TITLE: Divergent Square Averages ABSTRACT: I plan to outline some ideas behind my proof with Zoltan Buczolich that the squares are L^1 universally bad: For every non-atomic separable probability space with an ergodic transformation T there is a non-negative function f in L^1 such that the arithmetic averages of the observations: f(x), f(T(x)),f(T^4(x)),...,f(T^{(n-1)^2}(x)) diverge for a set of x with positive measure.