Sophie Zhu
Williamsville East High School
East Amherst, New York
About Sophie Zhu
Sophie, motivated by the unique factorization of natural numbers by multiplication, studied when semirings of evaluated Laurent polynomials admit unique factorization by addition. She also characterized when these semirings satisfy the ascending chain condition on principal ideals, an important property in mathematical algebra.
Factorizations in Evaluation Monoids of Laurent Semirings
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Sophie Zhu, 16, of Buffalo, studied factorization, one of the oldest and most fundamental topics in mathematics for her Regeneron Science Talent Search project. Every positive whole number admits a unique factorization into prime numbers, meaning that it can only be written as the product of prime numbers in one way. In her project, Sophie studied this problem, but in a much more abstract setting. Instead of whole numbers, Sophie studied when semirings of evaluated Laurent polynomials admit factorization by addition. She went even further by characterizing precisely when these semirings satisfy the ascending chain condition in terms of certain factorization properties.
She has published two peer-reviewed journal papers on abstract algebra and is the sole author of one of them. Sophie has served as a youth fellow and ambassador of the Just Buffalo Literary Center. She also writes poetry, studies literary criticism and promotes literary arts to her city’s youth. At Williamsville East High School in East Amherst, Sophie is co-editor-in-chief of the literary digest and heads the math club. An award-winning pianist, she has performed classical music at Carnegie Hall.
Beyond the Project
Sophie is a two-time recitalist at Carnegie Hall and was invited to perform at the Royal Albert Hall. Once a classical-only pianist, she recently began appreciating and performing jazz.
FUN FACTS: Sophie is a poet who has won several significant writing honors and received the Editor’s Choice Prize from the National Poetry Quarterly, placing in the top eight out of 20,000 entries.
