Mirror Symmetry and Geometry of Calabi-Yau Manifolds

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Abstract for NSF proposal DMS-0103355: In this project, the principal investigator investigates the geometry of Calabi-Yau manifolds and mirror symmetry. First the PI plans to describe the degeneration of Kahler-Einstein metrics on Calabi-Yau manifolds near the large 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 complex geometry 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 conjecture gives a duality transformation of this geometry. This project is towards uncovering this amazing symmetry principle.