This page collects my expository writings on various subjects. I don’t have any original research papers yet.
October 2021
My Honours thesis, supervised by Asilata Bapat. We study the bounded derived category of representations for an acyclic quiver, occupied chiefly by derived reflection functors.
June 2021
We state and prove a version of the Riemann-Roch theorem over finite fields, including an interpretation of Serre duality in this context. This essay was written for a course on Riemann surfaces run by Ian Le at the ANU.
June 2021
We present Montesinos and Neuwirth’s proof that 2-fold cyclic branched covers of S3 are precisely the (closed, orientable) 3-manifolds which can be obtained via surgery on a strongly-invertible link in S3. The proof uses rational tangle replacement, of which we give a short exposition. This paper was written for a course on low-dimensional topology run by Joan Licata at the ANU.
November 2020
This essay gives a brief introduction to the theory of representations on Banach spaces. It was written for a functional analysis course taught by Pierre Portal at the ANU.
June 2020
We give an introduction to tropical algebraic geometry, motivated by many examples. We build towards the statement of the structure theorem for tropical algebraic varieties. This exposition was written for a course run by Martin Helmer at the ANU.
June 2019
This paper was written for a project supervised by Scott Morrison, in which we attempted to formalise the basic definitions of combinatorial games using the interactive theorem proving language Lean. While this theory is mostly elementary, it interacted in surprising ways with Lean’s inductive type system. Combinatorial game theory was later incorporated into mathlib, in part based on the work done in this project.