Nadia Larsen: Multispinal groups over the field with 2 elements and simplicity of *-algebras of their groupoids

Abstract: I will present an approach to showing simplicity of groupoid *-algebras associated to multispinal groups over Z_2 extending the methods by Clark-Exel-Pardo-Starling-Sims for the case of the Grigorchuk group (this being, in a precise sense, the "first" example of a Z_2-multispinal group). Along the way we come across some curious full-rank matrices of a kind appearing in the theory of 2-designs. This is joint work with Carla Farsi, Judith Packer and Nathaniel Thiem at UC Boulder, Colorado, USA.