An oligomorphic group is a permutation group on a countably infinite set with only finitely many orbits of n-sets for each n. These are precisely the automorphism groups of countable models of countably categorical theories.
I conducted (in 2021) a reading course on this subject. For the first half of the course we are reading parts of Peter Cameron's book Oligomorphic Permutation Groups, and in the second half of the course we will read recent articles on the subject.
Below are links to recordings of some of the sessions.
If you are interested in attending this seminar occasionally, please let me know.
November 30: Hrushovski constructions, Part 2
November 23: Hrushovski's counterexamples, as explained by Wagner, Part 1
November 4: More on P-oligomorphic groups
November 2: P-oligomorphic groups, part 1 (Falque and Thiery)
October 28: More on metrizable universal minimal flows
October 19: More on Cherlin-Harrington-Lachlan (Section 2)
October 14: Cherlin-Harrington-Lachlan's classification of strictly minimal geometries
October 12: Introduction to paper by Cherlin-Harrington-Lachlan
September 30: A survey of growth rates in oligomorphic groups
September 28: The 5 reducts of (Q, <) and Thomas's Conjecture
September 23: More on local orders, cycle indices (section 3.3)
September 16: growth rates of direct products and wreath products (section 3.2 of Cameron)
September 14: Growth rates and monotonicity (section 3.2 of Cameron)
September 9: more on Fraïssé, Uhryson space, boron trees
September 7: introduction to Fraïssé limits
September 2: the topology of symmetry groups (section 2.4 of Cameron)