Mark Demers, Ph.D., hopes he’ll soon find out. With the help of a $130,000 grant from the prestigious National Science Foundation, Dr. Demers, assistant professor of mathematics, is embarking on a three-year research project in dynamical systems and ergodic theory, a branch of mathematics that gave rise to “chaos theory.” He will study the evolution of systems that change over time and attempt to understand the stability and predictability of the systems. The grant provides funds for summer research, undergraduate research assistants and conference travel.
And the project isn’t just calisthenics for Dr. Demers’s nimble mind. His work has the potential for real-world relevance. “The topic of large deviations tries to quantify the occurrence of rare events,” he said. “This is very important, for example, to insurance companies or banks that may be concerned with how often catastrophic events occur.”
Dynamical systems theory also applies to weather, ocean current and ice flow prediction models, aerodynamics and ways to predict the movement planets and satellites and the collision of atoms.
Dr. Demers, who teaches in the College of Arts and Sciences at Fairfield, has long been fascinated with the complexity of behavior in simple systems. “As an undergraduate, I did a yearlong independent study in the subject,” he said. “Typical systems tend to have regions of chaotic behavior intermingled with regions of stability and rich structure. If you have ever seen a picture of a fractal, you begin to get a sense for how complex the interface between these two types of behaviors can be.”
Over the summer, Dr. Demers and one of his students, Janet Fusco ’12, worked on a specific mathematical model – “mathematical billiards” – which represents the dynamics of a particle bouncing around a table with obstacles. They studied some simple mechanisms that create regions of mixed behavior to see how regions form and break down. With support from the NSF grant, Dr. Demers was also able to travel to France for a conference related to his topic.
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