Joel Gibson

This is the personal website of Joel Gibson. I am a postdoctoral researcher at the University of Sydney: for more information view my research homepage.

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.