Franco Saliola is a young researcher in the Department of mathematics of Université du Québec à Montréal who has successfully integrated computer algebra exploration into many facets of his research program. He works in an area of mathematics where properties of algebraic and geometric objects can be explored by looking at the interactions between certain combinatorial data structures. A main thread of this research program is dedicated to developing techniques to decompose certain intricate objects (“representations”) and to applying these techniques to longstanding decomposition problems in linear algebra, probability theory, and group representation theory. Some of the uses of computer exploration include: the effective development of intuition and visualizations for research problems; the ability to explore elaborate examples that would be hard to explore otherwise; and the development of proof strategies through high-level formal algebra manipulations.
