Joel Gibson

This is the personal website of Joel Gibson. I was a PhD student and then postdoctoral researcher at the University of Sydney from 2016-2022: for more information view my research homepage. Since 2023 I have been working as a quantitative developer at Epoch Capital.

Mathematics software

I am a big proponent of using examples and visual aids to help communicate, teach, and build intuition about abstract domains.

Lievis is my largest (and most impressive) visualisation project, an attempt at illuminating aspects of Lie theory through interactive visualisations.
ASLoc is a Magma package for for calculating the p-canonical basis of Hecke algebras (joint with Thorge Jensen and Geordie Williamson).
IHecke is a Magma package for working with Iwahori-Hecke algebras.
Characters of the Symmetric Group: A calculator for characters of the symmetric group, able to calculate tensor product decompositions, and tensor/symmetric/exterior power decompositions. (Updated 2021-09-02: using a better algorithm to calculate characters, this now allows calculations in symmetric groups up to size 30).
Symmetric Algebra: A calculator for Littlewood-Richardson coefficients, which can compute linear combinations of Schur functions in the algebra of symmetric functions.
Convex Hull: An explanation of what the convex hull of a set of points is, and an interactive visualisation of an algorithm for finding the convex hull.
Lights Out: An implementation of the “Lights Out!” game for varying board sizes and shapes, and a pleasant application of linear algebra over the finite field of order 2.

Random stuff

A new and improved pitch pipe with support for just intonation intervals. The old pitch pipe is still kicking around.
Minimal Pairs: A small application for exploring words which begin or end in different letters, but are otherwise the same, for example “leader” and “cedar”, or “relief” and “release”.
Mandelbrot: An implementation of the Mandelbrot set using WebGL.
Fireworks!
A clock game which appeared in FFXIII-2.