Discrete Omega Surfaces
Omega surfaces, discovered by Demoulin in 1911, comprise a rich class of surfaces of classical interest, including linear Weingarten surfaces, isothermic and Guichard surfaces. They are an integrable system with a duality, Darboux transforms and a spectral deformation all of which can be traced back to their relation with isothermic surfaces in the Lie quadric. In this talk I shall sketch a satisfying discretization of this theory which retains all the details of the classical story.
Along the way, we will present a novel reformulation (and mild generalization) of the Bobenko-Pinkall theory of isothermic nets.