Canadian Association of Physicists ASSOCIATION CANADIENNE DES


2006 CAP/CRM Prize in Theoretical and Mathematical Physics

will be awarded to

Dr. John Harnad

"It is very gratifying to have work recognized in this award that is aimed at the precise use of mathematical constructions, whether very concrete or abstract, in the resolution of problems of real interest to physics"

Dr. John HarnadThe Canadian Association of Physicists (CAP) is pleased to announce that the 2006 CAP/CRM Prize in Theoretical Physics is being awarded to Dr. John Harnad of Concordia University for his deep and lasting contributions to the theory of integrable systems with connections to gauge theory, inverse scattering and random matrices.

John Harnad started his career as an elementary particle theorist with a first publication in 1972. He quickly turned to one of the most promising and mathematically profound areas in this field, namely non-Abelian gauge theories. Together with collaborators and students he published a series of fundamental papers in which he developed the theory of dimensional reduction and applied it to obtain a great number of exact and physically important invariant solutions of the classical Yang-Mills equations and their supersymmetric extensions. Those papers 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's leaders in this field. The list of areas in which he has made important contributions is long and impressive. It includes the following: nonlinear superposition formulas for certain types of nonlinear ordinary differential equations that later turned out to figure as Backlund 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. Here, John Harnad and his collaborators combined the use of algebraic geometry and loop groups to achieve a separation of variables in phase space for a wide class of integrable systems, both finite and infinite dimensional. He was also responsible for the introduction of "dual isomonodromic deformations" in the general framework of the Hamiltonian theory of isomonodromic deformations.

The most recent and ongoing series of John's publications is devoted to the theory of random matrices. He and his collaborators established a very interesting and beautiful 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's work has collected over 1000 significant citations. Most important, he has succeeded in building a very strong international research group centered in Montreal, working on integrable systems.

Like all leading scientists, he has developed his own "scientific signature". In his case, it is the combination of a profound physical insight with the use of the most sophisticated abstract mathematics, the development of deep understanding from specific and concrete calculations and the derivation of genuine physical results from first principles.

The annual CAP-CRM Prize in Theoretical and Mathematical Physics was first introduced in 1995. Dr. Harnad will receive the 2006 Prize during the CAP's awards banquet to be held in St. Catharines on June 13th, 2006.

The Canadian Association of Physicists, founded in 1945, is a professional association representing over 1600 individual physicists and physics students in Canada, the U.S. and overseas, as well as a number of Corporate and Departmental Members. In addition to its learned activities, the CAP also undertakes a number of activities intended to encourage students to pursue a career in physics.

The Centre de recherches mathématiques is a national research centre in mathematics and theoretical physics jointly supported by the federal government, the province of Quebec, and the Université de Montréal where it is based. Among the activities of the CRM are thematic years, summer schools, workshops, seminars, and the publication of monographs, proceedings, and lecture notes in mathematics and physics.

For more information, please contact:

Canadian Association of Physicists
Tel: (613) 562-5614
Fax: (613) 562-5615

or Centre de recherche mathématiques
Tel: (514) 343-7501
Fax: (514) 343-2254