Mathematical Sciences: Geometry of Teichmuller Space

首席研究员将研究Teichmuller空间的几何和流形结构。他将集中研究无限维和有限维的情况。该项目将应用于三维拓扑学、弦理论、动力系统和有理函数的迭代。一个Teichmuller空间由一个表面的所有“标记”的集合组成，该表面具有有限数量的孔和有限数量的穿孔。例如，穿孔的内胎有一个孔和一个穿孔。标记是表面基本组的区分基础。这可能包括在洞和穿孔周围画几个圈。首席研究员将把他的Teichmuller空间理论应用于数学中的各种其他应用。

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.