Akshay Venkatesh (Stanford University) will present the Trjitzinsky Memorial Lectures November 27-29, 2012. A reception will be held following the Nov. 27 lecture. Lecture I. The Cohen-Lenstra heuristics. The Cohen-Lenstra heuristics predict that class groups of number fields behave like (a certain model of) random abelian group. After explaining what this means (no knowledge of number fields or class groups is assumed) I will briefly discuss a proof of them in the function field setting with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology ("homological stability").