For a smooth proper variety over a field of characteristic
zero, the Hodge-to-de Rham spectral sequence (relating the cohomology
of differential forms to de Rham cohomology) is well-known to
degenerate, via Hodge theory. A "noncommutative" version of this
theorem has been proved by Kaledin for smooth proper dg categories
over a field of characteristic zero, based on the technique of
reduction mod p. I will describe a short proof of this theorem using
the theory of topological Hochschild homology, which provides a
canonical one-parameter deformation of Hochschild homology in
characteristic p.