Title: Symbolic and Ergodic Actions of the discrete Heisenberg group

Speaker: Ayşe Sahin (Wright State University)

Abstract: We describe two different actions of the Heisenberg group, Γ: odometer actions and aperiodic shifts of finite type. Both types of actions rely on the geometric structure of the Heisenberg group, but exploit different frameworks. We show in the first case that the odometer actions are indexed by a triple of data describing finite index subgroups of Γ, as described by a short exact sequence associated to the Heisenberg group. The aperiodic shift of finite type, on the other hand, is constructed using the Cayley graph structure of a semi-direct product group.