Hochschild Homology and the Detection of Smoothness
Time: 2026-07-18
Published By: He Liu
Speaker(s): Yu Shen (Florida State University)
Time: 10:00-11:30 July 23, 2026
Venue: Room 77201, Jingchunyuan 78, BICMR
Let X be a proper algebraic variety. Can the eventual vanishing of its Hochschild homology detect whether X is smooth? This question can be viewed as a geometric analogue of Han's conjecture, which asks whether the eventual vanishing of Hochschild homology detects finite global dimension for finite-dimensional algebras.
I will explain how these geometric and algebraic questions fit into a common DG-categorical framework and then discuss what happens for finite-dimensional DG algebras. In particular, I will show that, in the general DG setting, eventual vanishing of Hochschild homology does not necessarily detect smoothness.
This is based on joint work with Yeqin Liu.
