This paper is a survey of affine Anosov representations, a framework in which proper affine actions of hyperbolic groups are characterized by Margulis invariant spectra, mostly quoting the author's own results.
Finite step Rigidity of Hitchin representations and special Margulis-Smilga spacetimes
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abstract
In this article we use the "escape from subvarieties lemma" introduced by Eskin--Mozes--Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a similar finite step rigidity result for the Cartan spectra of representations of a finitely generated group inside a connected semisimple real algebraic Lie group with trivial center.
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Affine Anosov representations
This paper is a survey of affine Anosov representations, a framework in which proper affine actions of hyperbolic groups are characterized by Margulis invariant spectra, mostly quoting the author's own results.