Ville Nordström: A decomposition theorem for the Hochschild homology of symmetric powers of dg categories

Abstract: In 2023 Belmans, Fu and Krug computed the Hochschild (co)homology groups of the Hilbert scheme of points on a smooth projective surface. Along the way they proved a decomposition formula for the Hochschild homology of the stacky symmetric powers of a smooth projective variety and they conjectured that a similar formula should hold more generally for smooth and proper, small dg categories. It turned out to be even more general; the decomposition holds for any small dg category. In my talk I will discuss this decomposition and the proof of it.