Listening to Fairfield University associate professor Mark Demers, Ph.D., passionately discuss his research into chaos theory can make the mathematically challenged wish they had paid more attention in their calculus classes.

But the applications and implications of his theoretical mathematics research are wholly down to earth and may someday help us better predict catastrophic events. That's why the National Science Foundation (NSF) recently awarded the associate professor of mathematics a three-year, $168,500 grant to continue working with undergraduate researchers and travel across the country and around the world to present their findings and work with like-minded scholars.

What do Dr. Demers and his students study?

His research lies in the area of ergodic theory and dynamical systems - a branch of mathematics that studies how systems change over time and gave rise to chaos theory.  "It's the notion of evolving statistical probabilities," the Trumbull, Conn. resident said. "We know with average behavior over time something will eventually do X, but how fast and what are the deviations from this average behavior?  We're looking at the statistical properties of systems, which are closely tied to important concepts such as stability and predictability."

Dr. Demers is studying so-called non-equilibrium systems, in which mass or energy is entering or escaping from the system, and developing tools to determine how and at what rate these exchanges take place. The work is directly applicable to things such as weather systems, ocean currents and ice flow prediction models, areas in which insurance companies would have an interest, for example. Dynamical systems theory also applies to aerodynamics and ways to predict the movement of planets and satellites.

Even banks would benefit from insights into quantifying the occurrence of rare or catastrophic events, Dr. Demers said.

Dr. Demers began working in theoretical math while an undergraduate at Amherst College and he continued through his post-doctoral work at Georgia Tech. "Dynamical systems caught my interest because it's not a static thing," he said. "It talks about how things evolve and explores much of how the world works."

Dr. Demers received his first NSF grant for work in dynamical systems in 2008, two years after joining the Fairfield faculty. The new grant marks his third consecutive NSF grant. This grant provides funds for summer research, undergraduate research assistants and conference travel. Funds from previous grants have covered stipends and travel money for several promising math majors over the years.

"It affords a great opportunity for students and, for the University, the benefit is the students can stay here and work over the summer, too," Dr. Demers said.  "In addition, the enthusiasm of our summer research students spills over to our other math and science students during the academic year as they present their research to their classmates through our departmental colloquium."

James Simon, Ph.D., dean of the College of Arts and Sciences, said the project highlights some of the advantages of attending Fairfield and working one-on-one with such a renowned professor.

"The federal grant means that Dr. Demers' work is being recognized as cutting edge," Dr. Simon said, "and he is following a long tradition at Fairfield of faculty members encouraging students to work with faculty on major projects."

Posted On: 08-18-2014 03:08 PM

Volume: 47 Number: 27