Seminar 11.14.19 Vinhage

Title: New Progress on the Katok-Spatzier conjecture

Speaker: Kurt Vinhage –¬†Pennsylvania State University

Abstract: We will discuss recent progress on the Katok-Spatzier conjecture, which aims to classify Anosov actions of higher-rank abelian groups under the assumption that there are no nontrivial smooth rank one factors. We develop new techniques to build homogeneous structures from dynamical ones. The remarkable features of the techniques are their low regularity requirements and their use of metric geometry over differential geometry to build group actions. We apply these techniques to obtain a classification result in the totally Cartan setting, where bundles associated to the hyperbolic structure are one-dimensional. Joint with Ralf Spatzier.