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To Shanise Walker, the world is full of puzzles to solve.

Walker, a graduate student in mathematics, is researching partially ordered sets, abbreviated as “posets.” She is looking for the maximum size of families in different lattices that have no copy of a fixed poset.

“You have to figure out about the lattice, the properties, and all of those things, before you can try to apply what a forbidden subposet would look like within that lattice or a family in that lattice,” she said.

Walker looks for the largest families with particular properties. Most recently she and her advisor studied a poset called “?”, related to a well-known function in the theory of error-correcting codes.

“It’s an art form,” Walker said. “There’s no definite answer so you are taking part in creating the answer, but you’re also making sure that it doesn’t fail with all the other mathematical research that’s already out there.”

Walker’s first experience with research was through attending a Research Experience for Undergraduates at Iowa State during the summer of 2011. During the experience Walker worked with Leslie Hogben, professor of mathematics, on combinatorial matrix theory research.

The research was so much more specific and focused than anything she had worked on in classes, Walker said. “It was during that experience that I decided I wanted to come to grad school.”

After spending a summer working with graduate students and faculty at Iowa State, choosing to pursue graduate school here was an easy choice. In her second year, Hogben connected her with Ryan Martin, who became her major professor.

“He’s very invested in his students and that helps me everyday to push forward and want to be a better student,” she said.

While at Iowa State, Walker is also serving as the lead teaching assistant for graduate students. She is in charge of scheduling 85 graduate students for teaching assignments, taking into account each student’s schedule, eligibility for grading various other graduate courses, and balancing prep time
and grading work.

“I’ve gained an appreciation for how much hard work and dedication goes into the administrative side of things,” She said. “It takes a lot of dedication but I enjoy figuring it out.”

Walker aims to put that same dedication and problem solving into her research.

“I’m always trying to solve various things,” she said. “Tapping into the unknown — it gets the brain working.”

By Elizabeth Peterson