Lagrangian Torus Fibration of Calabi-Yau Manifolds and Application to Mirror Symmetry

点击翻译按钮获取中文摘要

Abstract for DMS - 0104150PI: Wei-Dong RuanDr. Ruan proposes to study the Lagrangian fibration structure of Calabi-Yau manifolds and of more general Kaehler manifolds, and their applications in mirror symmetry and other Kahler geometry problems as well. The objective of the proposed research is to further inderstand the Lagrangian torus fibration structures for moregeneral Calabi-Yau manifolds, exploring the interplay of sympleticgeometry and complex geometry in Kaehler manifolds, as indicated by Kontsevich's categorical mirror symmetry program. Mirror symmetry has its origin in string theory andsays that we have two theories, which appear to be completely distinct, describing the same physics. If we have two different models of the same universe, one can expect that one of the models can fill in the gaps in understanding the other model. This project is towards understanding this symmetry principle.Results from this proposal should be of interest to mathematicians fromvarious disciplines as well as physicists in string theory.