Mathematical Sciences: Symplectic Topology and Its Applications to String Theory

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9703870 Ruan This project lies in the area of Kahler geometry and its application to mirror symmetry. More specifically, the investigator is to use the idea of Kahler or Riemannian collapsing - a sequence of Kahler manifolds and their limit manifold are considered - to further our understanding of mirror symmetry. Riemannian manifolds are curved spaces equipped with a notion of distance, also called a metric. The totality of (compact) Riemannian manifolds itself can be given a metric so that when given an infinite collection of such manifolds it makes sense to talk about clustering or converging. Mirror symmetry is a phenomenon first discovered by physicists: in the popular 10-dimensional string theory model of the universe, the invisible 6-dimensions arise as so called Calabi-Yau manifolds possessing certain symmetry.