Mathematical Sciences: Geometry of Teichmuller Space

首席研究员将研究几何学， Teichmuller空间的流形结构 他将集中精力 研究无限维和有限维 例 该项目将应用于三维 拓扑学、弦理论、动力系统和迭代 有理函数 一个Teichmuller空间由以下所有“标记”的集合组成： 一个有有限个洞和有限个 穿孔 例如，刺穿的内胎具有一个孔， 一个穿刺。 标记是一个区别的基础， 曲面的基本群。 这可能包括几个 在洞和刺周围绕圈 校长 研究者将把他的泰赫穆勒空间理论应用于 数学中的其他应用。

The principal investigator will study the geometry and manifold structure of Teichmuller space. He will focus his investigations on the infinite as well as finite dimensional cases. The project will have applications to three-dimensional topology, string theory, dynamical systems, and iteration of rational functions. A Teichmuller space consists of the set of all "markings" of a surface with a finite number of holes and a finite number of punctures. For example, a punctured inner tube has one hole and one puncture. A marking is a distinguished basis for the fundamental group of the surface. This might consist of several circles about the holes and punctures. The principal investigator will apply his theories of Teichmuller space to a variety of other applications within mathematics.