Mathematics used to study abstract spaces

CHAMPAIGN, Ill., Aug. 16 (UPI) -- A University of Illinois mathematician is using topology to study abstract spaces and solve complex problems in a study funded by the U.S. government.

Mathematician Robert Ghrist says studying complex systems, such as the movement of robots on a factory floor, the motion of air over a wing, or the effectiveness of a security network, can present huge challenges so he is developing advanced mathematical tools to simplify such tasks.

Ghrist uses a branch of mathematics called topology to study abstract spaces that possess many dimensions, as well as to solve problems that can't be normally visualized.

While it may seem counterintuitive to initially translate such tasks into problems involving geometry, algebra or calculus, Ghrist says, doing so ultimately produces a result that goes back to the physical system.

"That's what applied mathematics has to offer," the UI-Champaign scientist said. "As systems become increasingly complex, topological tools will become more and more relevant."

The research is funded by the Defense Advanced Research Projects Agency and the National Science Foundation.

Ghrist is to describe his research during the International Congress of Mathematicians Aug. 23-30 in Madrid.