Automorphism groups of countable structures

Suppose M is a countable first-order structure with a ‘rich’ automorphism group Aut(M). We will study Aut(M) both as a group and as a topological group, where the topology is that of pointwise convergence. This involves a mixture of model theory, group theory, combinatorics, descriptive set theory and topological dynamics. Here, ‘rich’ is undefined and depends on the context, but examples which we are interested in include: homogeneous structures such as the random graph or the rational numbers as an ordered set; ω-categorical structures; the free group of rank ω. The plan for the lectures is: