论文标题
从千古理论的角度来计算问题：从原始整数到简单的封闭曲线
Counting problems from the viewpoint of ergodic theory: from primitive integer points to simple closed curves
论文作者
论文摘要
In her thesis, Mirzakhani showed that the number of simple closed geodesics of length $\leq L$ on a closed, connected, oriented hyperbolic surface $X$ of genus $g$ is asymptotic to $L^{6g-6}$ times a constant depending on the geometry of $X$.在这项调查中，我们详细介绍了Mirzakhani的证明，目的是针对非专家。我们从经典的原始晶格点计数中汲取灵感导致均匀动力学。重点是理解在晶格中驱动证据的一般原则如何也适用于双曲线表面的环境。
In her thesis, Mirzakhani showed that the number of simple closed geodesics of length $\leq L$ on a closed, connected, oriented hyperbolic surface $X$ of genus $g$ is asymptotic to $L^{6g-6}$ times a constant depending on the geometry of $X$. In this survey we give a detailed account of Mirzakhani's proof of this result aimed at non-experts. We draw inspiration from classic primitive lattice point counting results in homogeneous dynamics. The focus is on understanding how the general principles that drive the proof in the case of lattices also apply in the setting of hyperbolic surfaces.
