Peter Schmitt - The versatility of (small) sets of prototiles

A set of prototiles (which are usually assumed to be closed topological disks or balls) may or may not admit a tiling of the plane (or of n-space). The set of all (distinct) tilings admitted represents the versatility of a set of prototiles. It may be large or small, and the tilings may have quite different properties. The talk provides an survey of the versatility of small sets, with emphasis on periodicity properties, and describes some general constructions.