Alicia Hoffmann and Tim Doster (Rochester Institute of Technology) work on a presentation for the Young Mathematicians Conference at the Ohio State University. In the background, Stefan Sabo (University of Pennsylvania) and Eric Lownes (North Carolina State University) edit their paper.
Huntington, Ind.—Alicia Hoffmann, a senior at Huntington University, spent the summer in Buffalo, N.Y., participating in a research assignment through Canisius College.
Hoffmann, a mathematics major from Fort Wayne, Ind., spent eight weeks doing mathematical research through the National Science Foundation’s Research Experiences for Undergraduates. The program she was a part of was Geometry and Physics on Graphs, with an emphasis on fullerene graphs.
To a chemist, a fullerene is a spherically shaped molecule that resembles a soccer ball. However, to a mathematician, a fullerene is a graph that looks somewhat like the molecule, but smashed flat into two dimensions. Each vertex in the 2-D graph is like an atom in the 3-D molecule, and each edge in the graph is like a bond in the molecule.
(left to right) Dr. Terry Bisson, Tim Doster, Alicia Hoffmann, Chelsey Cooley, Eric Lownes, Chloe Johnson, Stefan Sabo, Alissa Pioli, Ben Lerman, Dr. Stratos Prassidis
Hoffmann took the fullerene graphs and put them on a torus, a ring-shaped surface, to give an average value for a graph's spectra, she said.
“I was looking at the graph theoretic properties of fullerenes, and in particular, I wanted to make some generalizations about the spectra of infinite fullerenes,” said Hoffmann. “To do this, I used a really cool function called the Ihara Zeta function and toroidal fullerenes.”
Researching was more than a full-time job for Hoffmann. On top of the typical 9-to-5 day full of research, the workload continued after dinner. Around 7 or 8 in the evening, the group of eight students would gather for “math parties” to work on their research until they were exhausted. Research even went over into the weekend.
Hoffmann takes a seat on the Tesla statue at the Niagara Falls State Park on Goat Island. The research group stopped at the park while visiting Niagara Falls.
From this experience, Hoffmann examined actual research problems, much like what a professional mathematician does.
“Through this experience, I gained more confidence in my skills as a mathematician,” she said. “I was able to engage in real research problems, and I got a taste of what some mathematicians do every day.”
After college, Hoffmann plans to attend graduate school.
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