Undergraduate Projects
Here are some things I did as an undergraduate.
Christopher Tedd supervised me for a summer research project on the relationship between partially-ordered sets and the prime spectra of commutative rings.
A first stab at maths research, the resulting report can be read here. The ideas contained within are simple but obscured by detail.
Andrew Lobb supervised me for an LMS funded undergraduate research project on results relating to the square peg problem.
I was able to very very slightly generalize an earlier result about $n$-rhombs inscribed in spheres embedded in $\mathbb{R}^n$. The paper can be read here. It has some nice pictures made using Inkscape.
Alexander Stasinski supervised me for my MMath project. It centres around Gerstenhaber's theorem, which states that for any field $F$ and commuting matrices $A, B \in M_n(F)$, the dimension of the (unital) algebra $F[A, B]$ is less than or equal to $n$. A similar statement for 4 commuting matrices does not hold, and the problem of whether a similar statement holds for 3 matrices is open, and actively being worked on. The problem has connections to algebraic geometry and an interesting canonical matrix form called the Weyr form. The final report can be read here.