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Dynamics seminar: Or Landesberg (Yale) Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces | Einstein Institute of Mathematics

Dynamics seminar: Or Landesberg (Yale) Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces

Date: 
Tue, 22/11/202214:00-15:00

Abstract: Horospherical group actions on homogeneous spaces are famously known to be extremely rigid. In finite volume homogeneous spaces, it is a special case of Ratner’s theorems that all horospherical orbit closures are homogeneous. Rigidity further extends in rank-one to infinite volume but geometrically finite spaces. The geometrically infinite setting is far less understood.

We consider Z-covers of compact hyperbolic surfaces and show that they support quite exotic horocycle orbit closures. Surprisingly, the topology of such orbit closures delicately depends on the choice of a hyperbolic metric on the covered compact surface. In particular, our constructions provide the first examples of geometrically infinite spaces where a complete description of horocycle orbit closures is known. Based on an ongoing joint work with James Farre and Yair Minsky.



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Meeting ID: 851 3233 4083
Passcode: 276352