Train Track Automata for Outer Automorphisms of Free Groups and Geodesics in Outer Space

Explore a 43-minute mathematics seminar lecture examining the relationship between outer automorphism groups of free groups and geodesics in Outer space. Delve into the train track theory of Bestvina-Feighn-Handel, which connects topological representatives of group elements with geodesics in the deformation space. Learn how the asymptotic conjugacy class invariant of the Handel-Mosher ideal Whitehead graph is used to stratify both the space of geodesics and dynamically minimal "fully irreducible" outer automorphisms into train track automata. Understand the broader context of geodesic flow, comparing the closed hyperbolic manifold and Teichmuller space settings with graph-based scenarios. Discover research findings developed in collaboration with Y. Algom-Kfir, D. Gagnier, I. Kapovich, J. Maher, L. Mosher, and S.J. Taylor that investigate potential properties of this mathematical flow.