Coping with Complexity
Smoke moving in the wind. Cream mixing in coffee. A wave breaking on a beach. These are among the simplest examples of how fluids move. Yet these movements are so complex that modern science has no easy way to describe them. What we do have is calculus and its sophisticated mathematical approach to modelling the actions of the world around us.
Non-linear partial differential equations (PDEs) are the mathematical language used to model the systems in the world around us that change over time. Modern examples include the transmission of data over fibre-optic cables, determining fluctuations in financial markets, the activities of drugs in biological systems, and the spread of infectious diseases. Formulating and studying the appropriate PDE always provides insight into the behaviour of the system, and hence has applications in its design and function.
Walter Craig is coming to McMaster University after teaching at the California Institute of Technology, Stanford University, and Brown University. He specializes in PDEs and their applications to a broad range of questions in fields as diverse as hydrodynamics and astrophysics. During the course of this work, he has also cultivated strong interdisciplinary links, particularly in theoretical physics and physical chemistry.
His research has regularly crossed mathematical frontiers, especially with respect to physical phenomena featuring waves. As the holder of a Canada Research Chair, he will continue to concentrate on some of most fundamental topics characterized by waves.
This work promises to address some major outstanding problems for which tidy mathematical solutions are not possible. Craig, however, will attempt to frame more sophisticated and elegant solutions. The result should be a significant development in mathematical terms, and a potentially valuable contribution to the mathematical tools available to researchers working in other disciplines.