Rachel Chen
Marlborough School
Los Angeles, CA
The Dual Canonical Basis in the Spin Representation via the Temperley-Lieb Algebra
Rachel Chen, 18, of Los Angeles, developed a concrete, visual way to describe quantum physics systems for her Regeneron Science Talent Search mathematics project.
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Since quantum particles interact with their environment in complex ways, it is hard to describe these systems mathematically. A 1997 paper showed that part of the quantum system could be described using simple point-and-curve graphics called Temperley-Lieb diagrams. Researchers across mathematics and physics use these diagrams as an intuitive tool for understanding phase transitions, mathematical knots and other concepts.
Rachel expanded on the 1997 work, using Temperley-Lieb diagrams to describe how an entire system of quantum particles acts under the influence of a magnetic field. This may be useful as an intuitive framework for researchers to understand the structure and connections among different quantum-mechanical states. She also used her results to understand alternative ways of working with the quantum system.
The child of Zhaoxu Chen and Jing Che, Rachel attends Marlborough School, where she plays volleyball and founded the math club. She is also an internationally ranked chess player and knows the words to over 200 Taylor Swift songs.
Beyond the Project
Rachel is an internationally ranked chess player and won the Pan-American Chess Festival in her age group in 2022. She is also Contests Director for Athemath, a nonprofit that builds community for girls interested in math.
FUN FACTS: Rachel is a devoted Taylor Swift fan and has memorized more than 200 of her songs. She is also the founder of her school’s math club, which now has over 100 members.
