The CRM is pleased to announce that the 2006 CAP/CRM Prize in Theoretical and Mathematical Physics is awarded to John Harnad (Concordia University and CRM), for his outstanding contributions to the theory of integrable systems with connections to gauge theory, inverse scattering and random matrices. Combining a vivid intuition of physical systems with a sound mastery of  geometrical aspects of the theory, his work has had, in the last thirty years, a deep and lasting impact on our understanding of these subjects.

After obtaining a B.Sc from McGill University in 1967 and a M.Sc. from the University of Illinois en 1968, John Harnad did a D. Phil. in theoretical physics at the University of Oxford under the direction of Professor J. C. Taylor. After postdoctoral years at the Eötvös Institute in Budapest and Carleton University in Ottawa (1972-1975), he became a research associate at the CRM (1975-1984), and an associate professor at the Stevens Institute of Technology (1985-1986) and at the École Polytechnique in Montréal. He became a faculty member at Concordia University in 1989 and is now the director of the Mathematical Physics Group at the CRM.

He began his career as an elementary particle physicist. Turning towards non-Abelian gauge theories, he developed, with collaborators and students, the theory of dimensional reduction and applied it to obtain a great number of exact invariant solutions of the classical Yang-Mills equations and their supersymmetric extensions. Those investigations are still quoted by both mathematicians and physicists.

Since the early 1980’s, John Harnad has been mainly working on the theory of classical and quantum integrable systems and has become one of the world leaders in this field. Numerous and important, his contributions include : nonlinear superposition formulas for certain types of nonlinear ordinary differential equations that later turned out to figure as Bäcklund transformations for soliton type equations ; the introduction of the soliton correlation matrix in soliton theory, relating the inverse spectral approach to the holonomic quantum field approach of Sato et al. ; the Hamiltonian theory of quasi-periodic solutions of integrable partial differential equations and the introduction of spectral Darboux coordinates; the introduction of "dual isomonodromic deformations" in the general framework of the Hamiltonian theory of isomonodromic deformations.

John Harnad’s most recent work is devoted to the theory of random matrices. He and his collaborators have established a relationship between isomonodromic deformations and the spectral theory of random matrices. This permitted them to establish connections between isomonodromic tau functions, orthogonal and biorthogonal systems of polynomials associated to random matrices and the corresponding correlation functions.

John Harnad has been invited to give a plenary lecture during the 2006 CAP (Canadian Association of Physicists) Congress at Brock University in St. Catharines, Ontario from June 11-14.