Let $R$ be a Borel equivalence relation with countable equivalence classes, on the standard Borel space $(X, \mathscr{A}, \mu)$. Let $\sigma$ be a 2-cohomology class ...

Say that a class of equivalence relations ${\cal C}$ has the finite union property if every equivalence relation that is the union of finitely many members of ${\cal C}$ must itself be a member of ...

This talk will be an introduction to the field of Borel equivalence relations (also called invariant descriptive set theory). No background will be assumed. We will motivate the main object of study: ...