SRU student exploring geometric manifolds as part of grant-funded project


Student working on the black board

Slippery Rock University student Elijah Saesan sketches geometric manifolds as part of his summer research project with Kirk McDermott, assistant professor of mathematics and statistics.

Aug. 10, 2022

SLIPPERY ROCK, Pa. — In addition to his job as a chef at a local restaurant, Elijah Saesan is cooking up some geometric manifolds as a student researcher at Slippery Rock University this summer. A junior mathematics major from Rice's Landing, south of Pittsburgh, Saesan is working closely with Kirk McDermott, assistant professor of mathematics and statistics, on a faculty-student research project funded by SRU's Summer Collaborative Research Experience grant program, which helps introduce undergraduate students to the world of academic research.

Instead of working with ingredients in a kitchen, Saesan is plotting graphs on paper and analyzing parameters with the help of computational software. This helps him find new examples of three-dimensional manifolds creating hyperbolic geometry. In mathematics, manifolds are topological spaces, and they are more difficult to visualize than, say, a dinner recipe.

"Manifolds are the idea of space that we can manipulate," Saesan said. "They refer to space itself. Whereas a surface is a two-dimensional manifold, a 3-D manifold would be the space in a room. If you have a 360-degree field of view, and you can look all around - up, down, left and right - and if you can be in that space, you can fold and fit certain parameters that we start to set for it. It's really fascinating to watch all the pieces fit together like a puzzle."



One way to think about what Saesan is doing is to imagine how six squares come together to form a cube. Now imagine forming a sphere from triangles. It's a lot more difficult because those triangles would need curvatures on their sides to create the symmetrical space. The research gets even more mind-bending when you try to use manifolds to describe something as vast as the universe.

"One of the things that we are thinking about is the idea of what the universe might actually look like, because it's unrealistic to assume it's just an infinite space," Saesan said. "If you think about Earth, you could travel in one direction and you'd still loop back to where you started. Maybe the galaxy is the same way and you can fly in one direction away from Earth and end up coming back to Earth."

Saesan's abstract reasoning makes him a good fit for this type of research.

"Elijah can do these things better than me in some ways," McDermott said. "He's really good at doing all the foldings and pairings. I had him for a calculus class and he was one of my best students, so I had him in mind for this project and he was on board."

Saesan is working 30 hours per week and is paid a stipend through the grant, but what's most valuable to him is the experience.

"In the career sense, this is obviously nice to have on your resume, but I'm also learning a lot about myself," Saesan said. "It is hard to stay focused on one subject for several hours, compared to jumping between classes."

Saesan and McDermott plan to present their findings at a conference during the upcoming academic year.

More information about SRU's SCORE grants are available on the University's website. More information about the mathematics and statistics academic programs at SRU is available on the department's webpage.

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