Aspects of the Large Scale Geometry of Out(Fn)

This lecture from the Joint IAS/PU Groups and Dynamics Seminar explores the large scale geometry of Out(Fn), the outer automorphism group of a rank n free group. Presented by Lee Mosher from Rutgers University - Newark, the talk delves into how hyperbolic hierarchy concepts can be applied to study Out(Fn), despite it not being hierarchically hyperbolic due to its rapidly growing Dehn function. Learn about the Two Over All Theorem (joint work with Handel) which demonstrates an exponential flaring property of "foldable" homotopy equivalence between rank n graphs, using distance in the free splitting complex as the exponential function argument. The presentation covers applications to the geometry of outer space and the free splitting complex, including a new proof of the exponential growth of the Dehn function of Out(Fn) (joint work with Lyman). The concepts extend to outer automorphism groups relative to free factor systems. The seminar takes place at Simonyi 101 at 4:30pm on May 06, 2025.