Stable Degenerations of Singularities

Explore the fascinating world of algebraic geometry in this mathematics colloquium talk delivered by Ziquan Zhuang from Johns Hopkins University. Delve into the groundbreaking discovery by Donaldson and Sun regarding metric limits of Ricci positive Kähler–Einstein manifolds and their algebraic structure. Examine the general algebraic geometry theory underlying this phenomenon, with a focus on the recent solution to Li-Xu's Stable Degeneration Conjecture. Learn how this conjecture predicts that every mild singularity on a complex algebraic variety possesses a canonical degeneration sharing characteristics with metric tangent cones. Gain insights into the intersection of differential geometry and algebraic geometry through this in-depth exploration of stable degenerations of singularities.