Symmetry methods for difference equations on non-rectangular lattices.

一般差分方程对称方法的发展还处于起步阶段。尽管人们对矩形格子上的差分方程了解很多，但在底层格子不是矩形的情况下（例如，使用移动标架在差分不变量的格子中创建洞），得到的证明相对较少。这个项目的目的是开始来解决这个问题，使用最近发现的结果移动框架和晶格品种。该项目将开始一般的差异移动框架建设多个独立的变量，这将产生第一组不变的诺特型偏差分方程定理。未来可能的发展方向包括利用移动标架构造的可解性和在格簇上创建全局差分结构

The development of symmetry methods for general difference equations is still in its infancy. Although a substantial amount is known about difference equations on rectangular lattices, relatively little has been proved in the case where the underlying lattice is not rectangular (for instance, where using a moving frame creates holes in the lattice of difference invariants). The purpose of this project is to begin to address this problem, using recently-discovered results on moving frames and lattice varieties. The project will begin by generalising the difference moving frame construction to multiple independent variables, which should yield the first group-invariant Noether-type theorems for partial difference equations. Likely future directions include exploiting solvability in the moving frame construction and creating global difference structures on lattice varieties