# Rankin Lecture: A machine for constructing representations of R. Thompson’s groups, unitary and otherwise

### Vaughan F.R. Jones (Vanderbilt University)

Friday 24th March, 2017 16:30-17:30 WILT Lecture Theatre

#### Abstract

Thompson’s groups are often realised as groups of homeomorphisms of the unit circle. We will give a “group of fractions” construction of them which makes it easy to construct actions from a diverse collection of data. Actions that arise in this way include actions by smooth diffeormorphisms, actions on the free group $F_\infty$ and a unitary representation on Hilbert space for each representation
of the ''Pythagorean’’ C*-algebra with presentation $<a,b:|a|^2+|b|^2=1>$. The inspiration for these constructions was the vision of the Thompson group as local scale transformations on a quantum spin chain.