Mathematics Department Colloquium: Metric collapsing of hyperkahler K3 surfaces

Colloquium | April 26 | 4-5 p.m. | 60 Evans Hall

 Song Sun, UC Berkeley

 Department of Mathematics

A K3 surface is a simply connected compact complex surface with trivial canonical bundle. Moduli space of K3 surfaces has been extensively studied in algebraic geometry and it can be characterized in terms of the period map by the Torelli theorem. The differential geometric significance is that every K3 surface admits a hyperkahler metric (a metric whose holonomy group is SU(2)), which is in particular Ricci-flat. The understanding of limiting behavior of a sequence of hyperkahler K3 surfaces gives prototype for more general questions concerning Ricci curvature in Riemannian geometry. In this talk I will survey what is known on this, and talk about a new glueing construction, joint with Hans-Joachim Hein, Jeff Viaclovsky and Ruobing Zhang, that shows a multi-scale collapsing phenomenon, and discuss the connection with the Kulikov classification in algebraic geometry.