Mathematician-physicist John Harnad honoured

Fascinated in childhood by Einstein and music

Janice Hamilton

At its annual meeting this June, the Canadian Association of Physicists (CAP) will present Concordia Mathematics Professor John Harnad with the CAP-CRM prize in theoretical and mathematical physics in recognition of his "deep and lasting contributions to the theory of integrable systems with connections to gauge theory, inverse scattering and random matrices."

Harnad is a professor in the Department of Mathematics and Statistics and also Director of the Mathematical Physics group at the Centre de recherches mathématiques (CRM), a national research centre in mathematics. Harnad calls the CRM "a crossroads in mathematics." Members include mathematicians from several Quebec universities, and people come from around the world to attend its conferences and workshops.

His own research is aimed at developing mathematical methods for tackling problems in physics.

Physics is concerned with understanding phenomena in the real world, he explained in an interview.

"For a physicist, mathematics is both a language to express concepts and relations, and a tool for the solution of problems, ultimately providing explanations about physical observables. My curiosity is motivated by physics, but my creative abilities seem to be more along mathematical lines."

Harnad was born in Budapest shortly after WWII, and his family immigrated to Canada in 1948. As a student in Montreal, he had two passions: physics and music. He and his brother attended the Jeunesses Musicales summer camp in the Eastern Townships throughout their high school years.

He was fascinated from an early age by ideas like Einstein's theory of relativity. While doing an honours degree in physics at McGill, he also studied the oboe at the Provincial Conservatory of Music. He then did his PhD at Oxford University on theoretical elementary particle physics.

After completing his doctorate, he spent a year in Budapest doing postdoctoral research, and then held a postdoctoral fellowship at the Physics Department of Carleton University. For several years following, he worked at the CRM, focusing full-time on research. He then moved to the U.S., spending a year at the Institute of Advanced Study in Princeton, then taking up an appointment as associate professor at the Stevens Institute of Technology in New Jersey.

In 1986 he returned to Montreal to teach in the Applied Mathematics Department of the ƒcole Polytechnique. He joined Concordia in 1989 and has been here ever since. Throughout these years, he maintained his interest in music, performing often with chamber music groups and occasionally with small orchestras.

The focus of Harnad's research has transformed during his career, but he notes that an underlying theme has run through all his work. He compares this theme, called dimensional reduction, to Plato's metaphor of shadows on the wall of a cave, in which viewers cannot see the origins of the shadow images, which are projections of moving figures.

He notes that when a simple mechanism, such as a rotating cube, is projected onto the wall, the image appears more complex than the original object.

Dimensional reduction provides a way of understanding seemingly complicated physical interactions by viewing them as projections of a much simpler system in a higher dimensional space. The plenary address that he will give at the CAP meeting discusses the use of dimensional reduction as a general geometrical principle underlying the dynamics of particles and fields. 

"My brain tends to function like a mathematician," Harnad said. "I need to have things logically clear. But my heart is that of a physicist: I care about nature and the way the real world works. I like to see some connection between my work and nature, and not just to solve abstract problems."