Rigidity of Anosov Zd actions on nilmanifolds
David Fisher (Indiana University and Radcliffe Institute for Advanced Studies, Harvard)
Abstract: It is conjectured by Katok and Spatzier that all
"irreducible" Anosov Zd actions on manifolds are conjugate
to affine algebraic actions on nilmanifolds. I will discuss motivation
and prior work on the subject before concentrating on recent
joint work with Kalinin and Spatzier.
There is a strong analogy between global rigidity results of this
kind and work on rigidity of invariant measures. I will try to
explain some of this analogy and point out how our work
is analogous to ideas of Lindenstrauss that led to breakthroughs
work on measure rigidity.