Research Initiation: Non-Planar Computational Geometry

建议的研究涉及非平面环境下计算几何的算法和组合问题。将考虑以下问题域：高维凸问题，特别是关于其可分解性的问题和查询问题，如点定位和射线射击；最后，黎曼曲面作为计算几何中潜在的计算和概念工具的概念。

The proposed research concerns algorithmic and combinatorial problems of computational geometry in a non-planar setting. The following problem domains will be considered: higher-dimensional convex problems, in particular questions about their decomposability and query problems such as point location and ray shooting; finally, the notion of a Riemann surface as a potential computational and conceptual tool in computational geometry.