Presented by: 
Bridget Webb, The Open University, UK
Date: 
Tue 31 Mar, 3:00 pm - 4:00 pm
Venue: 
Building 67, Room 442

The concept of homogeneity was introduced by Fraïssé in 1953, and lies at the interface of combinatorics, permutation group theory and model theory. A structure is homogeneous if every isomorphism between finite induced substructures extends to an automorphism of the whole structure. Thus homogeneity means that any local symmetry is in fact global, and so a homogeneous structure is highly symmetrical. A slightly weaker concept is set-homogeneity, where, if U and V are isomorphic finite induced substructures, then there is some automorphism of the whole structure that maps U to V.

I will start by illustrating the ideas using graphs before moving on to Steiner triple systems.