Order Out of Chaos
The field of dynamical systems is the study of mathematical models for the evolution of physical systems. Although the mathematical foundations are very old, the field has become one of increasing importance in the last twenty years. Part of this can be traced to advances in computational technology, but of equal importance is the discovery of the phenomenon now known as chaos and its pervasive role in nature. The study of dynamical systems has also played an important role in information theory and its application to information technology.
Operator algebras were developed as a model for quantum mechanics in the early part of the last century. The seminal work of Murray and von Neumann demonstrated the close connections between this subject and dynamical systems.
Dr. Ian F. Putnam, Canada Research Chair in Operator Algebras and Dynamical Systems, is recognized worldwide as a top expert on the interrelation of these two subjects. He is the leader of an international group of researchers who bring the powerful tools of modern operator algebra theory to the study of operator algebras associated to topological dynamical systems.
Dr. Putnam will continue his explorations using the tools of Alain Connes' program of non-commutative geometry. The goal of Dr. Putnam's research is two-fold: to construct from dynamical systems new examples of C*-algebras and to apply the tools of non-commutative geometry to these C*-algebras to obtain new information about the dynamics. Some specific immediate areas of interest are the study of aperiodic order, topological orbit equivalence and Smale's program for hyperbolic (i.e. chaotic) dynamics from smooth systems.
Dr. Putnam will be working closely with collaborators at the university and at the Pacific Institute for the Mathematical Sciences (PIMS), and plans to form a group of collaborators from among these and other institutions. With Dr. Putnam's appointment to this Chair, this group could soon become one of the strongest mathematical centres in Canada.