On January 22, 2019 I gave a talk at the (Arctic Set Theory Workshop 4) in Kilpisjärvi, Finland.

Abstract: In his PhD thesis Wadge characterized the notion of continuous reducibility on the Baire space ${}^\omega\omega$ in form of a game and analyzed it in a systematic way. He defined a refinement of the Borel hierarchy, called the Wadge hierarchy, showed that it is well-founded, and (assuming determinacy for Borel sets) proved that every Borel pointclass appears in this classification. Later Louveau found a description of all levels in the Borel Wadge hierarchy using Boolean operations on sets. Fons van Engelen used this description to analyze Borel homogeneous spaces and show that every homogeneous Borel space is in fact strongly homogeneous.