Topological design Theory

Terry Griggs
Open University

Topological Graph Thoery is concerned with graph embeddings in surfaces. It is a well established branch of Combinatorial Mathematics. The faces of such embeddings necessarily give rise to designs. However until recently little attention was paid to the study of these designs. Topological Design Theory therefore can be regarded as Topological Design Theory in which the main emphasis is on the faces of the embedding. It brings together ideas from both Toological Graph Theory and Combinatorial Design Theory. I will discuss recent work in this area focusing mainly on Steiner triple systems and Latin squares including many fascinating unsolved fundamental problems. Topological Design Theory is still very much in its infancy!