University of Sydney Algebra Seminar

Ryan Seelig

Friday 28 August, 12-1pm, in Carslaw 275

Forest-skein groups: constructing new simple groups with diagrams

Forest-skein groups are a class of infinite discrete groups, similar to Richard Thompson's famous groups F<T<V, introduced by Arnaud Brothier in 2022 to strengthen recent connections between subfactors and conformal field theory uncovered by Vaughan Jones. Forest-skein groups are also interesting from a purely group theoretic perspective and the goal of this talk is to show they fit into the active research area of finitely presented infinite simple groups. We will start by explaining what forest-skein groups are and how their defining diagrammatic calculus of coloured binary forests modulo ``skein relations'' can be used to study them. In particular, we will use this diagrammatic calculus to describe normal subgroup structure of any forest-skein group, and also use it to give some easily computable invariants for these groups. This leads us to obtain explicit examples of finitely presented infinite simple groups witnessing previously unforeseen dynamical phenomena.