Geometry, Topology and Dynamics Seminar
Brian Ray
UIUC
Spectral Rigidity in Free Groups
Abstract: Given a subset $S$ of a finitely generated free group, we say that $S$ is spectrally rigid if whenever $T$, $T'$ are trees in Culler-Vogtmann Outer Space for which $|| g ||_T = || g ||_{T'}$ for every $g \in S$, then $T = T'$.
Contrary to the analogous notion in Teichmuller space, there does not exist a finite spectrally rigid set. We will survey some recent results about (non) rigidity of certain `sparse' yet infinite sets. We will also explain
how this notion can be generalized to include the closure of Outer Space, as well as introduce additional notions of
rigidity in Outer Space.
Monday September 30, 2013 at 3:00 PM in SEO 636