linear Algebra, Methods of Problem Solving, Differential Equations

Upper Division: Abstract Algebra, Topology, Number Theory, Complex Analysis, Real Analysis, Partial Differential Equations

Publications

  • Casper, W. Riley, Emil Horozov, Plamen Iliev, and Milen Yakimov.  " A Burchnall-Chaundy-Krichever Theory for Fractional Differential Operators."  Submitted.

  • Casper, W. Riley and Milen Yakimov.  " The Restricted Discrete Fourier Transform."  Submitted.

  • Casper, W. Riley and Ignacio Zurrian.  "The Pascal Matrix, Commuting Tridiagonal Operators and Fourier Algebras ."  Submitted.

  • Anderson, Sara,  W. Riley Casper, Sam Fleyshman, and Matt Rathbun.  "Disconnected Cliques in Derangement Graphs ."  Submitted.

  • Casper, W. Riley, F. Alberto Grunbaum, Milen Yakimov and Ignacio Zurrian.  "Matrix valued discrete-continuous functions with the
    prolate spheroidal property and bispectrality." 2024 Commun. Math. Phys. 405 . 69 .

  • Casper, W. Riley, F. Alberto Grunbaum, Milen Yakimov and Ignacio Zurrian.  "Algebras of commuting differential operators for integral kernels of Airy type.", 2022 Operator Theory: Advances and Applications (Special issue in memory of Harold Widom).  Published by Springer Nature.

  • Casper, W. Riley, F. Alberto Grunbaum, Milen Yakimov and Ignacio Zurrian.  "Reflective prolate-spheroidal operators and the adelic Grassmannian", 2023 Commun. Pure Appl. Math 76.12:  3769-3810

  • Casper, W. Riley and Milen Yakimov.  "The matrix Bochner problem", 2022 American J. Math. 144.4: 1009-1065

  • Casper, W. Riley, Stefan Kolb, and Milen Yakimov.  "Bivariate continuous q-Hermite Polynomials and quantum Serre relations", 2021 J. Algebra Appl issue in honor of 60th birthday of N. Andruskiewitsch  20.01: 2140016.

  • Casper, W. Riley, F. Alberto Grunbaum, Milen Yakimov and Ignacio Zurrian.  "Reflective prolate-spheroidal operators and the KP/KdV equations", Proc. Natl. Acad. of Sci. USA 2019

  • Casper, W. Riley and Milen Yakimov "Integral operators, bispectrality and growth of Fourier algebras", 2019 J. Reine Angew. Math (Crelle's Journal)

    Casper, W. Riley "Elementary examples of solutions to Bochner's problem for matrix differential operators", 2018 J. Approx. Theory

  • Nadiga, Balu, W. Riley Casper and Philip Jones.  "Ensemble-based global ocean data assimilation" 2013 J. Ocean Modelling

Scholarly Work

The main focus of my research is on the interactions between noncommutative algebra, algebraic geometry, and integrable systems with applications to special functions.  I am also interested in numerical methods in geophysical fluid dynamics.