Minicourse 1: Finite permutation groups
Abstract: This course will be an introduction to finite permutation groups. The first lecture will give many of the key definitions required for Gabriel Verret’s course. After that we will go on to study the structure of various classes of permutation groups, focussing in particular on the primitive permutation groups. We will look at various especially nice actions on combinatorial objects that reveal unusual combinatorial and group-theoretic properties, and finish with some open problems.
Minicourse 2: Vertex-transitive graphs and their local actions
Abstract: The topic of this short set of lectures will be vertex-transitive graphs. (Graphs with automorphism group acting transitively on their vertex-set.) In the first half, we will discuss many basic examples and properties. In the second half, we will focus on the concept of local action in such graphs. (This is the permutation group induced by the stabiliser of a vertex on the corresponding neighbourhood.) We will first discuss some applications, and finish with some open problems.