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Geometry-Topology Seminar

Thursday, October 20, 2022 - 5:15pm

Ruobing Zhang

Princeton University


University of Pennsylvania


This talk will be streamed live via Zoom. Just e-mail for the Zoom link.

In this talk, we will establish a complete picture of metric geometry of Calabi-Yau metrics in complex dimension two. The main part will focus on the resolution of the following three well-known conjectures in the field.


(1) Any volume collapsed limit of unit-diameter K3 metrics is isometrically classified as: the quotient of a flat 3D torus by an involution, a singular special Kähler metric on the topological 2-sphere, or the unit interval.


(2) Any complete non-compact hyperkähler 4-manifold with quadratically integrable curvature, must have a classified model end.


(3) Any gravitational instanton can be biholomorphically compactified to be an open dense subset of certain compact algebraic surface.