Brendan Miller Wins Outstanding Research Award

April 17, 2019 | Joliet, Ill.

University of St. Francis (USF) mathematics major Brendan Miller of Minooka, Ill., recently earned the Outstanding Undergraduate Research Award through the Illinois Section of the Mathematical Association of America (ISMAA). The award was presented at ISMAA’s annual conference in Carbondale, Ill., on Saturday, March 30.

Miller, a third-year student at USF, earned the award based on his research on the categorification of matrices over the natural numbers.

“Most mathematics is based on what we call set theory. Set theory works very well as a mathematical foundation, but it does have its own limitations. Category theory is more of an abstraction of set theory, but it operates very differently and has fewer restrictions,” Miller said.

“The process of categorification is, generally speaking, a way of translating from set theory to category theory. However, this process is not formulaic, and it is very difficult to translate one mathematical structure. My research was focused on translating the concept of matrices over to category theory.  Specifically, I focused on the case when matrices only had positive, whole number entries,” he added.

Miller’s research, which was funded through the USF Summer Undergraduate Research Experience (SURE) program, was conducted during the summer following his second year of college. Miller’s USF faculty advisor and professor, Angela Antonou, Ph.D., supervised the research project.

“This topic is within the field of category theory, which is considered to be far beyond the scope of a typical undergraduate curriculum and even beyond introductory graduate topics in abstract algebra. His result is an extension of a theorem that was published in 2015 through the Rose-Hulman Undergraduate Mathematics Journal,” Antonou said.

After working with him through this process, Antonou is already looking forward to Miller’s future contributions to the field of mathematics.

“Working with Brendan was such a joy. He worked diligently and independently throughout the process, and the critical element to his proof was constructed entirely through his own innovation. His work was so clean that it felt as though I was working more with a colleague than a student. He is already working on graduate level mathematics as a junior – I look forward to seeing all of his other contributions to mathematics, which I expect will be numerous and significant, as he continues throughout his career,” Antonou said.

Following graduation, Miller plans to continue his education in graduate school in pursuit of a doctoral degree in mathematics.

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