Hochschild Homology and the Detection of Smoothness
发布时间：2026年07月18日
浏览次数：11
发布者: He Liu
主讲人： Yu Shen (Florida State University)
活动时间： 从 2026-07-23 10:00 到 11:30
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
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.
