Random dynamics on surfaces

In this talk, we will discuss smooth random dynamical systems and group actions on surfaces. Random dynamical systems, especially understanding stationary measures, can play an important role for understanding a group action. For instance, when a group action on torus is given by toral automorphisms, using random dynamics, Benoist-Quint classified all orbit closures under a mild assumption. We will study group actions on surfaces by diffeomorphisms, using random dynamics. We will discuss absolute continuity of stationary measures, classification of orbit closure, and exact dimensionality of stationary measures. This talk will be mostly about the ongoing joint work with Aaron Brown, Davi Obata, and Yuping Ruan.