Geometry Seminar

The analytic minimal model program of Song and Tian seeks to use the Kähler–Ricci flow, a geometric PDE, to realize the discrete algebraic transformations that simplify complex varieties. For Kähler surfaces, the global picture is fairly well understood, while the local geometry near singularities is much less clear. I will discuss joint work with Longteng Chen and Lucas Lavoyer showing that, for Kähler surfaces and in higher dimensions under a symmetry assumption, the flow near a finite-time singularity is modeled at small scales by a shrinker-expander pair of Kähler–Ricci solitons, confirming the local picture conjectured by Song.