Studies on Einstein Metrics and Related Topics

摘要奖：DMS-0072591主要研究者：Michael T. Anderson和LeBrun都计划研究低维流形的整体黎曼几何学，并着眼于将这些结果应用于光滑拓扑、代数几何和理论物理。安德森将继续研究瑟斯顿的几何化猜想，并研究该猜想与广义相对论中真空时空的整体存在性和奇点形成的关系。LeBrun将研究全标量曲率泛函的性质与光滑拓扑之间的关系，以及与二次曲率泛函相关的问题。 此外，安德森和勒布朗都计划调查主题的几何渐近双曲流形，关系到当前的问题，在弦理论和AdS/CFTcorrespondence.安德森的调查是直接相关的问题有关的物理黑洞和形状和长期演化的宇宙。LeBrun的工作研究了霍金量子引力计划中的基本问题，并将高能物理学的Seiberg-Witten方程与引力现象的研究联系起来。

AbstractAward: DMS-0072591Principal Investigator: Michael T. AndersonAnderson and LeBrun both plan to study the global Riemanniangeometry of low-dimensional manifolds, with an eye towards theramifications of these results for smooth topology, algebraicgeometry, and theoretical physics. Anderson will continue work onThurston's geometrization conjecture, and study relations of thisconjecture with global existence and singularity formation forvacuum space-times in general relativity. LeBrun will studyrelations between properties of the total scalar curvaturefunctional and smooth topology, as well as related problemsconcerning quadratic curvature functionals. In addition,Anderson and LeBrun both plan to investigate topics in thegeometry of asymptotically hyperbolic manifolds, and relationswith current issues in string theory and the AdS/CFTcorrespondence.Anderson's investigations are directly related to questionsregarding the physics of black holes and the shape and long-termevolution of the universe. LeBrun's work studies fundamentalquestions arising from Hawking's quantum gravity program, andrelates the Seiberg-Witten equations of high-energy physics tothe study of gravitational phenomena.