Website: http://www.cas.mcmaster.ca/~deza/

Coming to Canada from

Tokyo Institute of Technology, Japan

Research involves

Combining theoretical and computational approaches to generate algorithms.

Research relevance

Deepening our understanding of combinatory structures with a view to solving large-scale problems, especially those of telecommunications networks.

The Secrets and the Power of Symmetry

What do the following things have in common: the dome of the US pavilion at Expo `67, the SARS virus, and the three-dimensional stable carbon molecule (the discovery of which won the 1996 Nobel Prize for Chemistry)?

They are all "fullerenes," named after architect Richard Buckminster Fuller. In other words, they are all symmetrical geometric structures that resemble the shape of a soccer ball.

The importance of the fullerene lies in nature and humanity's search for stability by achieving maximum effectiveness with minimum effort-a major characteristic of, as the presenter of the Nobel Prize put it, this "unusually beautiful body."

Mathematicians have known about three-dimensional polyhedra since Antiquity, and have studied the more complex ones since the nineteenth century. However, in the late 1940s, the linear programming paradigm gave polyhedra a new importance. This paradigm allows us to explore specific properties of polyhedra to design efficient computational methods. These methods are now applied in a variety of fields including production, transportation, computer science, telecommunications and bio-informatics.

Inspired by this, Antoine Deza has developed new techniques for using symmetry to solve large-scale problems. As chairholder, he plans to generate efficient algorithms by exploiting the combinatory and geometric characteristics of the problems under study.

One of his objectives is to design innovative optimization techniques to solve major combinatory problems, particularly those related to freight transportation. For example, what is the most cost-effective itinerary for a ship that has to deliver goods all over the continent? Among other things, Antoine Deza's research will help answer this question by analyzing all the possible trip combinations.

Another crucial objective of his work is to be able to "see" or "guess" the structure of a problem so as to choose only the most productive research avenues and avoid those that appear promising at first, but ultimately lead to dead ends.