Algebra Seminar: Seelig -- Forest-skein groups: constructing new simple groups with diagrams

Ryan Seelig (UNSW Sydney) will be speaking in the algebra seminar.  We will go out for
lunch after the talk---all are welcome to join! 

When: 12-1pm Friday August 28 

Where: Carslaw 275 

Title: Forest-skein groups: constructing new simple groups with diagrams 

Abstract: 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.