Magic trees and mystic matrices

Tuesday, 2-July-2024 

Abstract

Be amazed at Ian's powers of prognostication! Or at least amused at his attempts at mathemagic. 

The mystic matrices are those which contain the distances between some finite set of objects $X = \{x_1,\dots,x_m\}$. The most classical question in the area of `distance geometry' is whether one can find a subset of Euclidean space with matching distances. Answering this involves looking at various properties of this distance matrix; $D_X = (d(x_i,x_j))_{i,j=1}^m$. In this talk we shall concentrate on some important examples such as metric trees, or sets of bit strings. In these settings the distance matrices have some rather magical properties. 

No knowledge beyond second year mathematics will be required, but a small amount of audience participation may be needed. 

This joint work with Anthony Weston.