Age: 17Potomac, MD
Project Title: On the Okounkov-Olshanski formula for the number of skew shapes
One of the more unexpected connections in mathematics is that between Young tableaux, seemingly simple objects that can be represented by numbers arranged in a grid, and a whole host of seemingly unrelated fields, which describe anything from quantum systems to the behavior of lines, planes, and hyperplanes in high-dimensional space. My project investigates a mysterious formula for counting Young tableaux, discovered by Okounkov and Olshanski, in order to better understand the structure and properties of Young tableaux. Among our many results are a description of the complexity of the formula, which aids in estimating the number of Young tableaux of a certain shape, and a generalization of the formula to count a broader class of objects.
My name is Daniel Zhu. For about as long as I can remember, I have been intrigued by the power and beauty of mathematics. This might seem inconceivable, given the common (mis)representation of math as an incomprehensible robotic conglomerate of gibberish. On the contrary, math is one of the most simple and creative fields that I know, stripping away unnecessary complexity to reveal the frictionless interplay of pure ideas. I am humbled to be honored as a Davidson Fellow and grateful to be recognized for my work.
My project studies mathematical objects called Young tableaux, which may seem innocuous at first; as defined, they are just grids of numbers obeying some simple rules and can even be interpreted as ways to place balls in a box! However, they are related to numerous seemingly disparate fields, like representation theory, which studies how exotic number systems can manipulate space and is a key tool in understanding quantum mechanics, and algebraic geometry, which studies the geometry of shapes determined by certain equations, often in a high number of dimensions. My project aims to investigate a mysterious formula counting Young tableaux to see how it, or related techniques, could be used to shed more light on these mysterious objects.
While math research doesn't require fancy equipment or meticulous experimentation, it's no walk in the park. For instance, since the validity of a statement is sensitive to the smallest alterations, one can only guess whether one is minutes away from proving a result, or hopelessly far away. For helping me navigate this landscape, I would like to thank my mentor, Prof. Alejandro Morales, a constant source of ideas, suggestions, or just simply motivation. I am also grateful for the support of the MIT PRIMES-USA program, which was instrumental in providing resources and assigning projects. I was also fortunate to be able to take advantage of a research class at my school, which provided resources at every step of the research process, from locating a mentor to writing a final report.
It is often difficult to evaluate the real-life impact of mathematical research, since many theories only find an application decades or centuries into the future. My project's significance derives not only from its ability to shed light on the structure of Young tableaux, but also its results linking different mathematical objects into a single cohesive framework and its new techniques which can be adapted to prove further results in the field.
For the past nine years, I have gone to school under a series of different magnet programs offered by the local public school system. These permitted me to take advanced classes, ranging from Organic Chemistry to Complex Analysis. Just as important, however, if not more, were the people that these educational environments brought together. From highly qualified teachers whose job was to teach talented students to peers with similar interests and concerns as mine, everyone did their part in fostering a community in which I could better learn and develop both as a student and as a person. This fall I will be attending MIT, where I plan to study math, and possibly physics as well.
I am an avid participant in math and physics competitions, which culminated in my representing the United States at the International Mathematical Olympiad and International Physics Olympiad in 2019 and 2018, respectively. For two years, I was a captain of my school’s math team, which involved co-organizing one of the largest student-run middle school math competitions in the country. Outside of the sciences, I enjoy playing the violin, solving puzzles, and participating in cybersecurity competitions.
Where do you see yourself in 10 years? I'm not particularly sure — I could see myself finishing a math PhD, but this is only one of numerous options.
If you could have dinner with the five most interesting people in the world, living or dead, who would they be?
Johann Sebastian Bach, Jorge Luis Borges, Jimmy Carter, Evariste Galois, I.M. Pei
If you could be on any TV show, which one would it be?BBC2's Only Connect
In the News
Potomac, Md. – The Davidson Institute for Talent Development has announced the 2019 Davidson Fellows Scholarship winners. Among the honorees are Evan Hu, 17, and Daniel Zhu, 17, of Potomac. Only 20 students across the country are recognized as scholarship winners each year.
“I am humbled to be honored as a Davidson Fellow and grateful to be recognized for my work,” said Zhu, who will be attending Massachusetts Institute of Technology (MIT) in the fall.
Zhu’s mathematics project, On the Okounkov-Olshanski Formula For The Number Of Skew Shapes, combines several areas of math with applications in design theory, developing cryptosystems that are resistant to attacks by quantum computers, and fluid dynamics.
Click here to download the full press release
Click the image to download hi-res photos of Daniel:
Started in 1999, the Davidson Institute for Talent Development is a 501(c)3 private operating foundation. Our mission is to recognize, nurture and support profoundly intelligent young people ages 18 and under, and to provide opportunities for them to develop their talents to make a positive difference.
Profoundly gifted students are those who score in the 99.9th percentile on IQ and achievement tests. Read more about this population in this article.