My research interests focus primarily on fractal-based methods in (applied) analysis, including a wide array of both direct and inverse problems, and, more broadly, mathematical imaging and qualitative properties of differential equations.
My work combines rigorous theoretical elements (analysis, fractal geometry, information theory, differential equations, integral equations) with application-driven issues (programming, algorithm design, numerical analysis, approximations).
I generally work with at most three graduate students at any time because of the extra teaching, guidance and mentoring I offer to each student in the hope of giving them the best experience I can.
All of my students have published and presented their work at international conferences; several have won conference prizes. I have 75+ refereed publications, am actively involved in journal editorial work and conference organization, and have received both an institutional and provincial teaching award.
- Applied analysis
- Fractal-based methods in analysis
- Inverse problems
- Mathematical imaging
- The Development and Analysis of a System of Ordinary Differential Equations to Examine Long-Term Stability of an Aquaponic Environment
Carly Bobak, Master of Science (2016).
- Set Inversion Fractals
Bryson Boreland, Master of Science (2016).
- Human Health Modelling: Delay Differential Equations Inverse Problems and a Model of the Minamata Pollution Epidemic
Michael Yodzis, Master of Science (2014).
- Fractal Imaging Theory and Applications beyond Compression
Matt Demers, Doctor of Philosophy (2012).
- A Collage-Based Approach to Inverse Problems for Nonlinear Systems of Partial Differential Equations
Kimberly Levere, Doctor of Philosophy (2012).