# Mathematics Faculty Awarded Grants to Foster Collaboration

Three faculty in the mathematics, computer science, and statistics department have been named inaugural recipients of AMS-Simons research grants.

Professor of Mathematics and Computer Science Nicholas Scoville and Assistant Professor of Mathematics and Computer Science Olena Kozhushkina have each received an AMS-Simons Research Enhancement Grant for Primarily Undergraduate Institution (PUI) Faculty. Each year for three years, grantees will receive $3,000 to support research-related activities and $300 in discretionary funds for the grantee’s department and $300 for administrative costs.

Assistant Professor of Mathematics and Computer Science Eric Mawuena Takyi has received an AMS-Simons Travel Grant, which awards $3,000 to support research-related travel and $600 in discretionary funds for the grantee’s department each year for two years.

These collaboration grants were established in 2012 and initially available to all mathematicians, but in 2016 they were restricted to mathematicians at R1 institutions, which are doctoral-granting universities where the primary focus extends beyond teaching. This year is the first since 2016 that primarily undergraduate institutions (PUIs) have been eligible to receive the grants.

“I think it’s a good sign that the Simons Foundation is recognizing the importance of research at primarily undergraduate institutions,” said Scoville, who is also the Joseph Beardwood III Chair of the department.

“Ursinus really is the place that models quite perfectly the teacher-scholar model where teaching is extremely important—it definitely is primary and we want to be excellent teachers—but also we expect serious research, serious scholarship from our faculty. Having these grants allows us to engage in that and do that research.”

All three recipients are “in very different areas of math, collaborating with very different people, and doing very different projects,” said Scoville, whose research focuses on digital topology, which employs mathematical tools to help decipher images.

“Something silly is maybe a blurry photograph, but something else might involve photos from space or a drone, and I’m trying to determine if something’s happening in a jungle, or maybe in the ocean, or remote places where maybe I can get a picture, but it’s not going to be an ideal picture. If it’s hard to tell what’s going on with the eye, I can use mathematical tools to study these objects and determine if they have the overall shape of the kind of thing I might be interested in finding.”

His proposal included five projects, with collaborators at the University of Florida, Fairfield University, the University of Utah, the University of Seville, the University of Santiago, and Cleveland State University (CSU), where he visited shortly after receiving the grant. There, he and Greg Lupton, professor and chair of mathematics and statistics at CSU, wrote an entire paper in one week together. “That really is the power of collaboration and being physically there together. It’s something that you don’t get when you meet with someone over Zoom,” said Scoville.

Eric Mawuena Takyi, whose area of expertise is math ecology, does modeling of populations to see how they evolve over time. His research examines biological control of invasive species using mathematical modeling.

“Invasive species are very harmful to the environment and cause so much damage to the ecosystem. A lot of times people use chemicals to control them, which is not ideal because it causes problems to the natural environment,” said Takyi. “Bio control is basically introducing a natural enemy to the invasive species, which would help control it, but there are other techniques used, such as disrupting the mating system, which simply means skewing a particular population towards males.”

For example, in invasive fish populations, when the population is skewed towards males over a long period time, female population will near extinction and reproduction will decrease or cease.

“Everything that changes with time is simply calculus. So for the modeling framework, you think about the birth rates, you think about the natural death rates, you think about how they interact. There are functions used in describing population interactions.”

Takyi recently used a portion of the grant to travel to the Society for Industrial and Applied Mathematics (SIAM) Central States Section (CSS) Annual Meeting in Lincoln, Nebraska, where he presented on “Sex-biased predation and predator intraspecific effects in a mating system,” work that was done jointly with Research Experience for Undergraduates (REU) students Charles Ohanian, Margaret Cathcart, and Nihal Kumar this past summer. In January 2024, Takyi will attend the annual Joint Mathematics Meeting in California. “This is the biggest math conference in the U.S. so it’s a big deal,” he said.

Olena Kozhushkina is a functional analyst whose project focuses on number theory.

“We study how divisible sequences are by certain numbers. On a higher level, it has lots of applications in computer science, finance, and algebra,” she said. “In my project, we look at the sequences of numbers and represent them as tree diagrams. Depending on the sequence, we can end up with a tree that looks like a finite tree: it splits and then it splits again and has two levels. Sometimes we end up with a tree that looks like an infinite tree that keeps going. What I really like about this project is it’s usually easy to draw pictures, which helps a lot because if you can visualize, it’s easier to grasp what’s going on.”

It was a 2019 Research Experience for Undergraduate Faculty (REUF) workshop hosted by ICERM and the American Institute of Mathematics that inspired the project and introduced Kozhushkina to her collaborators: Jane Long, professor of mathematics and statistics at Stephen F. Austin State University; Justin Trulen, associate professor of mathematics at Kentucky Wesleyan College; Bianca Thompson, associate professor of mathematics at Westminster College; and Maila Brucal-Hallare at the United States Air Force Academy.

When Trulen and one of his students visited campus to participate in the Research Experience for Undergraduates (REU) program at Ursinus this summer, it presented an opportunity for him and Kozhushkina to discuss their project in person. Their group, which previously contained two additional collaborators, has been meeting weekly since 2019. By June, Kozhushkina, Long, and Trulen had completed part of a paper, but were stuck on a problem.

“Once we were able to actually sit together and write and stuff on the board, we were done with that part in two days,” said Kozhushkina. “It was really remarkable.”