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Undergraduate Researcher

SMALL REU, Williams College

Worked on multiple research projects, including: developing a novel, structurally distinct variant of the Zeckendorf Game; significantly improving the algorithm for Zeckendorf vector decomposition; formulating a new additive uncertainty principle and substantially strengthening recovery conditions for missing signal frequencies; and implementing and analyzing a novel setup for a signal recovery problem that outperforms existing approaches.

• Signal Recovery
• Fourier Analysis
• Zeckendorf Games
• Zeckendorf Lattices

BA

Williams College

Mathematics and Chinese

• Functional Analysis
• Commutative Algebra
• Mathematical Modeling

The Ordered Zeckendorf Game

Submitted to Fibonacci Quarterly

We introduce and analyze the ordered Zeckendorf game, a two-player combinatorial game based on Zeckendorf’s Theorem, where enforcing order on summands transforms the classical game into a richer, more balanced, and strategically complex system with provable termination, quantified bounds on game length, and intriguing probabilistic behavior.

Nature by Numbers

Fibonacci Quarterly

Exploring mathematical patterns in nature through the lens of Fibonacci sequences and related structures.