Jaeho Lee
Spring Branch Academic Institute
Houston, TX
Affine Group of Integers Modulo n, Conjugacy Classes and Representations
Jaeho Lee, 18, of Houston, studied a collection of rules, called permutations, that shuffle around elements of a set of numbers, for his Regeneron Science Talent Search mathematics project.
He focused on a specific class of permutations that use a simple formula of multiplication and addition. These are called the affine permutations. They shuffle collections of numbers where arithmetic works like timekeeping: once the numbers get big enough, they circle back to 0, just as a day restarts after 24 hours.
In his project, Jaeho broke down the structure of any set of affine permutations by calculating its underlying building blocks. He hopes his work will extend the applications of affine permutations; simple versions have already helped researchers find networks that are highly connected and study how heat flows around a network.
The child of Hyeonjeong Lee and Jinseob Lee, Jaeho attends Spring Branch Academic Institute. He plays both violin and piano and is president of his high school鈥檚 symphony orchestra. As a freshman, Jaeho founded a math club for 4th and 5th graders at a Title I elementary school in Houston.
Beyond the Project
Jaeho is an accomplished violinist and pianist and the president of his high school鈥檚 symphony orchestra. Every month, he plays classical music for seniors with the Music of Harmony club.
FUN FACTS: Jaeho enjoys coming up with his own board games. His family tests out his creations every Friday night.
