Date/Time: 4 March 2022, 4:30pm EST Location: West Chester University, Anderson Hall 211 and on Zoom Speaker: Rylee Lyman (Rutgers-Newark) Title: Train track maps on graphs of groups and CTs for free products Abstract: A homotopy equivalence of a graph is a train track map when it sends vertices to vertices and the restriction of any iterate of the map to an edge yields an immersion. (Relative) train track maps were introduced by Bestvina and Handel in 1992; since then they have become one of the main tools in the study of outer automorphisms of free groups. More recently in 2011, Feighn and Handel introduced a stronger kind of relative train track map called a CT and proved their existence for all outer automorphisms of free groups after passing to a power. We extend the theory of relative train track maps to certain graphs of groups and the theory of CTs to free products (that is, graphs of groups with trivial edge groups).