Topological modular forms and duality

The goal of this talk is to describe the Anderson self-duality of the spectrum of topological modular forms, as well as the guiding analogous example of real K-theory. The results as well as some of the proofs will have the algebro-geometric flavor of Serre-Grothendieck duality.
The first part of my talk will consist of introductory material that could be summarized as "Tmf for the working algebraic topologist."