These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics
students.  Coffee, tea and drinks will be provided.
 
 

Finding the shortest network connecting a given set of points is sometimes called the roadway problem, since one can imagine joining a collection of cities by a system of roads of shortest total length. A solution is called a Steiner tree, after the 19th Century Swiss geometer, although Fermat, Napolean and others were aware of the basic idea also. In the 1960s, researchers at Bell labs became interested in this area, because of potential applications to communication networks. We have been studying the theory at Melbourne for around 12 years and have solved some basic questions for networks in both the plane and 3-space. Simple ideas from the calculus (of variations) have proved very helpful. Recently an important connection to efficient design of underground mines has been investigated.