Mathematical Sciences: Differential Structures

五名研究人员将研究相关问题，涉及微分几何、代数变异和动力系统的各个方面。第一部分将研究由曲率引起的变分问题。第二个将研究等谱变形，黎曼流形上的最优结构，以及大球体对球体的振动。第三部将研究爱因斯坦度量、各向同性不可约黎曼流形和对称空间的各向同性表示。拓扑学家将研究分层空间，特别是代数变异。第五课将学习高维的双曲几何、编织群的表示、链路群和不变链路。研究这个项目的微分几何学者的一个中心目标是理解空间曲率。特别是，他们将研究曲率与空间整体形状之间的关系，或者空间上可能存在什么样的函数。拓扑学家和动力系统理论家将利用他们对空间形状和允许的动力特性的理解以各种方式限制曲率。

Five investigators will study related problems involving various aspects of differential geometry, algebraic varieties, and dynamical systems. The first will study variational problems arising from curvature considerations. The second will study isospectral deformations, optimal structures on Riemannian manifolds, and fibrations of spheres by great spheres. The third will investigate Einstein metrics, isotropic irreducible Riemannian manifolds, and the isotropy representation of symmetric spaces. A topologist will study stratified spaces, particularly algebraic varieties. And the fifth will study hyperbolic geometry in higher dimensions, representations of braid groups, link groups, and invariant links. A central goal of the differential geometers working on this project is to understand spacial curvature. In particular they will study the relationship between curvature and the overall shape of the space, or what sorts of functions may exist on the space. The topologist and dynamical systems theorist will use their understanding of the shape of the space and allowable dynamical properties to restrict curvature in various ways.