Universal automorphism groups and canonical amalgams

Let M be a countable ultrahomogeneous structure (e.g. Q or the random graph), and let A be a structure which is embeddable in M. We will discuss when it is possible to find a "nice" embedding of A into M, where "nice" means that each automorphism of A extends to an automorphism of M in a way that respects composition (giving a group embedding Aut(A) to Aut(M)).

We will present some general theorems and nice examples (e.g. the generic ordered graph, generic two-graph and generic 3-hypertournament). This project is joint work with Aleksandra Kwiatkowska and Jeroen Winkel.