Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

In this talk I will discuss both Lie groups and lattices actions by conformal transformation of a pseudo-Riemannian manifold, related to the Lorentzian Lichnerowicz' conjecture.

I will first discuss dynamics of $SL(2,\mathbb R)$-actions on closed Lorentzian manifolds, and then I will detail recent advances for higher-rank lattices conformal actions, and ongoing works with Thierry Barbot in the specific Lorentzian case.