Colloquium: Or Landsberg (HUJI, Zuchovitzky prize lecture) — Rigidity of horospherically invariant measures and the geometry of hyperbolic 3-manifolds

Thu, 19/11/202014:30-15:30
Rigidity of horospherical group actions, and more generally unipotent group actions, is a well established phenomenon in homogeneous dynamics. Whereas all finite ergodic horospherically invariant measures are algebraic (due to Furstenberg, Dani and Ratner), the category of locally finite measures, particularly in the context of geometrically infinite quotients, is known to be much richer (following works by Babillot, Ledrappier and Sarig). The rigidity of such locally finite measures is manifested in them having large and exhaustive stabilizer groups.
In this talk I will present a measure classification result for locally finite horospherically invariant measures over hyperbolic 3-manifolds with a finitely generated fundamental group. This is an application of a more general joint result with Elon Lindenstrauss combined with fundamental results in the theory of hyperbolic 3-manifolds, most notably the Tameness Theorem by Agol and Calegari-Gabai. The interplay between the dynamics and the geometry of these spaces will be highlighted and relevant background will be presented.

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