A what?!

We will give a gentle introduction to gerbes and other assorted "higher structures" from topology and mathematical physics. Gerbes are a generalization of line bundles. For a line bundle, the space of sections forms a vector space, and a little extra geometric structure can make it into a Hilbert space, beloved by quantum physicists everywhere. After introducing gerbes, we will ponder the analogous construction: how do we define a "Hilbert space of sections" for a gerbe?

This expository talk is based on the work of Bunk and Szabo.