Greg Lewis, PhD
Associate Professor
Mathematics
Faculty of Science
Mathematics
Faculty of Science
Dr. Lewis' research is focused on the application of computational methods to the analysis of large-scale fluid dynamics.
Full biography
Climate change is one of the greatest threats to environmental and economic health, forcing the hand of governments, academia and industry to take increasing action towards a globally sustainable future. The dynamics of the atmosphere play a central role in the climate and climate change, and yet, this role is not well understood. A search for a better understanding of the atmosphere’s inherent behaviour and its relation to the climate is at the centre of the research of Greg Lewis, Ph.D., Associate Professor of Mathematics in the Faculty of Science. His research focuses on the mathematical analysis of geophysical fluid dynamics, the naturally occurring, large-scale flows in the ocean and the atmosphere. Although many factors such as changes in temperature, rotation, topography and the formation of clouds affect the dynamics of atmospheric systems, Dr. Lewis’ research centres on the effects of the primary factors, namely, heating and rotation. In particular, his research aims to determine the flow patterns that are expected as these factors are varied. A better understanding of such atmospheric dynamics may lead to improvements in the global climate models used to predict climate change. Appointed to his current role in 2008, Dr. Lewis joined 2003 as its first Assistant Professor of Mathematics. Since then, he has been rigorously building the university’s Applied and Industrial Mathematics, and Modelling and Computational Science undergraduate and graduate programs and growing the overall department. His early teaching and research influence has helped distinguish unique mathematics-based programs. His inherent desire to understand how things work, initially led Dr. Lewis towards physics, earning his Bachelor of Science in Honours Physics and his Master of Science in Physics from McGill University, before shifting gears and completing his Doctorate in Applied Mathematics from the University of British Columbia (UBC). Subsequently, he was awarded three post-doctoral fellowships with the Peter Wall Institute for Advanced Studies in the Departments of Mathematics and Earth and Ocean Sciences at UBC, as well as NSERC and Jerrold E. Marsden fellowships with The Fields Institute of Research in Mathematical Sciences at the University of Toronto. He has been an invited Distinguished Alumni Lecturer at UBC’s Institute of Applied Mathematics, and is an Adjunct Professor in the Department of Mathematics and Statistics at York University in Toronto. Ontario Tech University in Ontario Tech University's
Areas of expertise
Courses
- MATH 2050ULinear AlgebraThis course is designed to develop the fundamental ideas of linear algebra, and to demonstrate some applications of linear algebra to other areas. Topics include the algebra of matrices; qualitative and quantitative solutions of systems of linear equations; determinants and matrix inverses; real and complex vector spaces, and subspaces, linear independence, bases, dimension and co-ordinates; inner product spaces and the Gram-Schmidt process; inconsistent (over determined) systems of equations, least squares solutions and regression; linear maps and matrices, change of basis and similar matrices; eigenvalues, eigenvectors and matrix diagonalization; diagonalization of real symmetric matrices and quadratic forms.
- MATH 2060UDifferential EquationsA study of differential and difference equations that arise as models of phenomena in many branches of physical and biological sciences, in engineering, and in social science. Examples include Newtonian mechanics, chemical kinetics, and ecological system models. Students learn the basic properties of differential and difference equations, techniques for solving them, and a range of applications.
- MATH 4010UDynamical Systems and ChaosThe modern theory of differential equations studies the behaviour of solutions of nonlinear differential equations. In particular, the notion of dynamical system is crucial to the development of the theory and leads to the analysis of chaotic solutions. The course will provide the student with a rigorous treatment of the qualitative theory of ordinary differential equations, and an introduction to the modern theory of dynamical systems and to elementary bifurcation theory.
- MCSC 6120GNumerical Methods for Ordinary Differential EquationsDifferential equations are an indispensable tool for the modelling of physical phenomena. However, most often in practice, analytical solutions to model equations cannot be found and numerical approximations must be made. In this course, practical computational techniques for the numerical solution of ordinary differential equations are covered, with an emphasis on their implementation and the fundamental concepts in their analysis. Topics include numerical methods for initial value problems: forward and backward Euler and trapezoidal scheme; implicit and explicit Runge-Kutta methods, including general formulation; linear multistep methods: Adams-Bashforth, Adams-Moulton, Backward Differentiation Formulae (BDF); and numerical methods for boundary value problems: simple and multiple shooting and difference schemes. In association with the techniques, topics such as convergence, accuracy, consistency, 0-stability, absolute stability, Astability, stiffness, and error estimation and control are discussed.
Education
- 2000PhD - Applied MathematicsUniversity of British Columbia, Vancouver, British Columbia
- 1993MSc - PhysicsMcGill University, Montreal, Quebec
- 1991BSc - Honours PhysicsMcGill University, Montreal, Quebec
Speaking Engagements
- Waterloo, Ontario July 6, 2015A Numerical Study of the Effects of Inhomogeneous Media in Diffusion Weighted Imaging2015 Applied Mathematics, Modelling and Computational Science-Canadian Applied and Industrial Mathematics Congress
- Barcelona, Spain December 31, 1969Invited Talk: Hopf Bifurcation with 1:2 Spatial Resonance in an Air-Filled Differentially Heated Rotating AnnulusDynamical Systems in Fluid Mechanics Session of the 11th World Congress on Computational Mechanics/5th European Conference on Computational Mechanics/6th European Conference on Computational Fluid Dynamics
- Saskatoon, Saskatchewan December 31, 1969Invited Talk: Matrix-Free Methods for ElectroconvectionCanadian Symposium on Fluid Dynamics/2014 Canadian Applied and Industrial Mathematics Annual Meeting
- Berlin, Germany December 31, 1969Invited Talk: The Primary Flow Transition in the Baroclinic Annulus: Prandtl Number EffectsEUROMECH Colloquium 552
- Québec City, Québec December 31, 1969Single Parameter Spatiotemporal Model for the Depth Perception in Weakly Electric Fish2013 Canadian Applied and Industrial Mathematics Annual Meeting
- Toronto, Ontario December 31, 1969Invited Talk: Secondary Transitions and Instabilities in Geophysical FluidsCanadian Symposium on Fluid Dynamics/2012 Annual Meeting of the Canadian Applied and Industrial Mathematics Society
- University of Guelph December 31, 1969Secondary Transitions and Instabilities in Geophysical FluidsSHARCNet Research Day 2012
- Toronto, Ontario September 12, 2011Invited Talk: Mixed-Mode Solutions in an Air-Filled Differentially Heated Rotating Annulus. Spatial ResonanceFluid Dynamics Symposium of the Canadian Mathematics Society Winter Meeting
- Vancouver, British Columbia December 31, 1969Invited Talk: Secondary Flow Transitions in the Differentially Heated Rotating AnnulusInternational Congress of Applied and Industrial Mathematics - ICIAM 2011
Affiliations
- Canadian Applied and Industrial Mathematics Society
- Society for Applied and Industrial Mathematics
- Fields Institute Mathematics-in-Industry Case Studies Journal