Rices Landing native exploring geometric manifolds as part of grant-funded project
In addition to his job as a chef at a local restaurant, Elijah Saesan is cooked up some geometric manifolds as a student researcher at Slippery Rock University this summer.
A junior mathematics major from Rice鈥檚 Landing, Saesan is working closely with Kirk McDermott, assistant professor of mathematics and statistics, on a faculty-student research project funded by SRU鈥檚 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.
鈥淢anifolds are the idea of space that we can manipulate,鈥� Saesan said. 鈥淭hey 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 鈥� up, down, left and right 鈥� and if you can be in that space, you can fold and fit certain parameters that we start to set for it. It鈥檚 really fascinating to watch all the pieces fit together like a puzzle.鈥�
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鈥檚 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.
鈥淥ne of the things that we are thinking about is the idea of what the universe might actually look like, because it鈥檚 unrealistic to assume it鈥檚 just an infinite space,鈥� Saesan said. 鈥淚f you think about Earth, you could travel in one direction and you鈥檇 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.鈥�
Saesan鈥檚 abstract reasoning makes him a good fit for this type of research.
鈥淓lijah can do these things better than me in some ways,鈥� McDermott said. 鈥淗e鈥檚 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.鈥�
Saesan is working 30 hours per week and is paid a stipend through the grant, but what鈥檚 most valuable to him is the experience.
鈥淚n the career sense, this is obviously nice to have on your resume, but I鈥檓 also learning a lot about myself,鈥� Saesan said. 鈥淚t is hard to stay focused on one subject for several hours, compared to jumping between classes.鈥�
Saesan and McDermott plan to present their findings at a conference during the upcoming academic year.