Geodesic arcs and surfaces for hyperbolic knots and 3-manifolds

这个项目的目的是利用数学上的最新突破来确定数学空间上的显式几何信息，即纽结补和3-流形。这些空间出现在科学和工程领域的应用中。它们被分成几个部分，接受几何图形，其中双曲几何图形是最常见的。这个项目期望围绕一些关于纽结和3-流形的双曲几何的开放问题和猜想产生新的知识。预期的结果包括理论的发展和几何工具的改进。它将通过新的见解和改进的方法使数学界受益，并可能导致依赖几何的其他科学领域的下游应用。

This project aims to use recent breakthroughs in mathematics to determine explicit geometric information on mathematical spaces, namely knot complements and 3-manifolds. These spaces arise in applications across science and engineering. They break into pieces that admit geometry, where hyperbolic geometry is the most common. This project expects to generate new knowledge around a number of open questions and conjectures on the hyperbolic geometry of knots and 3-manifolds. Expected outcomes include development of theory, and improved geometric tools. It will benefit the mathematical community through new insights and improved methods, and possibly lead to downstream applications in other scientific fields that rely on geometry.