Mathematics Department Colloquium: Calabi-Yau metrics and algebraic singularities

Colloquium | January 19 | 4:10-5 p.m. | 60 Evans Hall

 Song Sun, Stony Brook

 Department of Mathematics

A Calabi-Yau manifold is a compact complex manifold with trivial canonical bundle. Yau’s solution to the Calabi conjecture gives rise to canonical Ricci-flat Kahler metric (Calabi-Yau metric) on such a manifold, and this has deep applications in algebraic geometry and mathematical physics. It is an interesting question to understand how the Ricci-flat metrics develop singularities when the complex structure degenerates. We will show that in certain natural situation one can understand the metric singularities precisely, and thus produce compact Ricci-flat manifold with isolated conical singularities. If time allows we will explain briefly the idea involved in the proof, which is based on a combination of PDE and complex algebro-geometric techniques.

This talk is based on joint work with Hans-Joachim Hein.