Symmetry methods for difference equations on non-rectangular lattices.

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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