Peter Giblin (University of Liverpool)
pjgiblin@liverpool.ac.uk
The medial axis of a shape in the plane is a 1-dimensional "skeleton" which in some sense captures aspects of the shape. It is the locus of centres of maximal (planar) disks which lie inside the shape. For about the last two decades I have been interested in the properties of these axes which can be deduced from singularity theory. In three dimensions one can of course consider maximal 3-disks. The medial axis is a subset of the symmetry set in which one considers the centres of all circles (or spheres) which are tangent to the boundary of the planar (or 3D) region. In the last few years I have looked at 3D symmetry sets/medial axes and also investigated definitions which are invariant under affine transformations of the plane rather than euclidean transformations. I shall talk about some of these ideas in I hope a not too technical way.