SEMINAR: Groups and Combinatorics Seminar: The Many Faces of Triangle Groups

Time and place: 15:00 Friday 17 April in Blakers LT.

Speaker: Alastair Litterick (University of Auckland)

Title: The Many Faces of Triangle Groups.

Abstract: Do the finite groups in a given class have generating sets of a prescribed form? Versions of this problem are as old as group theory itself, and still arise naturally today in enumerative geometry, combinatorics, the inverse Galois problem, and computational algebra.

This talk will consider `triangle-generated finite groups', i.e. 2-generated groups where the generators and their product have specified orders. We will discuss in particular the `rigidity conjecture' of Claude Marion, which relates triangle generation in a family of finite groups of Lie type to a property of the corresponding algebraic group. Recent progress on this conjecture has required a surprising variety of approaches, and we will discuss each of these and their limitations..