Mathematics department colloquium, Boise State University, April 2016 (slides)
Abstract: Much of mathematics is devoted to classifying the objects we study: groups or graphs up to isomorphism, metric spaces up to isometry, symmetries up to conjugacy, and so on. But of course, some classifications are harder than others. Borel complexity theory is an area of set theory that helps us rigorously make such comparisons. In this talk we will survey some recent applications of this theory to problems from group theory, model theory, graph theory, and functional analysis.