GEOMETRIES AND INTERFACES

This conference has shown that the topic of Geometry and Interfaces has congealed as a distinct subject area, perhaps to be called flexi-crystallography. As well as considering liquid crystals, it includes a large class of materials, natural and synthetic, which are not regular three-dimensional crystals, but which nevertheless have considerable order. Among these can be distinguished curved two-dimensional manifolds, some of which can be patched into crystals. New geometries, including those of S3, H2, H3, T2, becomes relevant, being made visible by computer graphics. Some representations, particularly periodic minimal, equipotential and nodal surfaces also illuminate the structures and properties of regular crystals. These surfaces, on various scales, can be discerned in materials by using microscopy and less direct techniques