"Geometry and Analysis on Groups" Research Seminar
One-relator groups and the Haagerup property.
Giles Gardam (Munster)
It is open whether every group admitting a presentation wih a single relator has the Haagerup property (aka Gromov's aT-menability). I will outline the theory of one-relator groups relevant to the Haagerup property, including both why establishing this property is easy in certain cases and some joint work with Dawid Kielak demonstrating the difficulty of the problem in general. We conclude with some cause for optimism.