### 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!