Symmetry through geometry
Prof Nalini Joshi (University of Sydney)
Monday 22nd June, 2015 16:00-17:00 Maths 516
The search for symmetries of differential equations set in motion the development of extraordinarily important areas of mathematics. In this talk, we provide a new perspective on the corresponding problem for difference equations, by using a simple, beautiful geometric structure revealed in our recent study. The objects of this study are partial difference equations that arise as discrete versions of famous PDEs. These discrete systems consist of equations fitted together in a self-consistent way on a square, a 3-cube or an N-dimensional cube. By using the beautiful geometric structure of space-filling polytopes, we show how to find their unexpected symmetry reductions.
N. Joshi, N. Nakazono and Y. Shi (2014). "Geometric reductions of ABS equations on an n-cube to discrete Painlevé systems." Journal of Physics A-Mathematical and Theoretical 47: 505201 (16pp).