Dynamical Systems Seminar

Starting in the 1990's, the rigidity of Weyl chamber flows have been studied. Unlike their classical counterparts like geodesic flow on hyperbolic surfaces or toral automorphisms, these actions demonstrate more striking rigidity phenomenon. In particular, structural stability is upgraded to \(C^\infty\) conjugacy, and the Livsic theorem is upgraded to full cocycle rigidity. Until recently, no unified argument existed to show this phenomenon in a partially hyperbolic setting: all existing arguments relied on classical algebraic K-theory or heavy computations in second group homology that were verified ad-hoc. In this talk, one such unified argument will be presented.