Abstract: Every outer automorphism of a finite-rank free group has a well-defined (possibly empty) set of "attracting laminations". In fact, these laminations are partially ordered by inclusion and thus give a canonical "lamination poset" associated to the automorphism. These structures were introduced by Bestvina-Feighn-Handel and play a crucial role in their proof of the Tits alternative for \(\mathrm{Out}(F_n)\). In this talk, I will explain that the poset of laminations is in fact an invariant of the associated free by cyclic group. That is, if a group can be expressed as a free-by-cyclic group in two ways, then the two outer automorphisms (of possibly different free groups!) have order-isomorphic lamination posets. This is joint work with Yassine Guerch, Radhika Gupta, Jean-Pierre Mutanguha, and Caglar Uyanik. \(\textbf{Please note the seminar has gone virtual.}\) \(\textbf{Use the associated Zoom link to join.}\)