Pure Maths Colloquium: H. Dugald MacPherson

A countable relational structure (e.g. a graph or partial order) is said to be homogeneous if every isomorphism between finite (induced) substructures extends to an automorphism of the structure. I will give an overview of various classification and structure theorems for homogeneous structures (for example graphs, digraphs, permutations, finite homogeneous structures). I will then focus on Cherlin’s programme to classify metrically homogeneous graphs, that is, graphs which become homogeneous when enriched by binary relation symbols interpreted by graph distance (this can be seen as a strengthening of the well-known property of distance transitivity for graphs). In particular, I will describe joint work with Amato and Cherlin classifying metrically homogeneous graphs of diameter 3.