From discrete differential geometry to the classification of discrete integrable systems
Meeting Room 3, CMS
(joint work with Vsevolod Adler and Yuri Suris) Discrete Differential Geometry gives a new insight into the nature of integrability. The integrability is understood as consistency, i.e. a discrete d-dimensional system is called integrable if it can be consistently imposed on n-dimensional cubic lattices for all n>d. We classify multi-affine 2-dimensional integrable systems and also give partial classification results for 3-dimensional integrable systems (without any assumption on the form of the equations).