Finite Element Methods for Surface Evolution and Applications

Zhiqin Lu Department of Mathematics, University of California, Irvine

ABSTRACT: The moduli space of polarized Calabi-Yau manifolds (CY moduli for short) is a complex orbifold. In this talk, I will introduce the differential geometric aspects of the CY moduli. With respect to the Weil-Petersson metric, some basic properties of the CY moduli have been studied. These include: the curvature of the Weil-Petersson metric, the finiteness of the Chern numbers, and the (distance) incompleteness of the moduli space. This work is joint with Michael Douglas and Eddie Natsukawa.