Mathematics Professor Konrad Aguilar Involves Students in Researching Quantum Metrics

Konrad Aguilar standing in front of blackboard that is covered with mathematical formulas

The white board in Konrad Aguilar’s office is filled top to bottom with formulas relating to the research he leads into matrix mathematics, a field of study important to quantum information theory. The recent recipient of a National Science Foundation (NSF) grant has come a long way since being a seventh grader who was two grade levels behind in math and had to master four years of the subject in just two before he could start high school with his class.

“That sort of ignited a fire in me,” he recalls. “I put in the time to catch up—it was a lot of hours outside of school.”

These days, Aguilar, assistant professor of mathematics and statistics, teaches courses such as Advanced Linear Algebra, Principles of Real Analysis I and Calculus III. He also involves undergraduates in his research, including a project now funded by a two-year, $189,661 grant from the NSF. It is titled LEAPS-MPS: Noncommutative Geometry and Topology of Quantum Metrics. Aguilar explains that “it’s the study of how information is passed on at the quantum level.”

While the research may sound daunting to those who haven’t studied advanced mathematics, Aguilar notes in his NSF project summary that little background is required for students to become involved in it. In 2023, he had three Summer Undergraduate Research Program (SURP) students working with him and even involved four high school students in the Pomona College Academy for Youth Success (PAYS) in studying quantum channels. Not only were the students exposed to high-level math, but “they were able to learn some computer language,” Python, says Aguilar. “And I also taught them how to communicate mathematics” using LaTeX software.

Doing math together

At a time when demand for mathematicians and statisticians is projected by the U.S. Bureau of Labor Statistics to grow much faster than average, math is a top major at Pomona College. Aguilar notes that math “deals with questions that are very abstract,” but students don’t have to struggle with the challenging problems alone. There is a math lunch every Friday. And professors in the department “advertise a lot of office hours. We make sure students know we are available any time,” he says.

Aguilar remembers his own undergraduate experience as a community college student who was afraid of advanced math. “What helped me a lot,” he says, “was to talk to the professor one-on-one. I started going to office hours.”

Now, he’s replicating that accessibility for his own students, telling them, “Just come to do work, to hang out.” His office often fills up with as many as nine students working together on math problems on the white board and chalk board on his walls. “It’s not just learning equations,” he says. “It’s a community, too.”

Aguilar’s office glows with bright hues reflected onto the ceiling by colored paper he has draped over the hanging lights. “I grew up around a lot of colorful things. I guess it comes from my Mexican and Brazilian background,” he says. His parents wanted him to get a college degree, “but they never really understood my desire to study mathematics.” Now, he encourages students from populations underrepresented in the field to pursue a degree in math. And along with Karla Cordova, visiting assistant professor of economics, he is working to reestablish a Claremont Colleges chapter of SACNAS, a national society for the advancement of Chicanos/Hispanics and Native Americans in the sciences.

Helping students feel supported

“Some of the most fun I have is working on research with students,” says Aguilar. It’s not surprising, then, that Aguilar was one of seven Pomona faculty to win a 2023 Wig Award for excellence in teaching, announced at the May commencement ceremony. One student wrote of Aguilar in their nomination: “Super considerate and always willing to help! He always makes me feel supported as a student and a person.” Another mentioned his “extra effort to memorize every student’s name in class as to seem approachable and caring.”

And one lauded the way Aguilar helps students overcome their apprehension. “In a class that has a reputation for being one of the most feared major requirements, Konrad is truly exceptional in making himself accessible to students and breaking down the content and structuring the class in a way that makes it feel manageable,” the student wrote. “He is also incredibly involved in representing the department and creating a culture of openness and friendliness.”

“I just love working on math with others, and the classes and the teaching,” Aguilar sums up. And with his students, he finds joy “in watching them enjoy it as well.”