Selected topics in discrete geometry

离散几何的选定主题：离散几何是一个年轻的和快速发展的领域的边界线上的纯数学和计算机科学。短语离散几何，这在一次主要代表的领域的包装，覆盖和平铺，已逐渐发展到包括这样的领域组合几何，凸多面体，和安排的线，圆，平面，球体和其他几何对象的平面和更高的维度。此外，离散几何在其他领域如数字通信中也有许多应用。也就是说，通信理论中的一个基本问题是确定多维空间中相等球的密度填充。实际上，所提出的研究是一个相当广泛的调查dennis球包装在球形空间，弯曲的类似物凸多面体称为球多面体，（部分）覆盖的圆柱体和木板，照明问题，以及（短）台球（凸）台球桌。建议的合作者包括我的研究生（分别为，卡尔加里大学的高级本科生，卡尔加里大学计算和离散几何中心的访客以及来自加拿大，美国和欧洲机构的主要研究人员。

Selected Topics in Discrete Geometry: Discrete geometry is a young and fast developing area on the border line of pure mathematics and computer science. The phrase discrete geometry, which at one time stood mainly for the areas of packing, covering and tiling, has gradually grown to include such areas as combinatorial geometry, convex polytopes, and arrangements of lines, circles, planes, spheres and other geometric objects in the plane and in higher dimensions. Also, discrete geometry has a number of applications in other fields such as in digital communications. Namely, one of the fundamental questions in communications theory is to determine the densest packing of equal balls in multidimensional space. Actually, the proposed research is a rather broad one investigating densest sphere packings in spherical space, curved analogues of convex polytopes called ball-polyhedra, (partial) coverings by cylinders and planks, illumination problems as well as (short) billiards of (convex) billiard tables. The proposed collaborators include my graduate students (resp., advanced undergraduate students) at the University of Calgary, the visitors of the Center for Computational and Discrete Geometry at the University of Calgary and leading researchers from institutions in Canada, USA and Europe.