New examples of torsion groups

We will talk about amenable infinite finitely generated torsion groups. The classical methods of constructing groups of Burnside type (by adding defining relations to the free group) typically produce non-amenable groups. A method inspired by topological dynamics produces amenable finitely generated infinite torsion groups starting from locally finite groups. This includes simple groups and simple groups of subexponential growth. The method also includes some old groups (e.g., the Grigorchuk groups) but it provides a perspective on these old examples.