Four students, Michael Ren ’18, Andrew Wang ’18, Andy Xu ’19, and Wendy Wu ’20, have been recognized by prestigious science, technology, engineering, and mathematics (STEM) competitions for their independent research this past year. Read on to learn about their projects.
Michael Ren ’18
Ren participated in the Regeneron Science Talent Search (Regeneron STS), one of the most prestigious science and mathematics competition for high school seniors, according to the “Student Science” online resource. According to “Student Science,” STS alumni hold more than 100 of the world’s most-distinguished science and math honors, including the Nobel Prize and the National Medal of Science.
Ren placed among the nation’s Top 40 STS competitors. During Spring Break, Ren and the 39 other finalists were invited to Washington D.C. to display their work, meet notable scientists, and participate in the final judging of the projects.
Ren said, “I was super excited [when I found out I was a finalist.] Everyone told me what a great time they had last year or a few years before and how it was life changing, so I was super pumped. It made me look forward to Spring Break a lot more.”
In his project, Ren used analysis, programming, and algebra to calculate the Hilbert series of quasi-invariant polynomials, an area of ‘pure mathematics,’ which involves the study of entirely abstract concepts.
Through MIT PRIMES, a program that matches high school students with research projects and mentors, Ren was able receive help on his project. When applying to the PRIMES program, Ren said that he indicated his interest in number theory and algebra.
Ren began his research in January 2017, and he continued his work over the course of the year. Ren fully developed his research before finally submitting to Regeneron STS this fall.
“There was a period of a month or so where I was just making no progress at all, and I was getting pretty frustrated. So then I talked about it with my mentor and we decided to focus on another area. I made some progress in that area, and then I applied what I learned in that area back into what I was originally doing and made some more progress,” said Ren.
According to Ren, there is still a lot of work to do in this field of quasi-invariant polynomials, and he hopes that his work will prove useful in quantum physics and quantum computing.
“These polynomials are related to many different fields of math like representation theory, mathematical physics, quantum geometry, and so on. I hope that eventually someone might be able to expand on my work and find deeper connections,” said Ren.
Andrew Wang ’18
Wang participated in the Regeneron Science Talent Search (Regeneron STS) and was recognized as STS Scholar, placing in the Top 300 of Regeneron STS. Influenced by his astronomy research through class and an Independent Project at Andover, Wang reached out to the Harvard-Smithsonian Center for Astrophysics in Cambridge about possible projects.
In his project, Wang built a tool that could be used to help cosmologists predict atmospheric characteristics at any place on earth. He then compared the predictions from his project to measurements at specific locations, such as the South Pole or plateaus in Chile.
“There are telescopes that people use to observe the cosmic meaning of the universe and all sorts of other things, and they’re located in different places across the earth. We need really dry locations in order to see through the earth’s atmosphere, but astronomers want to find new sites to put their telescopes, and so they take measurements of [the atmosphere] in these different locations,” said Wang.
Wang hopes to take cosmology research to the next level by adding a new generation of telescopes with increased accuracy and a wider scope of the universe. Cosmologists intend to add telescopes to new locations across the globe, and Wang hopes that his project will be useful in determining which locations would work well.
“The hope is that people who want to choose a new location to put a telescope can, instead of setting an instrument there that has to measure the conditions of the atmosphere for a couple years and costing a fair amount of money… use a kind of ‘site-testing’ campaign and use the software that I developed and get an estimate of whether or not this site is transparent enough, dry enough, for putting a new telescope there,” said Wang.
Wang began his research in November of 2016 and submitted his project to the competition in the fall of 2017.
“I was really honored to have been considered for these awards… I had presented my research at a conference before, but just having that extra validation, that extra show of support that this research is meaningful and have other people see that, is really cool,” said Wang.
Wang said that while the project went relatively smooth, he still faced obstacles with how to present his information, especially since this was his first ever independent research project.
“You have to figure out where you’re going to get your data, and how to present your results in a way that’s most useful to the scientific community and is most likely to attract attention. So having to think about how to present the data in the most useful, valid way took a while to figure out, and it took a lot of reading through other papers that other people have written and figuring out how my work is adding to the scientific body of knowledge,” said Wang.
Wang also placed in the Top 400 of the Siemens Competition in Math, Science, and Technology, a competition run by the Siemens Foundation, which provides young people with access to STEM education across the nation.
Andy Xu ’19 and Wendy Wu ’20
The Siemens Foundation also recognized students Xu and Wu, who placed as regional finalists for their research on gonality, a property that connects algebraic geometry and combinatorics in the “chip-firing game,” a one-player computer science game.
“We were considering various applications of elements of a certain type of game that you could play on a graph. The key operation in this game is a move which denotes ‘chip-firing,’ and basically [‘chip-firing’] is a special way that you can redistribute the entities of these chips around the vertices of this graph. It turns out to have interesting behaviors, and we often just tried to model some of these behaviors once we introduced an element of randomness into this model,” said Xu.
Wu wrote in an email to The Phillipian, “I feel like I learned a lot; especially at the beginning reading the background material was difficult itself, but with determination and a liberal amount of head-bashing, it worked out.”
Each year, only 60 projects in the nation are recognized by Siemens as regional finalists.
“[Placing as a regional finalist] was really surprising. I was certainly satisfied to know that we received semifinalist, so regional finalist sort of surprised me because only a few dozen projects actually get to move on to this level… It’s sort of like you finish this project and you work really well on this and it’s nice to be recognized for your hard work,” said Xu.
According to Xu, starting their research was challenging because it was a relatively new topic. Xu and Wu had to do further exploration in order to grasp terminology and understand what had already been done in the field. However, researchers at MIT, through the PRIMES program, suggested the topic to Xu and Wu, and they decided to run with it.
“At times, it was not very obvious how to proceed, and it was certainly a significant learning experience, because research isn’t really something you get a lot of experience doing in math class at school, or even something you can easily do on your own time,” said Xu.
Xu continued, “Once we had the research, one of the more challenging parts was also to compile all of our findings into a satisfactory report to convey everything we wanted to say with mathematical rigor.”
Every week, Xu and Wu met with a mentor to discuss their project. Outside of those meetings, they would communicate questions and discuss ideas with each other.
“Research is exploring new areas of mathematics that people haven’t [trod] upon before, so that aspect and broadening the horizon of human knowledge, that’s a really interesting feeling to have when you know that you’re on the frontier,” said Xu.
Wu wrote, “Math research consists of small advances (in the grand scheme of things), and each result is one small part. I also hope that our success in obtaining a result (of the research project, that is) show others the opportunity and possibility of conducting research in high school.”