Gorenstein duality for topological modular forms with level structure

The notion of Gorenstein duality introduced by Dwyer, Greenlees and Iyengar
allows one to view a number of dualities such as Poincaré duality for manifolds,
Gorenstein duality for commutative rings and Benson-Carlson duality for
cohomology rings of finite groups as instances of a single phenomenon. In this
talk I will set up an equivariant generalization of the framework and look at
examples coming from derived algebraic geometry, namely - the ring spectra of
topological modular forms with level structure.