A talk for the Boise math graduate student seminar, October 2015 (notes)
Abstract: Much of mathematics is devoted to classifying mathematical objects. One may wish to classify groups or graphs up to isomorphism, or topological spaces up to homeomorphism, or group actions up to conjugacy, etc. When is such a classification problem tractable and when is it hopeless? Set theory provides us with the appropriate defintion of “complexity” for classification problems. In this talk we’ll explore this notion and what it reveals about some classical examples.