Loop spaces, Hochschild-Kostant-Rosenberg isomorphisms and exponential maps.

In this talk we will explain a computation describing Hochschild-Kostant-Rosenberg isomorphism theorems as exponential maps. This computation uses the construction of a filtered circle obtained in collaboration with Moulinos and Toën. As applications we will describe motivic Donaldson-Thomas invariants in positive characteristic and an extension of Hochschild homology for elliptic curves.