Allan Willms

Professor, Mathematics
Email: 
awillms@uoguelph.ca
Phone number: 
519-824-4120 x52736
Office: 
MacNaughton 512
Website links: 
Website

My research is centered around dynamical systems models of biological or other processes.  It is weighted toward the applied end of the mathematics spectrum, often concerned with implementation details and issues of making the mathematics accessible to biologists and engineers.  My research spans a wide set of disciplines, including algorithm development, numerical analysis, dynamical systems, mathematical modeling, and bifurcation theory, but dynamics is a unifying theme throughout.  

I enjoy working closely with experimentalists helping solve the problems in which they are interested, but am also interested in the more mathematical issues which often surface from this research. 

Many of my master's students have gone on to Ph.D. studies, and one has completed teacher's college and is currently working as an I.T. training specialist. Two of my Ph.D. students have gone on to post-doctoral work, and one now has a faculty position.

  • Climate change modelling
  • Mathematical biology
  • Bifurcation with symmetry
  • Parameter estimation
  • Neuronal ion channel modelling
  • Dynamical systems.
  • Parameter Estimation of the Potassium Channel in the Hodgkin-Huxley Model, Pengfei (Maxwell) Yue, M.Sc. (2024)
  • OPTIMUS PEAK: Automatic Extraction of Peak Information of Multi-Dimensional Solution and Solid-State NMR Spectra, Rachel Brown, Ph.D. Bioinformatics (2023)
  • The Adaptive Memory Feature and The Lamplighter Puzzle, Connor Gregor, Ph.D. (2021)
  • Modelling the COVID-19 Pandemic Using SIR Models with Bifurcation, Himmat Kooner, M.Sc. (2021)
  • Mathematical Modelling of T Cell Infection during Oncolytic Viral Therapy, Emilee Carson, M.Sc. (2020)

B.Math. (University of Waterloo).

M.Math. (University of Waterloo).

Ph.D. (Cornell University).

  • Allan R. Willms, 2024. Resonantly Forced ODEs and Repeated Roots, SIAM Review, 64 (1), pp. 149-160. doi=10.1137/23M1545148.
  • Kolja L. Kypke, William F. Langford, Gregory M. Lewis, Allan R. Willms, 2022. Climate Bifurcations in a Schwarzschild Equation Model of the Arctic Atmosphere, Nonlinear Processes in Geophysics, 29, pp. 219-239, doi=10.5194/npg-29-219-2022.
  • Chien Hsien Kitty Yang, Shane W. Bateman, Xiu Ting Yiew, Allan R. Willms, 2022. Validation of 3-dimensional mathematical computation of feline bladder volume using ultrasonographic orthogonal bladder images, Canadian Journal of Veterinary Research, 86(3), pp. 200-217.
  • Connor Gregor, Daniel Ashlock, Allan R. Willms, 2021. The Algebraic Solvability of the Novel Lamplighter Puzzle, ICGA Journal, 43, pp. 203-225, doi=10.3233/ICG-210195.
  • Allan R. Willms, 2021. Uniform Sampling on the Standard Simplex, Missouri Journal of Mathematical Sciences, 33 (1), pp. 119-124.