Towards logarithmic Hochschild complex

We will explain how to reconstruct the log de Rham complex (more precisely, its mixed version) of a smooth algebraic variety from the DG category of perfect complexes. The construction works for an arbitrary DG category and is functorial. It uses non-commutative K-motives. The main ingredient is Quillen's Devissage Theorem. We will also explain how to obtain the weight filtration via Bondarko's weight structures on triangulated categories.