Some problems in Distance Geometry

Abstract: 

Distance geometry is the characterization and study of sets of points based only on given values of the distances between member pairs. A fundamental problem lies in deciding whether you can identify your points as elements of some space with more geometric structure than just the given distances. After looking at the history of these ideas, we shall introduce some of the main technical concepts such as roundness and negative-type, and discuss some of the currently open problems. Little background is required!