“Dr. Zhao is a mathematical genius, and to be able to work under his guidance itself is like a blessing and honor,” Angelina Kim (‘25) said, regarding their collaborative research. This winter break, Dr. Zhao and other students have been writing a new research paper. Previously, Dr. Zhao has published four research papers with Bishop’s students. Sienna Li (‘24) felt that she could not miss working with Dr. Zhao as it was a once in a lifetime opportunity.

This school year, Dr. Zhao is working with Jeremy Feng (‘25), Angelina, Sienna, Ryan Qin (‘25), and Logan Wang (‘25). Their research paper is based on Dr. Zhao’s book Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values, published in 2016. Dr. Zhao said, “This is a kind of a special field in number theory, which has a lot of relations with quantum and particle physics.” 

Dr. Zhao, a number theorist and an algebraic geometer by training, created a course called Advanced Honors Mathematics: Number Theory when he arrived at Bishop’s in 2016. So far, Dr. Zhao has published over 80 peer-reviewed research papers.

Regarding his work with students, Dr. Zhao said, “I want them to do some computing… I tell them the ideas and I share my programs with them… My original hope was that they could write their own programs using their language and not mine and hope they could corroborate my results using their computations.” In addition, Angelina also said that the students were “researching the relations between Multiple Mixed Zeta Values and Euler Sums.” And according to Sienna, these are similar to mathematical functions: “values that you can solve for if you plug in separate numbers.”

Ryan said, “We wrote programs in a math computation software, Maple, and then we just ran it for weeks, calculating different values, because we can’t prove the pattern, but we can produce some sort of numerical evidence that the pattern seems to look something like this.”

Helping with Dr. Zhao’s research paper has been a great opportunity for the students. Logan said, “Being able to do original research with such a distinguished and accomplished mathematician is just such a unique and once-in-a-lifetime opportunity that I couldn’t possibly pass it up.” 

Sienna added to this sentiment, saying, “I feel like this is a once in a lifetime opportunity… and in the very high levels of math, PHD students don’t get their names on certain papers because most of the time it’s just the core researchers… I don’t think I will ever have a chance to do this again, or at least not in the near future.”

To work on this research paper, Ryan borrowed computers from Dr. Marcus Jaiclin to develop his code in Maple. Sometimes other students would turn off the computers that he was working on by accident, causing all the work that was done to be lost. To fix this problem, Ryan created another program. He said, “All that we care about is the final number… So, I basically took that data, figured out a way to begin the program from the middle, and saved us some time.”

Impressively, with a computing server of her own, Angelina was able to check the weight thirteen case of a few special types of multiple mixed values. Finding this was complicated and difficult, but with a computing server of her own, Angelina was the only person in her class to check the weight thirteen case.

Dr. Zhao, with the help of Jeremy Feng, Angelina Kim, Sienna Li, Ryan Qin, and Logan Wang, contributed to a new discovery in the math world. And soon, Dr. Zhao is planning to write another research article on multiple L values with the students.