Here are the projects I have done in the past, or the ones that I am doing whether they are formally/informally or professional/personal.

The Capset Problem

Supervisor - Dr. Li Chun Che

This project is for the 2022-23 undergraduate research opportunity program (UROP) organized by the mathematics department of CUHK. As usual with undergraduate projects, I read (and presented) some literature regarding the problem of finding AP-free sets in $\mathbb{Z}$ and $(\mathbb{Z}/k\mathbb{Z})^n$. This included (but not limited to) reading the proofs of Roth’s theorem using Szemerédi’s graph regularity lemma, the exponential improvement of the capset problem in $\mathbb{F}_q^n$ by Ellenberg-Gijwijt polynomial method, and some lower bound constructions for capsets in $(\mathbb{Z}/k\mathbb{Z})^n$ with special focus on the case $k = 3$. The following are some of the notes I have written for my presentations during the project:

  • Croot-Lev-Pach-Ellenberg-Gijwijt Bound on Capsets pdf
  • From Szemerédi’s Regularity Lemma to Roth’s Theorem (still editing)
  • Some Generalizations of Roth’s Theorem for Groups pdf
  • Behrend’s Construction of AP-free sets in $\mathbb{Z}$ pdf
  • Three Constructions of Capsets in $(\mathbb{Z}/4\mathbb{Z})^n$ pdf
  • Final Presentation pdf


Short Reading Project on Ergodic Theory

Supervisor - Prof. Feng Dejun

During the above undergraduate research opportunity project, I was curious about the proof of Szemerédi’s theorem for AP-free sets in $\mathbb{Z}$. With my current interest in exploring more analysis (and its applications to combinatorics), I am reading through Ergodic Theory: with a view towards Number Theory by Manfred and Thomas, under the supervison of Prof. Dejun Feng.


COSINE Summer Research Exchange Program

Supervisor - Prof. Po Lam Yung

To be updated


မြန်မာနဲ့သင်္ချာ

I ocassionally write articles for the Burmese audience and post them on Facebook (aka Burmese google). These include several results that fascinated me when I first learned mathematics outside of the standard high school curriculum. See details on မြန်မာနဲ့သင်္ချာ.


YouTube

Channel - Snarky Math

I have created some YouTube videos in the past, the first one being due to The Summer of Math Exposition hosted by 3Blue1Brown. I haven’t posted in a while, but I do have some topics in mind for future videos. Maybe one day, when I am motivated for videos again, I will create more YouTube videos.