Major: Mathematics
Thesis: “Interactions Between Commutative Algebra, Galois Theory and Representation Theory”    
Summary: “Splitting algebra is hard to explain. Science can describe itself through science fiction: I wish there was a genre of ‘math fiction.’”
Polynomials
Felipe Pereira Debayle, who transferred to Amherst from Valencia Community College, did a thesis on pure math, in which he explored splitting algebra, via the Galois Theory and Representation Theory. This is the formula which inspired his thesis.

Raised in Nicaragua, where his schooling was spotty, Debayle joined part of his family in Florida when he was 17—and quickly realized he needed a better education. His mother and siblings were depending on him. “I Googled ‘high-paying careers’ and engineering came up, so I Googled ‘study engineering,’ and it said you had to be good at math,” says Debayle. He enrolled at Valencia Community College in Orlando and plunged into math classes.

It turned out Debayle excelled at the subject. Two Valencia professors helped him get ready to transfer to Amherst. “At a certain point everyone gets lucky,” he says. “My teachers in the Amherst math department have been super supportive.”

Especially his thesis adviser, David Cox, the William J. Walker Professor of Mathematics. Debayle chose a topic that related to Cox’s own work within Galois theory, in which certain problems in field theory can be reduced to group theory, which can be more easily understood. He worked with the splitting algebra, which provides a convenient way to study the roots of a polynomial.  

“When I got stuck, Prof Cox always wanted me to find the solution,” says Debayle. “But he was always willing to talk to me about it. At one point, I had arrived at a proof, but it was too complicated, with too many moving parts. It was quite a challenge even to type it. But a month before the thesis was due, we figured out a much more elegant proof. And I was very happy.”

Debayle plans to enroll in a Ph.D. program and become a math professor one day. It feels right, since he enjoyed tutoring at Valencia and regularly Skypes his younger siblings to help them with their math homework. “I don’t need to be a millionaire,” he says with a smile. “I’ll be able to help my family plenty being who I am, and what I intend to be.”