Kyle Yang
About Me
I'm Kyle Yang, a current senior at Deerfield Academy in Deerfield, Massachusetts. Some of my hobbies are squash (although I take it quite seriously, playing on my school's varsity team), chess, hiking, and mountain biking.
​
As for my academic passions, I love writing for a hobby, ranging from short stories to poetry. Here's a recent piece I've written, where I've tried to capture the emotional trauma of a war veteran:
https://drive.google.com/file/d/11UzErdZ-s3vJFZ-GaeO3xDWabyVfl0Su/view?usp=sharing
​
I am interested in both pure and computational mathematics. I am especially interested in dynamics, computational methods, and abstract algebra. In particular, I have researched the dynamical stability of stochastic replicator dynamics and designed an expository paper on Galois theory. Here are the links:
​
Dynamics:
https://drive.google.com/file/d/1maQm1MCqHNwL1eXt7a5RZHtWHzS2RlkH/view?usp=sharing
​
Galois Theory:
https://drive.google.com/file/d/1rj3wQViohjgaRcaVzyaLUg8w43WP3MLa/view?usp=sharing
Below, you can also find some more details about my current/past works:
Papers
A Numerical Analysis of Stability in Zero-Sum Rock Paper Scissors Stochastic Replicator Dynamics (conditional acceptance to the IJHSR)
ABSTRACT: Stochastic differential equations have a wide range of applications across various disciplines, including finance, physics, and biology. There are usually two primary ways to evaluate them: Stratonovich, which samples midpoints, and Ito, which samples left endpoints. However, unlike deterministic calculus, these two schemes give different results upon evaluation. This article primarily analyzes the dynamics of the neutral equilibria of zero-sum replicator dynamics when subject to noise under both the Ito and Stratonovich schemes. We add noise because in real-world modeling scenarios, almost all natural systems are subject to some form of it. We find that intrinsically symmetric Brownian noise acts asymmetrically in zero-sum games, thereby decreasing a system's stability. Hence, neutral equilibria with noise behave like deterministic, asymptotically unstable equilibria. Additionally, the Stratonovich scheme exhibits greater variation than the Ito scheme in both mean and variance for all of the cases we study.
​
LINK: https://drive.google.com/file/d/1maQm1MCqHNwL1eXt7a5RZHtWHzS2RlkH/view?usp=sharing
An Expository Paper: A Foundational Development of the Galois Theory Proof of Abel-Ruffini
After researching and giving a presentation on Galois theory and the general quintic's unsolvability in radicals at the Stanford University Mathematics Camp, I have been interested in presenting a minimalistic proof that would be more accessible than working through a long textbook. Yes, this approach eliminates some of the beautiful generalizations that Galois theory helps us make, but on the other hand, it is designed to help those learning the topic for the first time gain a general grasp of what's really going on beneath the advanced mathematical machinery that Galois Theory requires.
​
LINK: https://drive.google.com/file/d/1rj3wQViohjgaRcaVzyaLUg8w43WP3MLa/view?usp=sharing