91ÌÒÉ«

Abstract: The purpose of this talk is to trace a story linking a topological problem to some combinatorial gadgets called Gauss diagrams. The problem is to understand the geometry and topology of some configuration spaces, and I’d like to advertise Gauss diagrams as I’ve been finding them very useful when working on this problem: they are very efficient at encoding certain topological data. The story will go via various species of braid group and involves so-called ‘symmetric’ automorphisms of free groups. If I have time, I’ll then talk about recent work in which I introduce Gauss diagram-like objects to handle symmetric automorphisms of right-angled Artin groups (RAAGs), which are a class of groups well-studied by geometric group theory. This allows us to give a new proof of a known presentation of the symmetric automorphism group of any RAAG, and a diagrammatic incarnation of that group.