On a brisk Friday afternoon as flags outside Laurentide Hall whip straight out in the wind, two people in the Math Lab just inside the front door hunker over numbers which fill most of the available whiteboard space.
One is young and modish with thick, shoulder-length hair and a crisp blue shirt. The other is sturdy, scholarly and bespectacled. They both appear to have been thinking hard about something for a very long time.
The younger of the two, UW-Whitewater senior Ryan Schroeder, hopes one day to earn a Ph.D. in mathematics and has just received an honorable mention award from the Barry M. Goldwater Scholarship and Excellence in Education Foundation for work his work in the Math Lab with his mentor, Associate Professor Leon Arriola.
The two, with help on this day from assistant professor Aditi Ghosh, are looking for a key to a problem or maybe a key to heading off one.
Like the good teacher he is, Arriola can paint a picture of what the numbers mean.
"You are in the Goodyear Blimp over the Super Bowl and you're filming the people coming into the stadium," he says. "You are very high above; it's a very macro view. The people almost look like a fluid flowing. But what you don't see is the little accidental incidents like where somebody spills their beer and that leads to a fight and maybe a riot.
"It's an unlikely event that creates a horrendous result," he said. "It's what we call a ‘Black Swan Event.'"
Mathematicians like Arriola and Schroeder look at the growth, decay and stasis of objects — not from the Goodyear Blimp perspective but from a micro, quantum view — in order to identify in mathematical terms what interactions may make a Black Swan Event possible. While these interactions may be subtle, Arriola says they can be essential features of serious problems.
"In mathematical biology, we are interested in the spread of epidemics," Arriola said, pointing out random, unforeseeable interactions which have contributed to serious epidemics. He wrote papers advising the Centers for Disease Control and the World Health Organization on how to prioritize their efforts in the SARS outbreak of the early 2000s.
"We're looking at a quantum level trying to identify the basic building blocks of interactions and make predictions on what will happen most of the time," he said. "Once we understand those fundamental things, we can start forming scenarios."
Applications for this kind of knowledge are wide-ranging — everything from identifying the factors which can interact to cause disease outbreaks and bridge failures to examining how rumors travel.
"A carpenter will use a hammer, saw and other tools from the same box in many different projects," Arriola explains. "These tools (the mathematics) are powerful enough to apply to many different situations," he adds. "It's telling us about the problem in ways we didn't expect."
Arriola and Schroeder are collaborating with researchers at Los Alamos National Lab and Arizona State and Tulane universities. Their work will be published in a series of papers.
While Schroeder's laptop is open on the table between them in the math lab, the real work seems to be taking place on the equation-filled whiteboards around the room.
"It sometimes involves using computers and sometimes it involves using pencil and paper," said Arriola. "It's sheer brainwork and writing out the mathematics."
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