Tufts University
When
12:30 – 1:30 p.m., Nov. 10, 2026
Where
K-polystability of asymptotically conical Kähler-Ricci shrinkers
Non-compact shrinking gradient Kähler-Ricci solitons (Kähler-Ricci shrinkers) are fundamental objects in the study of the Ricci flow, characterizing much of the behavior of finite-time singularities. Recently, Sun--Zhang have developed an algebraic theory for Kähler-Ricci shrinkers, which in particular implies that such spaces naturally admit an algebraic structure. This gives rise to a so-called "YTD correspondence" between the existence of such a metric (i.e. the solution of a geometric PDE) and an algebro-geometric notion of K-stability. Such correspondences were proposed originally in the 1980s in the compact case and have been intensely studied since. In this talk, I will discuss the proof of one direction of the correspondence, namely that the existence of a Kähler-Ricci shrinker metric implies K-polystability, in the case that the Ricci curvature decays at infinity. This is joint work with Carlos Esparza.