Striking a balance

Not long after beginning his graduate program at Waterloo, Matthew Sullivan discovered a passion for Ultimate Frisbee. Today, he serves as the chief of the Ultimate Frisbee intramural program while continuing to referee and play as often as he can. Close to 450 students sign up to play every autumn. “Things like age, gender, or program don’t matter out there,” says Matthew. “Any student can go out and play. Like all the intramural sports at Waterloo, Ultimate provides a great way to de-stress, stay in shape, and balance the academic with the social.”

A predictable, well-defined game of 14 players feels like a much-needed respite for students like Matthew, whose chosen field of research is significantly less straightforward. At a basic level, graph theory examines sets of points (“vertices”) and lines (“edges”) that model relationships between objects on graphs. “You can draw a graph with many crossing edges or none at all, and these choices have applications in the real world,” explains Matthew. From optimizing road networks to designing computer chips, graph theory presents an infinite supply of complex problems to solve. “What initially piqued my interest about the field was that every problem seemed like its own puzzle to solve, and I find great satisfaction in coming up with a solution,” he shares.

As he completes his PhD studies in the Department of Combinatorics and Optimization, Matthew focuses his efforts on tackling the “Crossing Number Problem,” a longstanding mystery that researchers in his field have struggled to unravel since World War II, when a Hungarian mathematician tried to determine the number of crossings between tracks that connected brick kilns to storage sites. “We still don’t know the smallest number of edge crossings for a complete graph,” says Matthew. “There are only conjectures. I’m working on a specific concept to build toward solving that problem.”

In addition to his time spent playing Ultimate Frisbee, Matthew points to the many opportunities to collaborate with like-minded researchers as a highlight of his time at Waterloo. “As a graduate student, you get so many opportunities to connect with researchers from all over the world who invite you into their community,” he affirms. “This collaboration generates a great atmosphere for discovery.”