Honors thesis leads to new math discovery

By Loren Rhoades, Assistant News Editor

Senior math major Kelsi Guleserian uncovered a mathematical theorem with the help of assistant professor of mathematics Dr. Cherith Tucker.

The two came up with the theorem while researching topics for Guleserian’s honors thesis.

“I knew I wanted to write a thesis because I wanted to study math more in-depth than what we would in class,” Guleserian said.

The process began with Guleserian’s interest in knot theory, which led them to the topic of the linking of circles.

Eventually, they put their focus on the linking of circles in the three-sphere.

The three-sphere is a sphere that lives in four-dimensional space, unlike the normal sphere which lives in three-dimensional space.

“It’s hard to visualize, because we only have three dimensions at our disposal,” Tucker said.

There are circles in the three-sphere that can be linked together where one passes through the other, or they can be separate from each other.

“We started looking at circles in the three-sphere at how we can tell if circles are linked or not linked,” Tucker said. “It led us to a result that applies in any dimension.”

From then on, they started to work with circles not only in the three-sphere but also in the higher spheres and dimensions.

After getting into the higher dimensions, they started studying the linking of spheres.

“When you go up further dimensions, they can be linked somehow where one passes through the center of the other, but they don’t actually intersect in any way,” Tucker said.

After thoroughly studying the linking of spheres in different dimensions, they came up with a result that can help them to answer questions about how other things are linked together.

For example, they have been looking at Borromean rings, which is another interesting way that things are linked.

Altogether the process of this discovery took about a month to a month and a half.

Now Gulseserian is in the process of finishing her thesis that covers this foundational theorem, in the hopes of having it approved and published. The thesis will cover the history of links and convexity, higher dimensions and their properties and any definitions or already proven theorems that are necessary to prove the theorem they have come up with.

“I’m wanting to make this more accessible by telling a story, the history of it, how it came to be and what you can apply it to,” Guleserian said.

Guleserian and Tucker submitted the first draft of the thesis to the honors board subcommittee at OBU this semester and got it approved.

Now they are going forward with different corollaries, as well as different points they can continue to prove with the theorem.

“I was surprised that we were able to prove something new in math,” Guleserian said, “that’s really cool to me.”

Guleserian and Tucker already have a couple questions they have easily proven and answered since being approved by the board.

They will continue this process until the thesis is complete.

From there the thesis will be resubmitted to the board and an outside reader will look over all the information.

Guleserian said doing this research is helping her to solidify what she hopes to do as part of her profession in the future.

Just knowing she could do the research required for the thesis has put her at ease.

“I’ve always known I wanted to be a professor of mathematics,” Guleserian said. “So having the research for this theorem under my belt is nice and comforting.”

Both Guleserian and Tucker are content with the results they continue to find and are leaving room for the possibility of even more discoveries.

“Kelsi has worked very hard on this, and I am very happy with the interesting result we have come up with,” Tucker said. “I am excited to see where it might lead and what other sorts of results we could get as corollaries to this theorem.”

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