Consider a real projective surface X(\mathbb{R}), and a group \Gamma acting by algebraic diffeomorphisms on X(\mathbb{R}). If \nu is a probability measure on \Gamma, one can randomly and independently choose elements f_j in \Gamma and look at the random orbits x, f_1(x), f_2(f_1(x)), ... How do these orbits distribute on the surface? This is directly related to the classification of stationary measures on X(\mathbb{R}).

I will describe recent results on this problem, all obtained in collaboration with Romain Dujardin.
The main ingredients will be ergodic theory, notably the work of Brown and Rodriguez-Hertz, algebraic geometry, and complex analysis. Concrete geometric examples will be given.

Zoom link: https://iu.zoom.us/j/661711533?pwd=RTFVTjMrQ1pYTCtIZzIvVGVvODV2QT09
password is 076877 if needed. Speaker(s): Serge Cantat (University of Rennes)