Homogeneous structures, . . .

I aim to give the flavour of a selection of topics based around Fräıssé’s notion of homogeneous structure. This is an area connecting ideas from model theory, permutation group theory, combinatorics, descriptive set theory, complexity theory, and other subjects. I will touch superficially a number of these subjects, with little in depth. The background assumed will be basic first order logic (languages, structures, interpretations, compactness), but of course, some familiarity with other subjects will help. The notes below contain no original material. Outline of lectures. 1. Homogeneous and ω-categorical structures. Fräıssé amalgamation. Examples and classification results. 2. Model theory of homogeneous and ω-categorical structures. 3. Automorphisms of homogeneous and ω-categorical structures. Polish groups. Recovering a structure from its automorphism group. 4. Structural Ramsey theory and homogeneous structures. 5. Ramsey theory, homogeneous structures, and topological dynamics.