Scott Harper

Symmetry breaking: base size and distinguishing number of graphs and groups

Think of your favourite graph. What is the smallest number of vertices such that the identity is the only automorphism that fixes them all? And what is the smallest number of colours needed to colour the vertices such that the identity is the only automorphism that preserves the colours? The base size and distinguishing number are the invariants that capture these questions. In this talk, I will show how recent group theoretic developments shed light on these questions, and I will mention some work on this topic joint with Alice Devillers and Luke Morgan.