Abstract:
The Hochschild-Kostant-Rosenberg theorem gives an important relationship between Hochschild homology and derivations. I will state and prove the classical HKR theorem, but also explore a generalized derived version. This will be an opportunity to introduce the formalism of "nonabelian derived functors", and also serve as a blueprint for more subtle "motivic filtrations" on topological Hochschild homology and its variants, which we will explore later in the semester.