Nalini Joshi, Department of Mathematics, Sydney University
When Applied Mathematics Collided with Algebra
Imagine walking from one tile to another on a lattice defined by reflections associated with an affine Coxeter or Weyl group. Examples include triangular or hexagonal lattices on the plane. Recently, it was discovered that translations on such lattices give rise to the Painlevé equations, which are reductions of integrable systems that are more familiar to applied mathematicians and mathematical physicists. I will explain this surprising development through introductory examples and explain the background to the discovery of continuous and discrete Painlevé equations.