A Property of Lyapunov Function

“Thinking is one of the greatest pleasures of the human race.” — Bertolt Brecht

In 2018, I collaborated with Gouruyue Yuan to participate in the S.-T. Yau Mathematics Award competition. This prestigious award deviates from traditional paper-delivered or standardized tests and instead allows students to participate by submitting academic papers. The competition required us to select an interesting topic in mathematics, conduct research, write a paper, and present it to Dr. Shing-Tung Yau if we successfully advanced to the final round.

We received guidance from Dr. Dun Zhou, who provided us with an idea regarding the potential properties of the integer-valued Lyapunov function for a specific class of totally nonnegative matrices. Together, we dedicated the entire summer to studying linear algebra and attempting to prove this property. Despite facing numerous setbacks and failures, our perseverance eventually paid off. We emerged as winners of the first prize in the regional finals, allowing us to progress to the global final stage.

During the final competition, we presented our findings to Dr. Shing-Tung Yau, as well as other professors, and answered their questions. Our hard work and dedication led us to receive an Honorable Mention for the S.-T. Yau Mathematics Award, which also granted us the opportunity to be interviewed by Tsinghua University.

This experience not only enhanced our mathematical knowledge and research skills but also provided us with invaluable opportunities to showcase our abilities and interact with renowned mathematicians.