Solved and Unsolved Problems Around One Group

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Hausdorff dimension in a family of self-similar groups (2006, background): “5 in [15] (the proof itself claims that G is the closure of a self-similar regular branch groupH , branching over Hs+1, but a careful reading reveals that the argument works equally well for Hs).”
Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups (2011, background): “See [48] for other question concerning the growth of groups and, in particular, of Grigorchuk groups.”
Milnor's Problem on the Growth of Groups and its Consequences (2011, methodology): “Groups of intermediate growth were used and continue to be used in many different situations: in the study of amenable groups [96, 101], in topology [82], in theory of random walks on groups [77, 137, 73], in theory of operator algebras [110, 112, 109], in dynamical systems [24, 47], in percolation ”
Notes on the Schreier graphs of the Grigorchuk group (2011, background): “In partic- ular, we describe the invariant set of the Schreier graphs corresponding to the action on the boundary of the binary rooted tree and dynamics of the group action restricted to this invariant set.”