# Locally compact automorphism groups of first order structures

**Date**: Wednesday 30 January 2019, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Algebra, Logic and Algorithms, Seminars, Pure Mathematics**Cost**: Free

#### Dugald Macpherson, University of Leeds. Part of the Algebra, Logic, and Algorithms Seminar Series.

An automorphism group of a countable structure M is locally compact if there is a finite subset F of M such that the group of automorphisms of M fixing F pointwise has all its orbits finite. I will discuss several results and questions around such groups. In joint work with Praeger and Smith, we use a Hrushovski amalgamation construction to show that for every k there is a (non-discrete) locally compact automorphism group which is k-transitive but not (k+1)-transitive. We ask for an example of a non-discrete locally compact subgroup of the symmetric group which is maximal subject to being closed, and we give a related classification result. I will also discuss maximal closed subgroups of the symmetric group on a countably infinite set and connections to categoricity.