Distinguished Fellow Analyzes Abstract Math

Editor’s Note: Distinctive Stockton Students will feature students who receive the Board of Trustees Fellowship for Distinguished Students. This is the last of five posts on the students who received those fellowships this past spring/summer.

“I really love math and learning new things about math,” said Wayne Laffitte, a senior double major in Mathematics and Computer Science.

He’s particularly drawn to the mysteries of abstract algebra, and through the Fellowships for Distinguished Students program, he is studying conjugacy in Thompson groups.

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“Group theory is a subfield of mathematics — it can be thought of as the study of symmetry,” explained Laffitte, a native of the Villas section of Lower Township in Cape May County.

A simple example of a group is the set of all positive and negative numbers and the addition operation. More complex groups don’t necessarily deal with numbers and can “describe crystal structures and the symmetries of molecules in chemistry,” Laffitte said.

“Groups play a large role in quantum mechanics and elementary particle physics. They can even be used to describe solving a Rubik’s Cube,” he added.

Stockton’s math courses explore group theory—there’s an entire course dedicated to the topic—but Laffitte is delving deeper into the mathematics to explore a specific group discovered in the 1960s, the Thompson group.

Conjugacy in group theory means that a group satisfies a specific equation, and there is a different solution to the conjugacy problem for every group. It’s important to explore this math property because some solutions are so complex that a computer cannot make the calculation fast enough. Mathematicians seek out groups with complex conjugate solutions for cryptography.

Laffitte is currently exploring the conjugacy of the Thompson group because he is seeking background information for his next endeavor in which he’ll work with a newly discovered group. “[The newly discovered group’s conjugacy] hasn’t been solved yet and I want to see if I can solve it,” Laffitte said.

“The fellowship has given me an opportunity to experience independent research and better prepare myself for graduate school.  I’ve been able to learn about something that is outside of a standard classroom curriculum and have a lot of fun doing it,” he said.

Over the last two years, Laffitte has helped fellow students in his role as a math and programming tutor in Stockton’s Tutoring Center. “My job as a tutor is very rewarding.  I think I benefit from tutoring just as much if not more than the students that come to me for help,” he said.

His tutoring work carries over into the summer months when he works with incoming freshmen in the Educational Opportunity Fund (EOF) program.

Laffitte plans to attend graduate school and to pursue a career as a math professor.

“I’m very thankful for all of the help that I’ve received from my project advisor, Dr. (Bradley) Forrest.  He’s been a key part of my success over the last four years at Stockton,” he said. He also credits Dr. Chia-Lin Wu, Dr. Judith Vogel and Dr. Juan Tolosa with making a big impact on his undergraduate math experience.

“I’ve had an amazing time during my last four years at Stockton.  Everyone in the math program, the EOF program, and the tutoring center has made my time truly special and memorable.”