Full groups of minimal homeomorphisms of the Cantor space

The first part of the talk will be an introduction to the theory of minimal homeomorphisms and their full groups (and why these objects are interesting). In the second talk I'll sketch the proof of the following result (joint with T. Ibarlucia): the full group of any minimal homeomorphism is a coanalytic non Borel subset of the homeomorphism group of the ambient Cantor space.