The modeling of the thermodynamic properties of complex materials, such as liquid crystals, lipid multilayers and soft materials.

In 1970, André Caillé obtained his doctorate in physics from McGill University, under the direction of Philippe Wallace. The same year, he decided to work with Pierre-Gilles de Gennes, whom he accidentally met aboard a plane making a trip to Grenoble in France. It will be a turning point in his scientific career. In 1971, he moved to Paris to study fluid mechanics. He decides to determine the mathematical model explaining the behavior of liquid crystals. He succeeds, developing what will be called the Caillé's exponents. Subsequently, while continuing to work on crystals, he held various positions at the Université du Québec à Montréal, Université de Sherbrooke and the Université de Montréal.