Mathematical Sciences: The Mapping Class Group and the Geometry of Teichmuller Space

9503449马苏尔这个建议涉及到TeichMuller空间的几何和映射类群。提出者将使用复杂几何、概率和动力系统的方法来研究Teichmuller度量。特别地，作者希望考虑Teichmuller空间上的随机游动来研究映射类群的刚性问题。TeichMuller空间表示具有固定拓扑型的椒盐卷曲曲面的全体；这些曲面，即所谓的具有固定亏格的Riemann曲面，在复值函数的研究中是至关重要的，因为它们推广了复数域。而拟议的研究试图从几何和度量的角度来理解Teichmuller空间。

9503449 Masur This proposal concerns the geometry of Teichmuller space and the mapping class group. The proposer will use methods from complex geometry, probability, and dynamical systems to study Teichmuller metrics. In particular, the proposer wishes to consider random walks on Teichmuller space to study rigidity problems about the mapping class group. Teichmuller space represents the totality of pretzel-like surfaces with a fixed topological type; these surfaces, so called Riemann surfaces of a fixed genus, are crucial in the study of complex-valued functions as they generalize the complex number field. And the proposed research seeks to understand Teichmuller space from a geometric and metric point of view.