USU Mathematician Matthew Young Receives NSF CAREER Award

In the conceptual and sometimes murky world of mathematical theory, how do you make abstract objects and ideas more understandable?

The answer, says Utah State University mathematician Matthew Young, lies in using tools from linear algebra to distill abstractions into simpler, more concrete representations.

“For example, algebraic tools can help us understand exotic symmetries that occur in physical systems,” says Young, assistant professor in USU’s Department of Mathematics and Statistics. “Such tools are useful in understanding the behavior of quantum systems — a crucial aspect of quantum mechanics — as well as in understanding particle physics or properties of molecules. Representation theory is also used in computer science and social sciences — in any field where a framework is needed to explore symmetries in varied systems.”

Young, who has long studied representation theory, including Hall algebras, quantum groups and matrix factorizations, is the recipient of a five-year, $450,000 Faculty Early Career Development Program (CAREER) award from the National Science Foundation. The competitive award will fuel Young’s research program, much of which he conducts jointly with students, along with colleagues at USU and other institutions, while allowing him to pursue statewide collaborations and educational outreach.

Among these collaborations is Young’s involvement in the annual Moab Topology Conference, which he organizes with USU colleague Nathan Geer and mathematicians from other universities. The gathering provides early-career graduate students and postdoctoral fellows with opportunities to focus on recent developments in geometric and quantum topology and to publicly share their work.

Young is also working with colleague Nghiem Nguyen, Mathematics and Statistics professor, who coaches USU’s annual Putnam Mathematical Competition team, which consistently places in the top quartile of the international contest.

“The Putnam competition is the preeminent mathematics competition for undergraduates in the U.S. and Canada,” Young says. “The event itself is challenging and fun, but the preparation is the process that builds mathematical skills and camaraderie.”

Young’s efforts will reach beyond USU’s Logan campus, into Utah’s secondary educational system. With USU mathematics professor and associate dean Brynja Kohler, who is leading a statewide, NSF-funded effort to bolster training for secondary math teachers throughout Utah, Young will develop tools to connect USU math education to statewide high school curricula. Part of this involves guiding graduate and undergraduate students in developing math learning videos for high school teachers-in-training.

“This project will create valuable, hands-on learning opportunities for university-level students, from which high school students and their teacher will greatly benefit,” he says. “On the university side, college students will develop skills in math teaching, curriculum development, video production, learning evaluation and overall communications planning and management. On the high school side, teachers will gain effective teaching tools that will engage teens and, hopefully, make learning more relevant and fun.”

No stranger to outreach, Young, with undergraduate researcher Seth Porter, presented to hundreds at USU’s Science Unwrapped public event for all ages in spring 2025.

“An important part of the NSF CAREER grant is demonstrating how research can have broader impacts — that is, how it benefits society,” Young says. “I look forward to sharing my enthusiasm for mathematical knowledge with my students, my peers and people throughout Utah and beyond.”