Stable degenerations of singularities - Ziquan Zhuang

Mathematics Department Colloquium - April 25, 2024
Stony Brook University
Ziquan Zhuang, Johns Hopkins University
Title: Stable degenerations of singularities
Abstract: Donaldson and Sun discovered around 10 years ago that metric limits of Ricci positive Kähler-Einstein manifolds are algebraic varieties, and their metric tangent cones also underlie some algebraic structure. I will talk about a general algebraic geometry theory behind this phenomenon. In particular, I will survey the recent solution of Li-Xu's Stable Degeneration Conjecture, which predicts that every mild singularity on a complex algebraic variety has a canonical degeneration that shares many features of the metric tangent cones.