I am broadly interested in applied mathematics, but I have specific interests in mathematical modeling, differential equations, measure valued PDEs, numerical analysis, dynamical systems, optimization, etc.
I will gladly work on any interesting mathematical problem with applications to the natural sciences.
I have taught the following courses:
- College Algebra (University of Louisiana at Lafayette (UL)),
- Precalculus Algebra (UL),
- Precalculus Trigonometry (UL),
- Survey of Calculus (UL),
- Elementary Linear Algebra (UL).
My main collaborator at this time is Adrian Muntean here at Karlstad University. Some other collaborators include:
- Sander Hille (Leiden University),
- Emilio N. M. Cirillo (Sapienza University of Rome),
- Andrea Muntean (Karlstad University),
- Azmy S. Ackleh (University of Louisiana at Lafayette),
- Nicolas Saintier (University of Buenos Aires),
- Annette M Ostling (University of Texas at Austin),
- Ursula Trigos-Raczkowski (University of Michigan).
Originally from New Orleans, Louisiana, I attended the University of Louisiana at Lafayette for my Bachelor of Science in Mathematics (2016), Master's of Science in mathematics (2019), and Doctor of Philosophy in Mathematics (2021).
R.Lyons, S. A. Muntean, E. N. M. Cirillo, , A. Muntean, A Continuum Model for Morphology Formation from Interacting Ternary Mixtures: Simulation Study of the Formation and Growth of Patterns, preprint.
A. S. Ackleh, R. Lyons, and N. Saintier, Finite difference schemes for a size structured coagulation-fragmentation model in the space of Radon measures, IMA Journal of Numerical Analysis, 2022; https://doi.org/10.1093/imanum/drac071
A. S. Ackleh, R. Lyons, and N. Saintier, Structured Coagulation-Fragmentation Equation in the Space of Radon Measures: Unifying Discrete and Continuous Models, ESAIM: Mathematical Modelling and Numerical Analysis, 2021;
During my time here as a postdoctoral fellow, I am supported by The Carl Trygger Foundation for Scientific Research.