(2017). Almost algebraic actions of algebraic groups and applications to algebraic representations. GROUPS GEOMETRY AND DYNAMICS. 11:705-738. Abstract
Let G be an algebraic group over a complete separable valued field k. We discuss the dynamics of the G-action on spaces of probability measures on algebraic G-varieties. We show that the stabilizers of measures are almost algebraic and the orbits are separated by open invariant sets. We discuss various applications, including existence results for algebraic representations of amenable ergodic actions. The latter provides an essential technical step in the recent generalization of Margulis-Zimmer super-rigidity phenomenon .
(2017). Equicontinuous actions of semisimple groups. GROUPS GEOMETRY AND DYNAMICS. 11:1003-1039. Abstract
We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of continuous homomorphisms, nonexistence of weaker topologies, metric ergodicity of transitive actions and vanishing of matrix coefficients for reflexive ( more generally: WAP) representations.
(2016). Equicontinuous actions of semisimple groups. to appear in Geometry Groups and Dymnamics.
(2016). Amenable Invariant Random Subgroups. to apear in the Israel Journal of Mathematics.
(2016). Almost algebraic actions of algebraic groups and applications to algebraic representations. to appear in Geometry Groups and Dymnamics.
(2016). Boundary unitary representations - right- angled hyperbolic buildings. to apear in Journal of Modern Dynamics.
(2015). Rigidity of group actions on homogeneous spaces III. Duke Math. J. 164 (2015), no. 1, 115-155.
(2015). On the structure and arithmetic- ity of lattice envelopes. Math. Acad. Sci. Paris 353 (2015), no. 5, 409413.
(2004). Thesis: Conformal actions of simple Lie-groups on Pseudo- Riemannian manifolds. .
Supervisor: Amos Nevo
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