Explore the intricacies of countable Borel equivalence relations and their realizations through continuous actions on compact spaces in this 27-minute conference talk. Delve into the space of subshifts as a natural setting for investigating these relations. Examine the complexity and genericity of properties such as hyperfiniteness within this space. Learn about the collaborative research conducted with Josh Frisch, Alekos Kechris, and Zoltán Vidnyánszky as part of the Measured Group Theory program at the Centre de recherches mathématiques (CRM).