Symmetries of integrable difference equations
This talk describes our approach to symmetries of integrable difference equations in the famous Adler-Bobenko-Suris (ABS) classification. By using the direct method, we have been able to obtain point symmetries and higher symmetries for each of the ABS equations. In particular, we have found mastersymmetries for each equation – these produce an infinite hierarchy of local symmetries. We also demonstrate a connection between the symmetries of quad-graph equations and those of the corresponding Toda type difference equations.