Senior Thesis - My biggest project was my senior thesis on approximating Riemann maps \(f:\Omega \to D\) with circle packings that I did with Dr. Jeffrey Diller... It was based on Terrance Tao’s notes on his blog. My goal was to prove all of the exercises and give more detailed proofs/definitions where I felt needed. This project spanned from Summer 2018-Summer 2019. There is a juicy proof of the Riemann mapping theorem for ring domains that doesn’t use Perron’s method or any theory of prime ends, and I am pretty proud of this. I also made a program showing the realization of a maximal planar graph as a circle packing in the unit disc.
Previously, I did an REU at Fresno State on the discrete Fourier transform in Summer 2017. We found a cool way to find the determinant of the discrete Fourier transform using properties of Vandermonde matrices.