论文标题
差异的模量和Teichmüller动力学
Moduli of Differentials and Teichmüller Dynamics
论文作者
论文摘要
数学家感兴趣的一个越来越重要的领域是对阿贝里亚差异的研究。这一主题在现代数学中所发挥的跨学科作用可以归因于代数几何，动力学系统，几何学和拓扑的各种问题。我们可以在我们的研究代数，分析，组合和动态观点中使用这是一种自然的结果。这些讲义旨在为该主题提供说明性介绍，该讲义将强调不同数学领域之间的上述联系。我们将与Abelian差异相关联，具有圆锥形奇点的平坦表面，以便通过通过翻译彼此识别边缘来从多边形获得下面的riemann表面。我们将专注于在家庭中研究这些对象，并描述轨道的某些属性，因为我们通过$ gl_2^{+}的作用改变了多边形（\ Mathbb {r}）$。
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of algebraic geometry, dynamical systems, geometry and topology lead to the study of such objects. It comes as a natural consequence that we can employ in our study algebraic, analytic, combinatorial and dynamical perspectives. These lecture notes aim to provide an expository introduction to this subject that will emphasize the aforementioned links between different areas of mathematics. We will associate to an Abelian differential a flat surface with conical singularities such that the underlying Riemann surface is obtained from a polygon by identifying edges with one another via translation. We will focus on studying these objects in families and describe some properties of the orbit as we vary the polygon by the action of $GL_2^{+}(\mathbb{R})$ on the plane.
