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Abstract

ÌýAbout ten years ago Vaughan Jones discovered beautiful and powerful connections between Richard Thompson's groups F,T,V, subfactor theory, and quantum field theory. Inspired by these connections, Arnaud Brothier recently introduced forest-skein categories and their forest-skein groups which mix the binary forest calculus of Thompson's groups with skein theory from subfactors. A core motivation of Brothier's program is to produce many explicit examples of infinite discrete groups that satisfy rare properties. In this talk we will give a characterisation of simplicity of forest-skein groups in terms of categories and in terms of dynamics. We will then produce explicit examples of finitely presented infinite simple groups and discuss some previously unseen dynamical properties they possess.

This is joint work with Arnaud Brothier.