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Edward Yu

Edward Yu

Edward Yu

2023 Davidson Fellow Laureate
$50,000 Scholarship

Age: 18
Hometown: Bellevue, WA

Mathematics: “Turán Problems for Mixed Graphs

About Edward

Hailing from Bellevue, WA, I’ve been an enthusiastic math student since I was little. I strive to be  both a thinker and a doer—I love to think deeply on simple things, and have a passion for projects that  bring greater insights and productivity to myself and others. I will be attending MIT in fall 2023, planning  to study mathematics and computer science. 

Outside of school, I led our local math circle and performed in the city youth orchestra. I’m an  avid reader interested in all genres of books, magazines, and even advertising fine print. I am also a cellist; my favorite pieces are the Bach cello suites, which I often play when I’m in a reflective mood. In  my free time, I enjoy taking random walks with friends and/or my pet drone. 

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"I’m extremely thrilled to be named a 2023 Davidson Fellow. I’m deeply honored and grateful for the opportunity to join a cohort of inspiring creators, scientists, and artists. I feel both humbled and lucky to have my research be recognized by the Davidson Institute, and I am thankful for the encouragement to continue pursuing my passion in math and science."

Edward Yu

Project Description

Mixed graphs are networks whose nodes can be connected by directed or undirected edges. They are applied in neural networks, propositional logic, social networks, and more. My research studies the structure and density of mixed graphs satisfying certain special constraints. I established a connection between graph densities and quadratic forms to give an exact variational characterization for the mixed graph Turán density coefficient, giving a full characterization of mixed graph Turán properties. This theoretical framework can contribute to our understanding of mixed graph properties, and help us analyze large-scale data networks with complex structures.

Deeper Dive

My project is about the extremal properties of mixed graphs, which are networks whose nodes can be connected by directed or undirected edges. One of my favorite games is Wikiracing, where one tries to reach one Wikipedia article from another through as few internal links as possible. The game is a version of “six degrees of separation” that showed me a fresh view of the world: everything, and everyone, is connected in one intricate graph. Mixed graphs are a versatile and powerful tool capable of representing all sorts of data and the complex relations within them, and I studied the structure and density of mixed graphs satisfying certain special constraints.

In order to understand the landscape of extremal graph theory, mixed graphs, and partially directed hypergraphs, I read dozens of lecture notes and research papers. While fascinated by high dimensional networks and investigating multifaceted structural relationships, I also encountered numerous brick walls. Sometimes I thought I’d thrown every mathematical method I could think of at a problem, but still failed to reach a desired bound. On another occasion, I attempted to solve part of a problem with computational methods, but was overwhelmed by a million-hour expected run time… This year-long research experience has taught me that staying both optimistic and skeptical, though it sounds paradoxical, is crucial to the research process. I’m infinitely grateful to my mentor, Nitya Mani, for her continuous support, warm encouragement, and generous guidance. I’m also very thankful for the MIT PRIMES-USA program, for giving me the opportunity to conduct mathematical research, and to Professor Yufei Zhao of MIT for inspiring me to study extremal graph theory. Last but not least, I’d like to thank my parents for their unconditional encouragement and love throughout my mathematical endeavors.

Mixed graphs are convenient modeling tools in scientific research to represent relational data. For example, problems in job scheduling, neural networks, and propositional logic in computer science can all be modeled using mixed graphs. My research establishes a theoretical framework for extremal properties of mixed graphs. These results can help other scientists deepen their understanding of large scale data networks with complicated structures, and apply mixed graph models with a new understanding of their asymptotic complexity. The program I developed to compute extremal properties of partially-directed hypergraphs is generalizable to many hypergraph computational problems; I hope that graph theorists, as well as researchers in other fields, can benefit from this implementation when performing hypergraph computations to test their hypotheses and develop intuition in their research.


If you could magically become fluent in any language, what would it be?

Proto-Indo-European, or some variant thereof. Although no one has spoken it for a good number of millenia, it would shed a fascinating light on our common linguistic ancestry.

Do you have any pets? What are their names?

I have a pet algae eater, named Ancalagon. It does an excellent job of cleaning the fish tank.

What is your favorite tradition or holiday?

Making pancakes on Sunday mornings with family.

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In The News

Seattle – The Davidson Fellows Scholarship Program has announced the 2023 scholarship winners. Among the honorees is 18-year-old Edward Yu of Bellevue. Yu won a $50,000 scholarship for his project, Turán Problems for Mixed Graphs. He is one of only two students nationwide to be recognized as a Davidson Fellows Laureate and one of only 21 scholarship winners in the 2023 Fellows class.

Download the full press release here