# Vortrag

Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

## Horospherically invariant measures on geometrically infinite quotients

Vortrag von Or Landesberg

Sprecher eingeladen von: Prof. Dr. Corinna Ulcigrai

Datum: 16.12.19   Zeit: 14.00 - 15.00   Raum: ETH HG G 43

We consider a locally finite (Radon) measure on SO(d,1)/Gamma invariant under a horospherical subgroup of SO(d,1) where Gamma is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not observe any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable flow (geodesic flow). Measure classification results are deduced, in particular for the case of a normal subgroup of a geometrically finite Zariski dense discrete group. This is joint work with Elon Lindenstrauss.