Steven Scheirer, assistant professor of mathematics and computer science at Susquehanna University, and Alessia Revelli ’27, a mathematics and data science double major from Harleysville, Pennsylvania, collaborated to explore how abstract mathematics can model real-world systems.
“One of the beauties of mathematics is the ability to frame real-world systems, such as moving robots throughout a factory, in an abstract setting,” Scheirer said. “By studying these systems abstractly, we can discover properties that must always hold, regardless of the specific real-world implementation.”
The duo built upon his prior research on configuration spaces.
“You can think of this as a way of mathematically modeling a system of robots that move along a set of tracks throughout a factory,” Scheirer said. “Different versions of configuration spaces depend on specific rules the robots must follow, with each configuration representing a snapshot of where the robots are at a given moment.”
In their project, Scheirer and Revelli introduced a new structure called a grouped configuration space. In this setting, the robots must follow two key rules: certain predefined locations must always be occupied by at least one robot, and the robots are divided into groups, with no two robots from the same group occupying the same location.
With this framework in place, they set out to answer a fundamental question: is it always possible to move the robots from one valid configuration to another without breaking the established rules? The answer was dependent upon the number of groups involved.
“If there are only two groups, there are certain cases in which it’s not possible to move from one configuration to another,” Scheirer said, “but we were able to show that if there are at least three groups, then it’s always possible to move between any two configurations.”
For Revelli, the project constituted a personal milestone: her first experience writing a research paper.
“Learning how to write for a mathematical audience — being precise and clear while still making the ideas accessible — was a new experience,” Revelli said. “I had to adjust to the revision process, which involved rethinking explanations, restructuring arguments and refining proofs. It was challenging at first, but it ultimately helped me grow as both a writer and a mathematician.”
Scheirer and Revelli presented their work at the fall meeting of the Eastern Pennsylvania and Delaware Section of the Mathematical Association of America at York College.
“Sharing our research and engaging with mathematicians was an amazing experience,” Revelli said. “It helped me develop confidence in communicating mathematical ideas and gave me insight into the broader research community.”
Revelli believes the skills she gained through this experience will serve her well as she pursues her dream of working at NASA. This summer, she will intern with Barrios Technology at NASA’s Johnson Space Center in Houston, Texas, where she will gain hands-on experience applying mathematics and data science in a research environment.
“This research has strengthened a wide range of skills that are directly applicable to both engineering work and graduate-level research: problem solving, communication and collaboration,” Revelli said. Should Revelli choose to pursue an advanced degree, she adds that “having experience with a full research process will be extremely beneficial.”
