Math professor wins award for innovative work

By Peter Kim

Imagine having the power to monitor precise weather patterns, detect every possible movement in a room or play a perfect game of minesweeper every time.

Thanks to research on wireless sensor networks currently being performed by University math professor Robert Ghrist, this may be a possibility.

Collaborating with Vin de Silva, professor of mathematics at Pomona College in California, Ghrist solves problems in engineering and technology, particularly wireless sensors. Using topology, a branch of mathematics, he has found ways to map points within sensor networks.

Ghrist likens his work to three coins lying on a table.

“In a given space (the table), the three coins collectively represent one point. Now, that point forms a curve that you can map. As the coins move around, you can look at the curve, and it will tell you how the coins move around,” Ghrist said.

Now imagine that the coins are replaced by sensors.

According to Science News, one example is a network of sensors monitoring boats in a harbor. The sensors must be placed such that their areas of detection do not overlap or miss areas. If they overlap, a boat gets counted twice. If they miss an area, a boat slips through the cracks. Ghrist’s research uses topology to optimize the area covered by the sensors.

Nathan Dunfield, University math professor and topology researcher, relates the importance of such an application.

“Sensors are very small, very lightweight, and very cheap. However, since the sensors are cheap, they’re also very dumb,” said Dunfield.

A sensor doesn’t tell its exact location unless there are other sensors near it.

This also has many other useful applications in, among other areas, robotics control and pursuit and evasion games.

In the case of pursuit and evasion games, imagine now that the coins on the table are policemen in a building.

“If they are chasing a criminal through a building, where do they go? How do they catch the bad guy?” Ghrist said.

Using topological methods, the logistics of the chase can be mathematically calculated to neutralize the target as effectively as possible.

Ghrist first started his research in 1995, and attributes his involvement in topology to providence. His interest was first sparked by a book he found on topology.

“I read through it, didn’t understand it, but saw a lot of pictures,” Ghrist said. “I spent a lot of time just looking at the pictures and learned a lot just thinking about it.”

In recognition of his research, Scientific American has nominated Robert Ghrist as a recipient for the “Sciam 50” award. The monthly science magazine officially announced Ghrist’s selection for the award in its January 2008 issue. The annual award recognizes people who have lead significant advancements in science and technology.

“His research is radically different and brilliant,” said Sheldon Katz, professor and chair of the University’s math department. “He’s a real star. We’re very proud of him.”

Ghrist said he likes the award because it included mathematics under the category of technological advancement.

“A lot of people think mathematics is all just figure it out,” Ghrist said. “Everyone reads about the latest computer chip in a magazine, but not everyone subscribes to a math journal. I’m just glad math is getting its credit.”