# Joel Gibson

I’m a mathematics PhD student from Sydney, Australia. This is a collection of some small projects I’ve made.

- NSW COVID-19 case locations: An interactive visualisation of the case locations for the June COVID outbreak in NSW.
- LieVis: An ongoing project to create interesting visualisations of phenomena in Lie theory
- Characters of rank 2 algebraic groups: A collection of visualisations concerning crystallographic root systems, Weyl characters, the Jantzen filtration, and a calculator for characters of representations in prime characteristic.
- Characters of the Symmetric Group: A calculator for irreducible character tables of the symmetric group, which can compute tensor products of characters, along with exterior and symmetric powers, and decompose these back into irreducible characters.
- Symmetric Algebra: An online Littlewood-Richardson calculator, which can compute linear combinations of Schur functions in the algebra of symmetric functions.
- 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”.
- 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.
- A pitch pipe
- Mandelbrot: An implementation of the Mandelbrot set using WebGL.
- Fireworks!
- A clock game which appeared in FFXIII-2.