Exeter senior in running for national math honor

Yunseo Choi '21 is one of 40 finalists in the nation’s oldest science and mathematics competition.

January 22, 2021

Matchmaking requires agreement from both sides. One side can’t simply choose; it must also be chosen. And a variety of limiting factors affect the outcome.

Yunseo Choi ’21 wants to figure out what happens when those finite limitations are lifted.

The four-year senior’s project “On Two-Sided Matching in Infinite Markets” has been chosen as a finalist in the 80th Regeneron Science Talent Search — the nation’s oldest and science and mathematics competition for high school seniors.

Choi, from Seoul, Korea, is one of 40 finalists selected from more than 1,700 entrants. Each the finalists is awarded at least $25,000, with the top 10 prizes ranging from $40,000 to $250,000. The top 10 winners will be announced during a virtual awards ceremony March 17.

Choi’s project seeks to build off the Gale-Shapley algorithm which seeks to solve the problem of finding a stable match between two equally sized sets of elements. The two California professors for whom the algorithm is named proved in 1962 that, for any equal number of men and women, it is always possible to find matches to make all marriages stable.

“Gale and Shapley proposed a seemingly impossible question: ‘How can we form stable marriages?’ (as if they had watched any season of The Bachelor!),” Choi wrote in an email. “Now, of course, this question cannot be answered with mathematics alone. However, matching theory begins to answer this question by characterizing the problem through models of men and women and their preferences on each other.”

Economic theorists have since applied matching algorithms in countless ways.

“Matching markets dominate the world, from Tinder to Airbnb,” Choi said. “Economic theory seeks to understand the properties of these markets, but some theory predictions are wrong because they depend on unrealistic assumptions. How do we find the most fundamental results? Go infinite!

“My project seeks to characterize the properties of matching that are the most fundamental. By characterizing these results, I aim to help design matching algorithms that are more robust to frictions in the market that are not fully captured by the restrictive finite models. This created the perfect opportunity to translate the beautiful mathematics in these models into a result that is important for practical market design.”

Choi was named a semifinalist — along with Exeter classmates Tony Xiao and Lin Zhu — earlier this month and was anticipating the announcement of whether or not she had survived the cut.

“I found out through a phone call the day before the results were supposed to be announced; I was totally in shock because I wasn't expecting to hear from them for another day!” she said. Choi credits her teachers and mentors — including Exeter Math Instructor Jeff Ibbotson and a cast of college mathematicians, including Scott Duke Kominers at Harvard, where she’s headed in the fall.

“Without them, none of this would have been possible,” she said. “Although progress should never be judged by the resulting outcome alone, being named a Regeneron STS Finalist is such an incredible honor.”

“Yunseo is a fabulous student and always approaches mathematics with a depth of insight and continuing interest in various subfields of math,” Ibbotson said. “She loves sharing new proofs of well-known results and she is constantly thinking about extensions of the things she has learned. She truly lives the life of a mathematician!”