Abstracts for IMPRS mini course "Elliptic cohomology and dualizability"

The ring of topological modular forms arises as functions on the moduli stack of elliptic curves, suitably interpreted in a homotopical sense. To see more of the geometry of elliptic cohomology, we would like to interpret the cohomology of classifying spaces similarly, in terms of schemes related to symmetric powers of elliptic curves.