Equivariant Gorenstein Duality

This thesis concerns the study of two flavours of duality that appear in stable homotopy theory and their equivariant reformulations. Concretely, we look at the Gorenstein duality framework introduced by Dwyer, Greenlees and Iyengar and the more classical notion of Anderson duality. We study examples of ring spectra that exhibit these duality phenomena, both non-equivariantly and equivariantly, coming from the ring spectra of topological modular forms. Along the way, connecting the work of Greenlees, Meier and Stojanoska we make contact with Serre duality phenomena that arise in derived algebraic geometry and record an unexpected interlace of Anderson, Gorenstein and Serre duality.