Ergodic properties of boundary actions, growth and Nielsen-Schreier method

We will speak about ergodic properties (ergodicity and conservativity) of the action of a subgroup of a free group on its boundary with respect to the uniform measure. The Hopf decomposition of boundary action will be described in terms of Nielsen-Shreier theory coming from combinatorial group theory. Growth and cogrowth will be used to characterize conservativity and dissipativity. Amenability and Liouville property will be mentioned to illustrate some extreme cases.An open problems will be formulated at the end of the talk.