## Department Colloquium - Catherine Pfaff (UC-Santa Barbara)

### Friday, February 16th, 2018

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Catherine Pfaff (University of California-Santa Barbara)

**Title:** A Nielsen-Thurston Inspired Story of Iterating Free Group Automorphisms and Efficiently Deforming Graphs

**Abstract: **While many fundamental contributions to the study of outer automorphisms of free groups date back to the early 20th century, the real explosion of activity in the eld came with two much more recent developments: the denition by Culler and Vogtmann of the deformation space of metric graphs on a surface, namely Outer Space, and the development by Bestvina, Feighn, and Handel of a train track theory for outer automorphisms of free groups. The explosion was a result of a new ability to study free group outer automorphisms using generalizations of techniques developed to study surface homeomorphisms (mapping classes) via their action on the deformation space of metrics on the surface (Teichmuller space). In our talk, we focus specically on a Nielsen-Thurston inspired story jointly studying: 1) outer automorphism conjugacy class invariants obtained by iteratively applying the automorphisms and 2) geodesics in Culler-Vogtmann Outer Space.

**Catherine Pfaff, (University of California-Santa Barbara):** Catherine Pfa obtained her Ph.D. in Mathematics from Rutgers University in 2012 under the supervision of Lee Mosher. Dr. Pfa was Postdoctoral Research Fellow at the Universite d'Aix-Marseille (2013-2014) and at the Universitat Bielefeld (2014-2015). Since 2015, she is Ky Fan Visiting Assistant Professor at the University of California, Santa Barbara. Catherine Pfa's research focuses on geometric group theory and geometric topology. In particular, she studies the outer automorphism group of the free group and Outer Space from a mapping class group perspective.