In the Homotopy theory folder, see Goerss Copenhagen lectures (prereqs + slides). Synopsis: I would like to give a concise introduction to derived algebraic geometry over the moduli stack of formal groups. Put another way, I would like to discuss when continuous families of Landweber exact homology the- ories can be lifted to families of structured ring spectra. I would also like to explain why we care: this is part of long standing program (going back to Morava and others) of using arithmetic algebraic geometry to understand phenomena in stable homotopy theory. While very much a developing the- ory, the work of Hopkins, Miller, Lurie, Behrens, Lawson, and others over the last ten or so years have given us very precise tools. The theory and practice of these tools is the emphasis of these lectures. Topics we be a subset of the following list, depending on time and the background of the audience.
nLab page on Topological algebraic geometry