Student Research Spotlight - Roman Vasquez
Roman Vasquez won third place in the oral presentation category, University-Wide Graduate Student Winners in Science, Technology, Engineering and Mathematics, during the virtual 2021 Auburn Research: Student Symposium.
Hometown: Oviedo, Florida
Degree and major: Doctorate in Mathematics
College: College of Sciences and Mathematics
Class year: Second year of doctoral program
Faculty mentor: Steven Schlicker (Grand Valley State University)
Bipartite Graphs and Line Segments Defined by Sets
What are you researching?
We studied an interesting connection between metric geometry and combinatorial graph theory. Most of my work involved counting matrices and bipartite graphs, but it was motivated by a special way of measuring distance called the Hausdorff metric.
How could the results benefit individuals, agencies or companies?
The metric we used has applications in machine learning and is even used in visual recognition by robots and in computer-aided surgery. We also found interesting connections between previously studied fields of math, including knights' problems and hypercubes.
Tell us why you enjoy research.
I love the philosophical aspect of pure mathematics research, just sitting back and thinking my way through potential proofs or coming up with new problems. The fact that this research only needs some paper and a pencil means it can be done anywhere, and I've found that I sometimes do my best work before drifting off to sleep.
What advice would you give to other students considering doing a research project?
Try not to go in with any preconceived ideas of what a certain field might be like; a lot of my favorite projects were ones which I knew next to nothing about before getting started. What matters far more than the topic of your research is your advisor—a poor advisor could make even the most exciting projects feel like a chore, but an advisor whom you get along with will make any topic worthwhile.
Tell us about any hobbies or activities you enjoy.
I was a dancer almost all my life and I was only months away from testing for my fourth-degree black belt in karate before some health issues got in the way. I funneled my energy into marching band as an undergraduate, and these days I spend most of my time reading or participating in local activism.