Compact Riemannian manifolds with essential conformal group are conformally equivalent to the round sphere S^n, by a celebrated theorem of Lelong-Ferrand and Obata. Conformal dynamics on the type-(p,q) Einstein spaces, the pseudo-Riemannian analogues of the round sphere, are more complicated than the source-sink dynamics on S^n. In this talk, I will present the dynamics of unipotent conformal flows on these spaces. I will discuss the tight bound on the degree of a nilpotent group of conformal flows on any compact pseudo-Riemannian manifold M, and our theorem that any M admitting a group of conformal automorphisms of maximal degree is locally conformally equivalent to flat R^{p,q} on a nonempty open subset. These results support the pseudo-Riemannian Lichnerowicz conjecture.
This is joint work with Charles Frances.