Appears in collection : 2024 - T2 - WS1 - Low Dimensional Actions

For a group acting on a surface, one may want to classify orbit closures or invariant/stationary measures. I’ll discuss an older result of myself and Rodriguez-Hertz—adapting the exponential drift methods of Benoit-Quint and Eskin-Mirzakhani—to classify stationary measures under certain dynamical hypotheses on the action. I’ll also discuss more recent related works, work in progress, and open questions.