Mirror Symmetry and Geometry of Calabi-Yau Manifolds

点击翻译按钮获取中文摘要

Abstract for NSF proposal DMS-0103355:In this project, the principal investigator investigates the geometry ofCalabi-Yau manifolds and mirror symmetry. First the PI plans to describe thedegeneration of Kahler-Einstein metrics on Calabi-Yau manifolds near thelarge complex structure limit. Second the principal investigator studies special Lagrangian submanifolds and deformed Hermitian-Yang-Mills bundles on Calabi-Yau manifolds. Third, using Fourier transformation, Legendre transformation and their variations, the principal investigator explains the mirror duality of complexgeometry and symplectic geometry between mirror manifolds.The geometry of Calabi-Yau manifolds is an important subject in Mathematics,and also in Physics. Originated in String theory, mirror symmetry conjecturegives a duality transformation of this geometry. This project is towardsuncovering this amazing symmetry principle.