Distinguished University Professor, Senior Canada Research Chair, Ph.D. (Courant, N.Y.U.)
Dept. of Mathematics & Statistics, McMaster University
1280 Main Street West
Canada L8S 4K1
905-525-9140, ext. 23422
Research Area: Analysis, Applied Mathematics, Fluids & Turbulence
Research Profile: Nonlinear partial differential equations and dynamical systems
My research interests are in the theory of differential equations, concerning particularly those which arise in problems in mathematical physics and applied mathematics. The principal focus of my work has been on nonlinear equations, and for the most part these involve questions of time evolution and dynamics. Questions in this area arise in many areas of the physical sciences, and some of the topics of my research include quantum mechanics, fluid dynamics and cosmology. It is particularly pleasing to me when a mathematical question in one area brings up a problem of substance in another completely different and surprising area. Some examples of this in my own work include (1) the connection between free surface waves, Hamiltonian dynamical systems, and Morse-Bott equivariant cohomology of singular varieties, (2) Hamiltonian dynamical systems, Hamiltonian PDE and unusual questions on diophantine approximation, (3) Riemannian invariants, completely integrable systems and the ergodic theory of negatively curved manifolds, and (4) the reheating problem for the inflationary model in cosmology and the theory of Anderson localization in condensed matter physics.