Abstract: Serre duality is a twisted form of Poincare' duality satisfied by a very special class of projective schemes. For a variety of reasons the moduli stack of elliptic curves doesn't meet the hypotheses needed and doesn't quite exhibit Serre duality; however, when we consider a derived version of this stack -- replacing the structure sheaf by a sheaf of ring spectra -- suddenly and mysteriously the duality reappears. The purpose of this talk is to explain these ideas and calculations. This is a meditation on work of Hopkins, Miller, Lurie, Behrens, and many others.