# Pure Maths Colloquium: H. Dugald MacPherson

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: | Lecture Theatre C |

When: | Feb 13 2020 @ 16.00 |

Video: | Not recorded |

Speaker: | H. Dugald MacPherson University of Leeds |

Title: | Classification for homogeneous relational structures |

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 Cherlinâ€™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.