Pure Mathematics Seminar: Ian Doust
Ian Doust, University of New South Wales
Wednesday 15 January 2014, 1500-1600
A54, Postgraduate Statistics Centre Lecture Theatre
p-negative type and metric space embeddings
A natural question, and one which arises in applications, is whether a discrete metric space can be realized as a subset of Euclidean space Rn, where Rn is given its usual Euclidean distance, or perhaps another standard metric. If this is the case, then one can use the great array of geometric tools in Rn to attack these graph theoretic problems. In this talk we shall concentrate on the special case that the metric space is a tree with the graph metric.
We shall discuss some of what is known in this area, as well as some recent work with Tony Weston and Stephen Sanchez on calculating a geometric constant associated with these metric spaces which arises in considering these sorts of embedding problems.