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This summer, Aydin Gerek ’07 (Istanbul, Turkey) discovered many different ways to examine a four-dimensional shape through a collaborative project made possible by Lafayette’s Research Experiences for Undergraduates (REU) program.
The REU program is an intensive, eight-week summer research experience in which undergraduate students from colleges and universities throughout the country investigate unsolved problems in mathematics. Student participants work in small groups with a faculty mentor.
Gerek worked under the guidance of Gary Gordon, professor of mathematics. Other members of his team included Andre Perunicic of Bard College and Stephii Fried of Grinnell College.
The researchers examined the combinatorial symmetries of a four-dimensional shape called the 24-cell. Gerek explains that combinatorial symmetry is “geometric symmetry with its definitions somewhat loosened,” which involves maintaining relationships between vectors coming from the object. The group’s task was to find out if there were any extra symmetries produced from this loosening of the definition.
Gordon plans to compile the group’s research results and submit them to an academic journal. The students also will present their research in January at the Joint Mathematics Meetings in New Orleans.
“It was a fun question to work on and everyone had a different approach to solve it,” Gerek, a mathematics major, says. “As such, trying to understand everyone’s methods and proofs was a challenging and rewarding experience – challenging because I learned a lot of new math and rewarding because often those methods would contain answers to the problems I had in my own methods. In the end, we found that there’s only one more symmetry when the definition is loosened.”
Each student brought individual strengths from various academic backgrounds to help the team complete its problem.
“There was no formal division of labor,” he says. “We often used each other’s methods, and swapped questions and findings, which proved very useful. I was more interested in the algebraic properties of the shape we were working on and [focused] more on that aspect.”
Gerek enjoyed interacting with students from other colleges, especially the ways they approached the research. Gerek also found working with Gordon to be a valuable experience. He took the team to the NSF/CBMS Regional Conference on Cluster Algebras and Applications at North Carolina State University in June.
“He’s a very fun guy,” Gerek explains. “You’re always at ease around him. This makes it very easy to communicate ideas back-and-forth and learn efficiently. The math department at Lafayette is superb. The professors are certainly encouraging, and they organize many events. In higher-level classes, the professor-to-student ratio is very good. As such, learning one-on-one from a professor is quite possible.”
Gordon was impressed with Gerek’s enthusiasm and commitment to the project.
“Aydin is a terrific problem solver, and he has lots of imagination,” he says. “I thought he could really contribute a lot of ideas to the group, and he did. He generates lots of different approaches to a problem. He also combines a geometric intuition with a very strong background in proofs.”
Gerek believes he learned a great deal about mathematics and working as part of a research team by participating in the REU program, two of the program’s main goals.
“Lafayette’s REU program is really the signature program for the math department,” Gordon explains. “There are about 25 such program sites nationwide. [Lafayette’s REU program] brings lots of very strong students to campus and exposes Lafayette students to top students from all over the country.”
As a national leader in undergraduate research, Lafayette sends one of the largest contingents to the National Conference on Undergraduate Research each year. Forty students were accepted to present their research at this year’s conference.