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The Applied Mathematics Research Group stands among Canada's most extensive and innovative teams. Their work encompasses diverse contemporary areas in applied mathematics, including numerical analysis, scientific computation, modeling, and theoretical analysis. Primary investigations concentrate on nonlinear partial differential equations and their extensive scientific applications. Computational research areas feature compressed sensing, fluid dynamics simulations, surface PDE numerical techniques, image/signal processing, spectral approaches, medical imaging, integral equation solutions, and adaptive mesh techniques. Modeling and analytical studies explore differential equation applications in atmospheric science, kinetic theory, fluid mechanics, cognitive research, biological mathematics, emergent collective behaviors, along with computational spectral theory and numerical method accuracy assessments.